Optimization of Fresh Produce Supply Chain Resilience Capacity: An Extension Strategy Generation Method

Abstract

Fresh produce, as a primary source of nutrition, plays a pivotal role in daily life. However, the unique characteristics of fresh produce—such as perishability, widespread production, short shelf life, long distribution cycles, and high volatility in both supply and demand—render the fresh produce supply chain particularly vulnerable to disruptions. These vulnerabilities not only impact daily consumption but also pose significant challenges to the operational efficiency of enterprises. Enhancing the fresh produce supply chain resilience is crucial for businesses to effectively mitigate risks, ensure consistent product quality, and maintain overall supply chain stability. Nevertheless, there remains a lack of clear, process-oriented guidance for developing resilience improvement strategies within the fresh agricultural product sector. Specifically, there is insufficient clarity regarding which elements should be prioritized for investment in resilience strategies, how these strategies should be formulated, and the absence of a theoretically sound framework to guide the strategic development of supply chain resilience improvements. To address the lack of scientific, quantitative, efficient, and specific processes for generating supply chain resilience improvement strategies in fresh agricultural product enterprises, this study adopts the framework of extensible primitive theory. Initially, an evaluation index system for the fresh produce supply chain is constructed, and the extendable evaluation method is employed to assess the resilience level of fresh agricultural product enterprises. This approach facilitates the identification of the key challenges that must be addressed to enhance supply chain resilience and helps generate strategies that reconcile previously incompatible issues. Next, the core objectives and conditions underlying the resilience incompatibilities in fresh agricultural product enterprises are quantitatively analyzed. Finally, the expansion transformation of both target and condition primitives is carried out to derive the optimal strategy for improving supply chain resilience. The study uses company M as a case example, where the evaluation results indicate that the company’s supply chain resilience is rated as “good”. However, several issues were identified, including inefficiencies in product supply, limited financing capacity, low enterprise visibility, and inadequate production and processing equipment. Based on these findings, the paper proposes a series of optimization strategies aimed at improving the fresh produce supply chain resilience through extension transformation.

1. Introduction

Food is fundamental to life and well-being, with fresh produce holding particular significance due to its rich content of vitamins and minerals. As a primary source of nutrition, fresh produce plays a critical role in the daily consumption habits of individuals, occupying a central position in maintaining overall health and vitality [1]. In recent years, with improved living standards, modern consumers have increasingly higher quality requirements for food, including fresh produce. However, they may not be aware of the extensive transportation distances involved in complex supply chains, nor do they realize the time taken for fruits and vegetables to travel from production or harvesting to their final destination [2]. Fresh produce is distinguished by its short shelf life and high perishability. Furthermore, due to information asymmetry, consumers often cannot ascertain the duration that fresh produce has been stored on retailers’ shelves, and even after receiving and unpacking the products, this information remains elusive [3]. Due to the perishable nature of fresh produce, long-distance transportation often leads to quality deterioration. Unlike supply chains for other products, the quality of fresh produce in its supply chain is highly susceptible to decline over time, even when utilizing the most advanced facilities and optimal conditions. This unique challenge highlights the need for careful management throughout the supply chain to preserve the freshness and quality of the product.

Fresh produce is extremely sensitive to environmental conditions, and the increasing frequency of extreme weather and natural disasters triggered by climate change can lead to reduced crop yields, lower quality, and logistics disruptions, thereby severely impacting the fresh produce supply chain. With the advancement of globalization, the fresh produce supply chain has become more complex and extended, with cross-border transportation and multi-node supply chains becoming the norm. The increase in supply chain links and the extension of pathways significantly heighten the supply chain’s vulnerability and uncertainty [4]. For instance, cross-border transportation may face tariff adjustments, trade policy changes, and cross-border logistics disruptions. Public health events like the COVID-19 pandemic have further exposed the vulnerability of the fresh produce supply chain, causing logistics disruptions, labor shortages, and market demand fluctuations, leading to unsold agricultural products and significantly impacting the global fresh produce supply chain [5,6]. These challenges necessitate strong supply chain resilience to respond and adapt. The fresh produce supply chain involves multiple stages, including production, distribution, and consumption, each characterized by cycles of centralization and decentralization. During this process, unsold products and price fluctuations are common occurrences, reflecting the inherent volatility and challenges of managing supply and demand within this sector [7]. However, in an emergency, the supply chain is more prone to anomalies or breaks, affecting people’s daily lives, severely disrupting business operations, and significantly impacting socio-economic stability. By enhancing the fresh produce supply chain resilience, enterprises can better cope with various risks and challenges, ensuring product quality and supply chain stability, thereby improving market competitiveness and sustainable development capability [8,9]. Therefore, improving the fresh produce supply chain resilience has become an urgent and critical issue that must be addressed to mitigate risks and ensure stability in the face of these challenges.

Research on the fresh produce supply chain resilience remains insufficient. While there is a substantial body of literature on supply chain resilience in general, studies specifically addressing the resilience of fresh agricultural product supply chains are still relatively limited. This gap highlights the need for more focused research to understand the unique challenges and strategies for enhancing resilience in this sector. The existing literature is relatively scarce, and most of them use a combination of simple evaluation methods, which lacks sufficient explanatory power. Secondly, the discussion and analysis of supply chain resilience at home and abroad are mainly theoretical, which not only lacks quantitative analysis in specific situations, but also cannot automatically generate supply chain resilience improvement strategies. Therefore, this study first develops an index system to assess the supply chain resilience of fresh agricultural products and calculates the corresponding comprehensive weights. Following this, through data collection and the application of extension theory, the resilience of each dimension within the fresh produce supply chain is evaluated. Finally, the study optimizes supply chain resilience improvement strategies through extensible innovation to enhance the overall resilience of the fresh produce supply chain. Given the inherent uncertainty and disruption risks associated with supply chain disturbances, this paper employs extension theory to explore the mechanisms and optimization strategies for improving the fresh produce supply chain resilience. Two key questions are addressed in this research.

RQ1: What are the mechanisms and influencing factors of fresh produce supply chain resilience under supply chain risks?

RQ2: How to solve the generation law of incompatibility problem-solving strategy, and realize the generation of the supply chain resilience optimization strategy through the extensible policy generation method?

The potential innovations of this paper are as follows: (1) Through a systematic analysis of the fresh produce supply chain resilience, the key influencing factors are identified. These factors are then organized into a database of resilience determinants, represented in the form of primitives, and used to construct a comprehensive supply chain resilience evaluation system for fresh produce. (2) The study identifies the incompatibility issues related to the fresh produce supply chain resilience through the resilience assessment. Subsequently, an improvement strategy is developed to address these incompatibilities, following a structured process for generating resilience enhancement strategies. This approach offers a novel perspective and methodology for studying the fresh produce supply chain resilience.

2. Literature Review

2.1. Fresh Produce Supply Chain

Fresh produce exhibits distinct characteristics such as perishability, dispersion, a short lifecycle, long delivery periods, high supply and demand uncertainty, and low profitability [10,11]. The fresh produce supply chain’s value is mainly in terms of “freshness” and sustainability. The shelf life refers to the length of time during which food maintains optimal safety and quality under specified storage conditions, influenced by various factors, including the production process, packaging type, temperature, storage conditions, and ingredients [12]. The time before food deterioration can be fixed or uncertain, while fresh produce exhibits random perishability throughout its lifecycle. The production of fresh produce is notably seasonal, occurring once or a few times a year, with a relatively long production period. Due to biological variability, seasonal changes, and random factors related to weather, pests, and other biological hazards, the yield and quality of fresh produce exhibit significant uncertainty [13]. Similar products may differ in taste, smell, appearance, color, and size, leading to product heterogeneity [14].

Early definitions of the supply chain were limited to activities within a single enterprise, encompassing all processes involved in producing a product and selling it to retailers and consumers. However, as research progressed, the concept of the supply chain expanded to incorporate external environments, evolving into a more comprehensive supply chain ecosystem [15]. After successfully applying the supply chain management theory in industrial sectors, scholars introduced these ideas into agriculture. Fresh produce, characterized by its perishability, susceptibility to spoilage, contamination, and short shelf life, requires stringent management throughout the production, distribution, and sales processes. Consequently, given its unique characteristics, the fresh produce supply chain has garnered significant attention. The fresh produce supply chain includes multiple stages from farm to table: production, harvesting, processing, storage, transportation, and distribution. Due to the perishability of fresh produce and its high sensitivity to environmental conditions, any issues in one stage can significantly impact the entire supply chain [16]. The fresh produce supply chain begins with procuring raw materials for agricultural production, followed by stages including planting, processing, procurement, transportation, and distribution, ultimately delivering the produce to buyers through various distribution channels. Throughout this process, information asymmetry is common: buyers often struggle to identify high-quality products, while sellers have insights into the product’s history and condition. This information asymmetry adds complexity and challenges to managing the fresh produce supply chain [17].

The primary objective of managing the fresh produce supply chain is to fulfill consumer demand. Given the distinctive characteristics of fresh produce, consumer demand is predominantly driven by factors such as product quality and price. High quality and competitive pricing are crucial factors in enhancing consumer satisfaction. These elements serve as fundamental strategies for sales enterprises to bolster their competitiveness and drive higher profitability [18]. Therefore, the management of the fresh produce supply chain should prioritize the objective of achieving “high quality at low cost”. Within this framework, all supply chain participants must focus on ensuring product quality while minimizing costs. Specifically, management strategies should concentrate on optimizing the production, distribution, and sales processes to foster internal and external coordination and integration. By implementing these strategies, enterprises can enhance profitability, deliver benefits to consumers, and maximize the overall profit of the fresh produce supply chain system, thereby creating a win-win situation for all stakeholders.

Quality and cost management are pivotal challenges in fresh produce supply chain management. Due to the limited shelf life of fresh products, along with the risk of commercial value loss from transportation delays or inadequate temperature control during production and distribution, effective management of both quality and cost becomes especially crucial. In academic research, many scholars focus on analyzing quality loss, quantity loss, and the preservation measures taken to reduce these losses. For instance, Liu et al. [19] proposed a dynamic control model involving online retailers and offline producers to explore how incentives can enhance preservation efforts among supply chain members to achieve optimal preservation levels for fresh produce. Furthermore, other scholars have examined the optimization of the fresh produce supply chain from a variety of perspectives. For example, Gokarn and Kuthambalayan [20] analyzed the influence of supply, demand, and price uncertainties on the sustainability of the fresh produce supply chain. In response to growing consumer concerns regarding the quality and provenance of fresh produce sold on e-commerce platforms, Tan et al. [6] explored the potential applications of blockchain technology in this context. Their study considered factors such as the costs associated with blockchain technology, perceived quality, and actual quality to evaluate its potential impact on the fresh produce supply chain.

2.2. Supply Chain Resilience

A fundamental assumption of supply chain resilience is that the risks encountered by the supply chain cannot be fully avoided [21]. Supply chains are frequently impacted by unforeseen events and risks, such as natural disasters, political instability, economic fluctuations, and public health crises, which can disrupt the supply chain and affect business continuity. Enhancing supply chain resilience enables enterprises to more effectively manage and respond to unforeseen events and risks, thereby ensuring the uninterrupted operation of the supply chain.

Wieland and Wallenburg [22] define supply chain resilience as the capacity of the supply chain to respond effectively to changes. Brandon-Jones et al. [23] describe it as the ability of the supply chain to rapidly return to its original or an improved state following a disruption. Dubey et al. [24] characterize supply chain resilience as the system’s ability to recover to its original state within an acceptable time frame. These definitions primarily approach supply chain resilience from a reactive perspective, highlighting its passive characteristics. However, to effectively reduce the likelihood of disruptions and minimize their impacts, supply chain resilience should also incorporate a proactive dimension, focusing on the prevention of disruptions. Hohenstein et al. [25] argue that supply chain resilience encompasses the ability of the supply chain to prepare for unforeseen risk events, respond promptly, and recover to its original or improved state. Chowdhury and Quaddus [26] view supply chain resilience as a composite capability that integrates both proactive and reactive elements, enabling supply chain members to reduce the likelihood of disruptions or mitigate their impacts, thus fostering a more robust and sustainable state. Li et al. [27] highlight that supply chain resilience involves the ability to absorb disturbances before disruptions occur, the capacity to respond swiftly and adapt to environmental changes following disruptions, and the recovery capability to restore the supply chain to its original or even an enhanced state.

A review of supply chain resilience definitions reveals that while a unified definition has not yet been established, scholars’ understanding of the concept has become increasingly comprehensive. It has evolved from being solely reactive to including proactive prevention before and reactive responses after disruptions. Additionally, supply chain resilience encompasses a learning capability, allowing the supply chain to not only recover but also enhance its performance levels beyond the original state [28].

Academic research on supply chain resilience primarily focuses on two key aspects: first, identifying the factors that influence supply chain resilience, and second, developing and applying methods for evaluating resilience. In studies examining the factors that affect supply chain resilience, scholars have identified numerous critical elements that contribute to its robustness. For instance, several scholars have synthesized and categorized the core elements of supply chain resilience through systematic literature reviews, as presented in

Table 1. Elements of supply chain resilience.

Scholar	Element
Sawyerr and Harrison [29]	Collaboration, Flexibility, Redundancy, Agility, Decision making, Security, Culture, Robustness, Integration, Avoidance, Sustainability, Logistics capability, Human resource management
Zavala-Alcívar et al. [30]	Flexibility, Shared information, Trust, Velocity, Visibility, Redundancy, Robustness, Contingency planning, Disruptive environment awareness, Knowledge management, Innovation, Strategic alignment, Leadership
Luo et al. [31]	Product supply resilience, resource resilience, partner resilience, information response resilience, capital resilience, and knowledge resilience
Dashtpeyma and Ghodsi [32]	Adaptability, Anticipation, Collaboration, Commitment, Flexibility, Information Technology, Innovation, Integration, Leadership, Redundancy, Responsiveness, Risk Management, Robustness, Vulnerability
Ekanayake et al. [33]	Flexibility, Capacity, Efficiency, Visibility, Adaptability, Anticipation, Recovery, Dispersion, Collaboration, Market position, Security, Financial strength
Stadtfeld and Gruchmann [34]	Visibility, Flexibility, Recovery, Responsiveness, Agility, Redundancy, Velocity, Security, Anticipation, Efficiency, Resilience culture, Preparedness, Robustness, Social capital building, Strong market position
Li et al. [35]	Adaptability, Leanness, Business intelligence, Flexibility, Geographic dispersion, Knowledge transfer, Reactivity, SC governance, SC integration, SC learning, Strategic configuration, Collaboration, Communication, Information sharing, Outsourcing, Robustness, Flexibility, Knowledge management, Modularity, Product design, SC design and planning, Resource reconfiguration, SC reengineering, Velocity, Visibility, Innovation, Information sharing, Process design, SC analytics, SC security

. To enhance the practical applicability of these findings, future research should aim to streamline and integrate these resilience elements into a more concise and user-friendly framework. Such a framework would enable companies to more effectively build and maintain the resilience of their supply chains, ensuring a swift response and recovery in the face of uncertainty. Moreover, there is a need for further exploration on how to translate theoretical evaluations into tangible improvement measures, ultimately enhancing the supply chain’s ability to effectively respond to challenges.

The assessment of supply chain resilience is a fundamental basis for optimizing and improving the supply chain system. Numerous methods have been proposed in academic research for evaluating supply chain resilience. Kaviani et al. [36] introduced a method for measuring supply chain resilience based on gray system theory, identifying distribution issues and supply constraints as the most significant vulnerabilities that threaten the normal functioning of the supply chain. Qi et al. [37] enhanced the gray prediction model by incorporating a buffer operator and combined it with the TOPSIS to dynamically predict the resilience level of the supply chain. Mohammed et al. [38] applied the AHP to calculate the weight of the supply chain resilience index and used TOPSIS to rank resilient product suppliers, providing valuable insights for managers aiming to enhance supply chain resilience based on evaluation results. Ekanayake et al. [39] developed a multi-level, multi-criteria supply chain resilience evaluation model using fuzzy comprehensive evaluation, focusing on the perspective of supply chain vulnerability. Wang et al. [40] assessed the resilience of the green building supply chain using a network analysis method combined with fuzzy comprehensive evaluation, offering improvement recommendations based on their findings. Xu et al. [41] established a resilience evaluation model for material security supply chains based on the matter-element extension model, validating the model’s feasibility and providing a valuable reference for decision makers in management.

2.3. Supply Chain Resilience Optimization Strategy

The output and demand of fresh produce exhibit high randomness. Due to the lengthy production cycles of fresh produce, it is susceptible to adverse weather conditions and natural disasters, such as pests and diseases, leading to significant variability in output. Additionally, the demand for fresh produce is influenced by various factors, including the remaining shelf life, market supply conditions, prices of substitute products, and seasonal fluctuations. These factors contribute to significant downward pressure on market prices [42]. Uncertainty management involves both reducing uncertainty at its source—such as employing appropriate pricing strategies to mitigate demand uncertainty—and addressing uncertainty by implementing strategies like advanced forecasting techniques to alleviate the negative impacts of demand fluctuations. Technological advancements and digital transformation offer new tools and methods to strengthen the resilience of fresh produce supply chains. For example, technologies such as the Internet of Things, big data, and blockchain facilitate real-time monitoring, accurate forecasting, and efficient management of supply chain processes. These innovations enhance resilience by enabling better responsiveness to disruptions and improving overall supply chain performance [43]. Scholars have conducted extensive research on optimizing the fresh produce supply chain resilience. For example, MacKenzie and Apte [18] examined factors that affect the smooth operation of fresh produce supply chains, such as perishability, the time needed to detect contamination, demand fluctuations during disruptions, and the volume of produce that can be rerouted. He developed a mathematical model to analyze supply chain disruptions and quantified the benefits of various disruption management strategies. Liu et al. [44] explored the impact of freshness demand resilience and service demand resilience on optimal supply chain decisions, proposing a “revenue-sharing and two-way cost-sharing” contract. By carefully designing contract parameters, they achieved perfect coordination and Pareto improvement within the fresh e-commerce supply chain. Dan et al. [7] analyzed optimal pricing and preservation effort decisions under different information-sharing strategies, further enhancing the fresh produce supply chain resilience.

Supply chain disruptions can lead to decreased productivity, increased customer complaints, delivery delays, and losses in shareholder value [45,46]. Enhancing supply chain resilience can improve its stability and reliability, allowing enterprises to maintain normal operations in the face of uncertainty. The advantages of high supply chain resilience include ensuring business continuity, increasing customer satisfaction, reducing operational costs, and enhancing competitive advantage [47,48]. Fresh produce, as a type of perishable plant-based food, has inherent uncertainties in its supply chain due to characteristics such as perishability, quality variability, and seasonality. For the fresh produce supply chain, resilience not only encompasses conventional risk forecasting and management capabilities but also requires maintaining product freshness and quality despite changes in environmental conditions, such as temperature and humidity [9]. This concept integrates the unique characteristics of the fresh produce supply chain with the core elements of supply chain resilience, highlighting the ability to sustain product quality and ensure the continuity and stability of the supply chain in the face of environmental changes, market fluctuations, and other external shocks.

2.4. Current Status of Research on Extenics

Extenics is an emerging interdisciplinary field that aims to transform incompatible problems into compatible ones and find solutions to them. Its core idea is that “things are extendable,” meaning that any entity has intrinsic extensibility and space for change. The subject of study in extenics is contradictory problems. Its foundational theory is extenics theory, and its methodological framework is the extenics innovation method. The application of these principles across various fields is referred to as extenics engineering. Extenics theory, the extenics innovation method, and extenics engineering together constitute extenics [49]. Scholars from different fields have used extenics to solve many real-world problems. For example, Cui et al. [50] introduced the representation method of basic elements in extenics into recommendation algorithms and proposed an extenics-based content recommendation algorithm for e-commerce. Zhang [51] established an evaluation model for regional technological innovation in China based on extenics theory. By comprehensively analyzing the evaluation results, the problems and deficiencies in technological innovation were identified, and strategies were proposed to enhance innovation capabilities. Lu et al. [52] explored the application of extenics strategy generation methods in emergency cold chain logistics, addressing the challenge of developing comprehensive emergency plans during unexpected events. Their study provides valuable insights into strategy formulation for cold chain logistics in complex emergency scenarios. Li et al. [53] introduced a new model based on extenics to investigate the process of brain creativity, helping individuals engage in multidimensional thinking to generate a greater variety of ideas. These case studies highlight the wide-ranging potential and significant practical value of extenics in addressing real-world problems.

Through the summary and analysis of the existing supply chain literature, scholars have made notable progress in the field of supply chain resilience, providing a foundation for further discussion in this paper. However, closer examination reveals that research on fresh agricultural products primarily focuses on pricing and cost control, with relatively few studies addressing the evaluation of supply chain resilience and improvement strategies. Similarly, in the field of extenics, research tends to concentrate more on the generation of extension strategies for areas such as innovation, while discussions on supply chain resilience remain limited. Moreover, supply chain resilience research primarily focuses on two areas: influencing factors and resilience evaluation methods. Although a variety of methods exist for assessing supply chain resilience, most studies do not propose specific strategies for improvement or actions to enhance resilience based on evaluation results. This highlights a significant research gap in how to translate theoretical evaluations into practical measures that can genuinely strengthen supply chain resilience. To address this gap, this paper focuses on the evaluation of fresh produce supply chain resilience. By comparing several commonly used methods for supply chain evaluation, this paper selects the matter-element analysis method as a research tool. After determining the evaluation method and obtaining the results, the paper employs the extension transformation method to propose specific, actionable strategies for improving supply chain resilience. This approach not only aids in assessing the current state but also offers guidance for future optimization, ultimately enhancing the supply chain’s capacity to withstand uncertainty and risk.

3. Research Methodology

3.1. Basic-Element Model

Extenics can formalize the language description of indicators in the fresh produce supply chain. Based on the axiomatic theory, this paper constructs an extensional model for specific indicators, laying the foundation for future research on the standardization and quantification of resilience indicators in the fresh produce supply chain.

3.1.1. Axiomatic Model

The axiomatic model includes object elements, event elements, and relation elements, represented by the following symbols:

$$B=(O,C,V)$$

(1)

Multiple axiomatic elements can be represented by a set of axiomatic elements. Let $\left\{O\right\}$ be the research object. For any $O\in \left\{O\right\}$, in this paper, $O$ represents the fresh produce supply chain resilience, with n resilience evaluation indicators as the characteristics $c_1$,$c_2$,···,$c_n$. The set consisting of the value $v_i(i=\mathrm{1,2},\dots n)$ of $O$ with respect to $c_i(i=\mathrm{1,2},\dots n)$ is denoted as follows:

$$B=\left[\begin{array}{ccc}O,& c_1,& v_1\\ & c_2,& v_2\\ & ⋮& ⋮\\ & c_n,& v_n\end{array}\right]=\left(\begin{array}{ccc}O,& C,& V\end{array}\right)$$

(2)

3.1.2. Matter-Element Model

A matter-element is an ordered triplet consisting of object $O_m$, characteristic $c_m$, and the value $v_m$ of $O_m$ with respect to $c_m$, as follows:

$$M=\left(\begin{array}{ccc}{O}_m,& c_m,& v_m\end{array}\right)$$

(3)

As a one-dimensional matter-element. When describing a multi-dimensional matter-element, the matter-element matrix consisting of the value $v_{mi}(i=\mathrm{1,2},\dots n)$ of $O_m$ with respect to $c_{mi}(i=\mathrm{1,2},\dots n)$ is the following:

$$M=\left[\begin{array}{ccc}{O}_m,& c_{m1},& v_{m1}\\ & c_{m2},& v_{m2}\\ & ⋮& ⋮\\ & c_{mn},& v_{mn}\end{array}\right]=\left(\begin{array}{ccc}{O}_m,& C_m,& V_m\end{array}\right)$$

(4)

3.1.3. Event-Element Model

An event-element is an ordered triplet consisting of action $O_a$, action characteristic $c_a$, and the value $v_a$ of $O_a$ with respect to $c_a$, as follows:

$$A=\left(\begin{array}{ccc}{O}_a,& c_a,& v_a\end{array}\right)$$

(5)

Similar to matter-elements, event-elements can also be one-dimensional or multi-dimensional. The matrix composed of action $O_a$ with n characteristics $c_{ai}(i=\mathrm{1,2},\dots n)$ corresponding to multiple values $v_{ai}(i=\mathrm{1,2},\dots n)$ is the following:

$$A=\left[\begin{array}{ccc}{O}_a,& c_{a1},& v_{a1}\\ & c_{a2},& v_{a2}\\ & ⋮& ⋮\\ & c_{an},& v_{an}\end{array}\right]=\left(\begin{array}{ccc}{O}_a,& C_a,& V_a\end{array}\right)$$

(6)

3.1.4. Relation-Element Model

A relation-element is an ordered triplet consisting of relation $O_r$, characteristic $c_r$, and the value $v_r$ of $O_r$ with respect to $c_r$:$A=\left(\begin{array}{ccc}{O}_r,& c_r,& v_r\end{array}\right)$.

Similarly, relation-elements can also be one-dimensional or multi-dimensional. The matrix composed of relation $O_r$ with n characteristics $c_{ri}(i=\mathrm{1,2},\dots n)$ corresponding to multiple values $v_{ri}(i=\mathrm{1,2},\dots n)$ is the following:

$$R=\left[\begin{array}{ccc}{O}_r,& c_{r1},& v_{r1}\\ & c_{r2},& v_{r2}\\ & ⋮& ⋮\\ & c_{rn},& v_{rn}\end{array}\right]=\left(\begin{array}{ccc}{O}_r,& C_r,& V_r\end{array}\right)$$

(7)

3.2. Extenics Innovation Method

3.2.1. Extensional Analysis Method

Extensional analysis, through the principles of divergent analysis, correlation analysis, implication analysis, and extensional analysis, performs the replacement, addition, deletion, enlargement, reduction, decomposition, and replication of elementary or complex elements to explore the possibilities of various extensional transformations for resolving the targets and conditions of problems that contain contradictions.

(1)

Divergent analysis in extensional analysis

When solving incompatible problems, one element can be extended to multiple elements of the same object with different characteristics and different values. The principle of divergent analysis is derived from the concepts of “one object with multiple characteristics” and “one characteristic with multiple objects”. It starts with the targets or conditions of existing contradictory problems. For object $O$, the transformation of object $O$ property $C$, or the value $V$ of object $O$ with respect to property $C$ forms new elements.

(2)

Correlation analysis

Correlation analysis expands based on the existing correlations between events, objects, and relationships. When applying the extensional transformation method to a specific object element, the transformation of one element may lead to changes in other related elements through the correlation network, resulting in elements that are suitable for solving the current contradictory problems.

(3)

Implication analysis

Implication analysis is the formal analysis of matter-elements, event-elements, or relation-elements. Both the target and condition elements AAA imply the subordinate element BBB. By realizing the subordinate element BBB, the element AAA is also realized.

(4)

Extensional analysis

Extensional analysis explores the possibilities of combining, decomposing, and expanding/shrinking events, objects, and relationships. Specific events or objects can be combined with other events or objects, decomposed into several new entities, or expanded and contracted to find feasible solutions to problems.

3.2.2. Conjugate Analysis Method

The conjugate analysis method explores products from multiple perspectives, including materiality, systematics, dynamics, and opposition, offering a more holistic understanding of their development and transformation. The terms virtual and real parts, soft and hard parts, latent and apparent parts, and positive and negative parts are collectively referred to as the conjugate parts of an object. This approach allows for a more nuanced examination of the inherent characteristics and interrelationships within a given system or product. For instance, in the case of a mobile phone, the physical phone itself represents the real part, while the brand constitutes the virtual part. The hardware is classified as the hard part, and the connections are considered the soft part. The battery power before usage is identified as the latent part, whereas the battery power during usage is deemed the apparent part. Regarding the enterprise’s profit, factors that negatively impact profit are categorized as the negative parts, while those with a positive impact are classified as the positive parts.

3.2.3. Extensional Transformation

(1)

Basic transformation

The basic transformations of extension transformations mainly imply five methods, which are substitution transformation $T\Gamma ={\Gamma }^{\prime }$, increase and decrease transformations $T{\Gamma }_0=\Gamma$ or $T_1\Gamma =\Gamma \odot {\Gamma }_1$, addition and deletion transformations $T\Gamma =\alpha \Gamma$, subdivision transformation $T\Gamma =\{{\Gamma }_1,{\Gamma }_2,\dots ,{\Gamma }_n\}$ which ${\Gamma }_1\oplus {\Gamma }_2\oplus \dots \oplus {\Gamma }_n=\Gamma$, and replication transformation $T\Gamma =\{\Gamma ,{\Gamma }^{\ast }\}$. In the basic extension transformation method, there exists the transformation $T$ that changes ${\Gamma }_0$ into another object of the same kind $\Gamma$ multiple objects ${\Gamma }_1,{\Gamma }_2,\dots ,{\Gamma }_n$, and is called $T$ as the extension transformation of the object ${\Gamma }_0$.

(2)

Basic operations of transformations

Performing two or more transformations simultaneously. If there exists $T_1$ and $T_2$ such that $T_1{B}_1=B_1^{\prime }$, $T_2{B}_2=B_2^{\prime }$, and $B_1^{\prime }\wedge B_2^{\prime }=B^{\prime }$, then $T_1{B}_1\wedge T_2{B}_2=B_1^{\prime }\wedge B_2^{\prime }=B^{\prime }$ $T_1{B}_1\wedge T_2{B}_2=B_1^{\prime }\wedge B_2^{\prime }=B^{\prime }$.

(3)

Conductive transformation

There exists a certain degree of connection and correlation between matter-elements. When performing extensional transformations on any matter-element within related matter-elements, changes in one matter-element will cause conductive changes in the related matter-elements.

3.2.4. Quality Evaluation Method and Correlation Function

The quality evaluation method is used to assess the quality of an object, such as things, strategies, etc. This method uses a correlation function to calculate the degree to which various measurement indicators meet the requirements. It involves analyzing the correlation degree of indicator scores within the evaluation range from a quantitative and objective perspective. The purpose is to reflect the degree of association between the resilience indicator scores and each evaluation range. The steps are as follows:

(1)

Determine indicators

The selection of resilience indicators for the fresh agricultural product supply chain should be reasonable, representative, scientific, operable, and comprehensive. Measurement indicators can be denoted as follows:

$$MI=\left\{\begin{array}{cccc}M{I}_1,& M{I}_2,& \cdots & M{I}_n\end{array}\right\}$$

(8)

Among them, $M{I}_i=\left(\begin{array}{cc}{c}_i,& v_i\end{array}\right)$ is the characteristic element, $c_i$ is the evaluation characteristic, and $v_i$ is the quantized value range, with $i=1,2,\cdots n$.

(2)

Determining the weight coefficient

To perform quantitative evaluation, after determining the measurement indicators, it is necessary to determine their weights, that is, the weight coefficients. Since the weight coefficients will affect the final result, they should be assigned reasonably based on the importance of the evaluation indicators.

$$\alpha =\left(\begin{array}{cccc}{\alpha }_1,& {\alpha }_1,& \cdots ,& {\alpha }_n\end{array}\right)$$

(9)

In the formula, ${\alpha }_n$ is the weight vector of each evaluation indicator, and the sum of all weight vector values equals 1.

(3)

Establishing correlation functions and calculating correlation

Calculate the distance between the values of the evaluated matter-element (resilience indicators) $i(i=1,2,\cdots n)$ and the intervals of the classic domain and the interval domain. The specific formulas for constructing the correlation functions for each indicator are as follows:

$$\rho \left(\begin{array}{cc}{v}_i(e),& V_{oej}\end{array}\right)=\left|\left.v_i-{\displaystyle \frac{a_{oej}+b_{oej}}{2}}\right|\right.-{\displaystyle \frac{b_{oej}-a_{oej}}{2}}$$

(10)

$$\rho \left(\begin{array}{cc}{v}_i(e),& V_{pj}\end{array}\right)=\left|\left.v_i-{\displaystyle \frac{a_{pj}+b_{pj}}{2}}\right|\right.-{\displaystyle \frac{b_{pj}-a_{pj}}{2}}$$

(11)

$$k_e\left(v_i\right)=\left\{\begin{array}{c}{\displaystyle \frac{\rho \left(\begin{array}{cc}{v}_i,& V_{oej}\end{array}\right)}{\rho \left(\begin{array}{cc}{v}_i,& V_{pj}\end{array}\right)-\rho \left(\begin{array}{cc}{v}_i,& V_{oej}\end{array}\right)}},\rho \left(\begin{array}{cc}{v}_i,& V_{pj}\end{array}\right)-\rho \left(\begin{array}{cc}{v}_i,& V_{oej}\end{array}\right)\ne 0\\ -\rho \left(\begin{array}{cc}{v}_i,& V_{oej}\end{array}\right)+1,\rho \left(\begin{array}{cc}{v}_i,& V_{pj}\end{array}\right)-\rho \left(\begin{array}{cc}{v}_i,& V_{oej}\end{array}\right)=0\end{array}\right.$$

(12)

Discrete correlation function. In certain fields, the feature values of objects are not easily measurable numerically. For example, when evaluating the resilience of an indicator in a fresh agricultural product supply chain, the following correlation function can be established:

$$k(x)=\left\{\begin{array}{cc}1.0,& x=Very high\\ 0.5,& x=High\\ 0,& x=Medium\\ -0.5,& x=Low\\ -1.0,& x=Very Low\end{array}\right.$$

(13)

(4)

Calculating quality

By multiplying the correlation degree by the weight of the indicator, you can construct the quality formula to obtain an objective evaluation result. The higher the quality value, the more the evaluated object meets the target requirements.

$$C(Z)={\displaystyle \sum _{i=1}^n{\alpha }_i}\cdot k_i=\left(\begin{array}{cccc}{\alpha }_1,& {\alpha }_2,& \cdots & {\alpha }_n\end{array}\right)\left[\begin{array}{c}{K}_1\\ K_2\\ ⋮\\ K_i\end{array}\right]$$

(14)

4. Construction of Incompatibility Issues in Fresh Agricultural Product Supply Chains

4.1. Establishing the Fresh Agricultural Product Supply Chain Resilience Evaluation Indicator System

To establish a scientific and accurate resilience evaluation indicator system for the fresh agricultural product supply chain, this paper has reviewed the relevant literature and research findings while considering the unique characteristics of the supply chain. Taking into account both the current state and development potential of the resilience of fresh agricultural product supply chains, a system has been constructed based on the principles of scientific validity, independence, and measurability. The evaluation indicator system is organized into four levels: goal level, criterion level, indicator level, and indicator explanation. This system includes the following components, as shown in

Table 2. Fresh Agricultural Product Supply Chain Resilience Evaluation Indicator System.

Goal Level	Criterion Level	Indicator Level	Indicator Explanation
Fresh Agricultural Product Supply Chain Resilience Evaluation	Product Evaluation B1	Product Safety Resilience C1	Product Quality and Hygiene Standards
		Product Traceability C2	Transparency and Record-Keeping of Agricultural Product Source and Distribution
		Product Demand Level C3	Customer Product Demand Quantity
		Product Supply Efficiency C4	Order Fulfillment Rate and Customer Satisfaction with Delivery
	Capital Evaluation B2	financing ability C5	Ability to Continuously Obtain High-Quality Long-Term Capital
		Innovation and R&D Investment C6	Investment in New Technologies, Products, or Processes
		Maintenance Costs C7	Repair and Maintenance Costs for Transportation Vehicles, Equipment, and Information Systems
		Profit Margin C8	Profit Margin as a Percentage of Total Revenue Over a Period
	Internal Enterprise Evaluation B3	enterprise visibility C9	Recognition and Influence in the Public and Market
		Information Flow C10	Transmission and Exchange of Information Between Individuals, Departments, or Organizations
		Corporate Culture C11	Shared Values, Beliefs, and Conduct Guidelines Developed Over Time
		Production and Processing Equipment C12	Capital Investment in Equipment and Production Capacity for Fresh Agricultural Products

. The demonstration of Calculated Partial can be found in Appendix A.

4.2. Comprehensive Evaluation of Extenics

The classical domain and the section domain determine the classical domain $M_{oe}$ and the section domain $M_p$ of the indicator, respectively:

$$M_{oe}=\left[\begin{array}{ccccc}{O}_{oe}& O_1& O_2& O_3& O_4\\ C_1& \left[0,59\right]& \left[60,65\right]& \left[66,85\right]& \left[86,100\right]\\ C_2& \left[0,59\right]& \left[60,65\right]& \left[66,85\right]& \left[86,100\right]\\ C_3& \left[0,59\right]& \left[60,65\right]& \left[66,85\right]& \left[86,100\right]\\ C_4& \left[0,59\right]& \left[60,65\right]& \left[66,85\right]& \left[86,100\right]\\ C_5& \left[0,59\right]& \left[60,65\right]& \left[66,85\right]& \left[86,100\right]\\ C_6& \left[0,59\right]& \left[60,65\right]& \left[66,85\right]& \left[86,100\right]\\ C_7& \left[0,59\right]& \left[60,65\right]& \left[66,85\right]& \left[86,100\right]\\ C_8& \left[0,59\right]& \left[60,65\right]& \left[66,85\right]& \left[86,100\right]\\ C_9& \left[0,59\right]& \left[60,65\right]& \left[66,85\right]& \left[86,100\right]\\ C_{10}& \left[0,59\right]& \left[60,65\right]& \left[66,85\right]& \left[86,100\right]\\ C_{11}& \left[0,59\right]& \left[60,65\right]& \left[66,85\right]& \left[86,100\right]\\ C_{12}& \left[0,59\right]& \left[60,65\right]& \left[66,85\right]& \left[86,100\right]\end{array}\right]M_p=\left[\begin{array}{ccc}{O}_p& C_1& \left[0,100\right]\\ & C_2& \left[0,100\right]\\ & C_3& \left[0,100\right]\\ & C_4& \left[0,100\right]\\ & C_5& \left[0,100\right]\\ & C_6& \left[0,100\right]\\ & C_7& \left[0,100\right]\\ & C_8& \left[0,100\right]\\ & C_9& \left[0,100\right]\\ & C_{10}& \left[0,100\right]\\ & C_{11}& \left[0,100\right]\\ & C_{12}& \left[0,100\right]\end{array}\right]$$

(15)

The fresh agricultural supply chain resilience indicator evaluation is divided into four quantitative value intervals: when a certain indicator Ci in the interval [0, 59] is very poor; in the interval [60, 65] when the indicator is poor; in the interval [66, 85] when the indicator is good; and in the interval [86, 100] when the indicator is excellent. The [0, 100] of the section field represents the range of values that the indicator can take.

This paper focuses on fresh produce supply chain enterprise M as the subject of evaluation. Based on the actual operations of the supply chain within enterprise M, experts are invited to score the supply chain using a qualitative questionnaire, following a predefined scoring standard. The preliminary evaluation of the scores for each index reflecting the supply chain status of the fresh produce enterprise is conducted through expert assessments and other methods. This process allows for the identification of the key object elements to be evaluated, which include the following:

$$M=\left[\begin{array}{ccc}O& C_1& 76\\ & C_2& 69\\ & C_3& 72\\ & C_4& 47\\ & C_5& 52\\ & C_6& 74\\ & C_7& 66\\ & C_8& 83\\ & C_9& 42\\ & C_{10}& 74\\ & C_{11}& 69\\ & C_{12}& 39\end{array}\right]$$

(16)

4.3. Constructing the Incompatibility Problem Model

In the resilience evaluation results of enterprise M, the indicators product supply efficiency C₄, financing capability C₅, enterprise visibility C₉, and production and processing equipment C₁₂ fall within the extension domain [0, 59]. This indicates that these evaluation indicators are in the “Poor” range. The evaluated enterprise M needs to optimize these indicators to reach a qualified resilience score range, and then strive to achieve an “Excellent” rating.

Based on the above analysis, the extension theory model of the incompatibility problem for the resilience of the fresh agricultural product enterprise M is constructed as follows:

$$\begin{gathered} P=G\ast L= \\ \left[\begin{array}{rrr}\hfill \mathrm{Elevation},& \hfill Dominating object,& \hfill \mathrm{Supply} \mathrm{chain} \mathrm{resilience}\\ \hfill & \hfill Acting object,& \hfill \mathrm{Enterprise} \mathrm{M}\end{array}\right] \\ \ast \left[\begin{array}{rrr}\hfill \mathrm{Resilience} \mathrm{factors},& \hfill \mathrm{Source},& \hfill \mathrm{Configuration} \mathrm{of} \mathrm{the} \mathrm{enterprise}\\ \hfill & \hfill \mathrm{Rating},& \hfill \mathrm{Low}\end{array}\right] \end{gathered}$$

(17)

The goal is to enhance the supply chain resilience of fresh produce enterprise M. To achieve this, while maintaining the original goal, the incompatibility issues are addressed by adjusting the conditions of the problem. This approach ensures that the underlying challenges are resolved in a way that supports the overall objective of strengthening supply chain resilience.

Based on the supply chain resilience evaluation, which incorporates the correlation function value and index scores for indicator selection, this paper identifies several indicators with lower scores that show significant potential for improvement. Specifically, the product supply efficiency C₄, financing capacity C₅, enterprise visibility C₉, and production and processing equipment C₁₂ fall within the poor grade range. Some of these indicators still offer substantial room for improvement. For enterprise M to enhance its supply chain resilience, it is crucial to optimize these indicators to strengthen the overall performance of the supply chain.

According to the evaluation value of enterprise M’s toughness indexes, we constructed the above material element model, as follows:

$$M=\left[\begin{array}{ccc}\mathrm{resilience},& product supply efficiency,& 47\\ & financing capacity,& 52\\ & enterprise visibility,& 42\\ & production and processing equipment,& 39\end{array}\right]$$

(18)

In this resilience enhancement strategy, the focus is on improving the resilience of fresh agricultural product enterprise M. The indicators for enterprise M are considered the key features, and their evaluation scores represent the values of these elements. With the objective remaining unchanged, an extension theory model is constructed to solve the core problem and address the incompatibility issues. This model is designed as follows:

$$p_0=g_0\ast l_0=\left[\begin{array}{ccc}\mathrm{elevation},& product supply efficiency,& \mathrm{level}\\ & financing capacity,& \mathrm{level}\\ & enterprise visibility,& \mathrm{reputation}\\ & production and processing equipment,& \mathrm{capability}\end{array}\right]$$

(19)

4.4. Calculating the Weights of Indicators of Fresh Produce Supply Chain Resilience

To construct the judgment matrix for the two-by-two comparison of indicators, the expert scoring method is used to assess the relative importance of each indicator. Experts conduct pairwise comparisons by assigning values to indicate the relative importance between each pair of indicators, as shown in

Table 3. Quantitative materiality values.

Factor i Compared to Factor j	Quantitative Value
equal importance	1
slightly important	3
more important	5
high importance	7
utmost importance	9
intermediate value of two adjacent judgements	2, 4, 6, 8
reciprocal	aij = 1/aji

. Based on these comparisons, the value of the final can be calculated at all levels of indicators of the weight value of $\omega$. Additionally, the judgment matrix of the largest characteristic root of the $\lambda \max$ is determined, followed by a consistency test. If the consistency ratio (CR) is less than 0.1, the judgment matrix is considered to meet the consistency requirement.

(1)

Calculation of weights for Level 1 indicators

The judgement matrices for Level 1 indicators Product B1, Funding B2, and Intrapreneurship B3 are shown in

Table 4. Tier 1 indicator judgement matrix.

	B1	B2	B3	ω	λmax	CI	RI	CR	Verdict
B1	1	2	1/2	0.29	3.0	0	0.52	0 < 0.1	The judgement matrix satisfies the consistency
B2	1/2	1	1/4	0.14
B3	2	4	1	0.57

.

(2)

Calculation of secondary indicator weights

Construct a weight determination matrix for the secondary indicator system of product B₁, product safety toughness C₁, product traceability C₂, degree of product demand C₃, and product supply efficiency C₄, as shown in

Table 5. Judgement matrix of secondary indicators for product B1.

	C1	C2	C3	C4	ω	λmax	CI	RI	CR	Verdict
C1	1	1/3	3	2	0.24	4.1050	0.0349	0.89	0.0393 < 0.1	The judgement matrix satisfies the consistency
C2	3	1	5	3	0.51
C3	1/3	1/5	1	1/3	0.08
C4	1/2	1/3	3	1	0.17

.

Constructing the weight determination matrix of the secondary indicator system of capital B₂, financing capacity C₅, investment in innovation and R&D C₆, maintenance cost C₇, and profitability C₈. The results are shown in

Table 6. Judgement matrix of secondary indicators for Fund B2.

	C5	C6	C7	C8	ω	λmax	CI	RI	CR	Verdict
C5	1	3	1/2	2	0.29	4.0458	0.0153	0.89	0.0172 < 0.1	The judgement matrix satisfies the consistency
C6	1/3	1	1/4	1/2	0.10
C7	2	4	1	2	0.43
C8	1/2	2	1/2	1	0.18

.

Construct the weight determination matrix of the secondary indicator system of B₃ within the enterprise, enterprise visibility C₉, information flow C₁₀, enterprise culture C₁₁, and production and processing equipment C₁₂. The results are shown in

Table 7. Judgement matrix of secondary indicators for B₃ within the enterprise.

	C9	C10	C11	C12	ω	λmax	CI	RI	CR	Verdict
C9	1	5	1/2	3	0.33	4.1308	0.0654	0.89	0.0732 < 0.1	The judgement matrix satisfies the consistency
C10	1/5	1	1/5	1/3	0.07
C11	2	5	1	2	0.43
C12	1/3	3	1/2	1	0.17

.

According to the results of the calculations for each indicator layer, the comprehensive weights of the evaluation indicators for the resilience of the agricultural product supply chain are obtained, as shown in

Table 8. Combined weights of evaluation indicators.

Level 1 Indicators		Secondary Indicators		Combined Weights $\mathbf{\alpha }$
Norm	Weights $\mathbf{\omega }$	Norm	Weights $\mathbf{\omega }$
B1	0.29	C1	0.24	0.0696
		C2	0.51	0.1479
		C3	0.08	0.0232
		C4	0.17	0.0493
B2	0.14	C5	0.29	0.0406
		C6	0.1	0.0140
		C7	0.43	0.0602
		C8	0.18	0.0252
B3	0.57	C9	0.33	0.1181
		C10	0.07	0.0399
		C11	0.43	0.2451
		C12	0.17	0.0969

.

Based on the correlation function formula and the comprehensive correlation function formula, the secondary indicator $C_{\mathrm{j}}$ of the resilience evaluation of the fresh agricultural product supply chain can calculate the correlation degree regarding level $O_1$. Taking the indicator C₁ of enterprise M as an example, the following occurs:

$$\rho \left(\begin{array}{cc}{v}_1,& V_{o11}\end{array}\right)=\left|\left.76-{\displaystyle \frac{0+59}{2}}\right|\right.-{\displaystyle \frac{59-0}{2}}=17$$

$$\rho \left(\begin{array}{cc}{v}_1,& V_{p1}\end{array}\right)=\left|\left.76-{\displaystyle \frac{0+100}{2}}\right|\right.-{\displaystyle \frac{100-0}{2}}=-24$$

Since 17−(−20) ≠ 0, the following applies:

$$k_1(v_1)={\displaystyle \frac{\rho \left(\begin{array}{cc}{v}_1,& V_{o11}\end{array}\right)}{\rho \left(\begin{array}{cc}{v}_1,& V_{p1}\end{array}\right)-\rho \left(\begin{array}{cc}{v}_1,& V_{o11}\end{array}\right)}}={\displaystyle \frac{17}{-24-17}}=-0.4146$$

Similarly, the order of correlation of the indicators of firm M with respect to the $O_1$ level is (−0.414,−0.244,−0.317,0.343,0.171,−0.366,−0.171,−0.585,0.68,−0.366,−0.244,1.053).

The value of the composite-dependent function k₁ for firm M with respect to evaluation level e = 1 is calculated as follows:

$$K_1={\displaystyle \sum _{i=1}^{12}{\omega }_i}{k}_1(v_i)=0.0282$$

The order of correlation of the indicators of firm M with respect to the $O_2$ level is (−0.314,−0.114,−0.200,−0.217,−0.143,−0.257,−0.029,−0.514,−0.237,−0.257,−0.114,−0.259).

$$K_2={\displaystyle \sum _{i=1}^{12}{\omega }_i}{k}_2(v_i)=-0.2070$$

The order of correlation of the indicators of firm M with respect to the $O_3$ level is (0.600,0.107,0.273,−0.288,−0.226,0.444,0,0.133,−0.364,0.444,0.107,−0.307).

$$K_3={\displaystyle \sum _{i=1}^{12}{\omega }_i}{k}_3(v_i)=0.1374$$

The order of correlation of the indicators of firm M with respect to the $O_4$ level is (−0.294,−0.354,−0.333,−0.453,−0.415,−0.316,−0.370,−0.150,−0.512,−0.316,−0.354,−0.547).

$$K_4={\displaystyle \sum _{i=1}^{13}{\omega }_i}{k}_4(v_i)=-0.4045$$

By analyzing the comprehensive evaluation correlation function values for enterprise M, it is concluded that for the evaluation interval rating e = 3, the value of the comprehensive correlation function is positive and the largest. This indicates that the resilience evaluation result of the fresh agricultural product supply chain enterprise M is “good”. When the evaluation rating is equal to 1, the value of the comprehensive correlation function is also positive, meaning that the original unqualified indicators are too poor, resulting in a score at the worst rating. Therefore, addressing unqualified resilience indicators is urgent. Additionally, when the evaluation rating is equal to 5, no resilience evaluation indicators are positive, indicating that no indicators are in the “excellent” state. Through analysis, although the correlation function shows it is closer to the “good” interval, low resilience indicators still significantly affect the overall resilience level of the enterprise. Therefore, improving unqualified resilience indicators becomes the focus of this paper.

To achieve the goal of improving the core issue of resilience for enterprise M, it is essential to combine the company’s current situation with the weight distribution provided in the indicators table. This allows for the classification of the classical domain for each conditional element. The expert group analyzes and establishes the target classical domain intervals for improving each indicator. The classical domain intervals for the conditional elements of the core issue target are as follows: the target classical domain interval for product supply efficiency is (66, 75), for financing capability is (60, 75), for enterprise reputation is (66, 80), and for production and processing equipment is (66, 75).

From the perspective of the enterprise development strategy and objectives, as long as the target of resilience improvement can be achieved as scheduled, less input of the elements is better for the enterprise; therefore, the conditional indicator to construct the characteristics of each optimal point xo is located in the left side of the classical domain interval $X=〈\begin{array}{ccc}{a}_{oej}& ,& b_{oej}\end{array}〉$, that is the optimal solution $x_0=a$. The dependent function of $x_0=a$ is as follows:

$$k\left(x\right)=\left\{\begin{array}{cc}{\displaystyle \frac{x-a}{b-a}}& x<a\\ {\displaystyle \frac{b-x}{b-a}}& x\ge a\end{array}\right.$$

(20)

Through the above formulas, the compatibility function between the current scores of each indicator and their respective target classical domains can be obtained as follows: k(x₁) = −2.11, k(x₂) = −0.53, k(x₃) = −1.71, k(x₄) = −3.

At this point, the total compatibility function is as follows:

$$\begin{gathered} K\left(p_0\right)=\underset{i=1}{\overset{4}{{\displaystyle \wedge }}}k\left(v_i\right)=k\left(v\left(l_1\right)\right)\wedge k\left(v\left(l_2\right)\right)\wedge k\left(v\left(l_3\right)\right)\wedge k\left(v\left(l_4\right)\right) \\ =-2.11\wedge -0.53\wedge -1.71\wedge -3<0 \end{gathered}$$

At this point, the total compatibility function for the core issue is $k\left(p\right)<0$. To resolve the current incompatibility issue, it is necessary to conduct extenics transformation and propagation of the condition element of the core issue.

4.5. Implementing Extension Analysis and Extenics Transformation

(1)

Divergence analysis of $l_{011}$ goods transport and $l_{012}$ order security obtained from the analysis of the $l_{01}$ product supply chain efficiency correlation of the conditional basic-elements, as follows:

$$l_{01}\sim \left\{\begin{array}{c}{l}_{011}=\left[\begin{array}{rrr}\hfill \mathrm{transported},& \hfill dominating object,& \hfill \mathrm{cargoes}\\ \hfill & \hfill \mathrm{carrier},& \hfill \text{manual mini-transporter}\\ \hfill & \hfill \mathrm{volume} \mathrm{of} \mathrm{freight},& \hfill v_{011}\end{array}\right]\\ l_{012}=\left[\begin{array}{rrr}\hfill \mathrm{guarantee},& \hfill dominating object,& \hfill \mathrm{orders}\\ \hfill & \hfill \mathrm{methodology},& \hfill \mathrm{contract}\\ \hfill & \hfill \mathrm{missing} \mathrm{order} \mathrm{rate},& \hfill v_{012}\end{array}\right]\end{array}\right.$$

(21)

In order to achieve the goal of solving the incompatibility problem, it is necessary to implement extension transformations on the conditioned basic-elements $l_{01}$ dispersed from $l_{011}$ and $l_{012}$ conditioned basic-elements, applying the methods in the method of extension transformations to carry out a variety of transformations on the dispersed basic-elements. Dispersed basic-elements have relevance, and eventually the initial conditioned basic-elements will be changed through the conductivity of things, the existence of $(T_{011}\wedge T_{012})\Rightarrow T_{01}$, $(T_{011}\vee T_{012})\Rightarrow T_{01}$, and the conditioned basic-elements $l_{01}$ of the relevance $l_{011}$ and $l_{012}$ of extension transformations as a substitution method, and the basic-element model is as follows:

$$T_{011}{l}_{011}\left\{\begin{array}{c}{T}_{011}^{\prime }{l}_{011}=l_{011}^{\prime }=\left[\begin{array}{rrr}\hfill \mathrm{transported},& \hfill dominating object,& \hfill \mathrm{fresh} \mathrm{produce}\\ \hfill & \hfill \mathrm{carrier},& \hfill \mathrm{intelligent} \mathrm{unmanned} \mathrm{transport} \mathrm{vehicle}\\ \hfill & \hfill \mathrm{volume} \mathrm{of} \mathrm{freight},& \hfill v_{011}^{\prime }\end{array}\right]\\ \begin{array}{l}{T}_{011}^{″}{l}_{011}=l_{011}^{″}=\left[\begin{array}{rrr}\hfill \mathrm{transported},& \hfill dominating object,& \hfill \mathrm{fresh} \mathrm{produce}\\ \hfill & \hfill \mathrm{carrier},& \hfill \mathrm{professional} \mathrm{distribution} \mathrm{vehicle}\\ \hfill & \hfill \mathrm{volume} \mathrm{of} \mathrm{freight},& \hfill v_{011}^{″}\end{array}\right]\\ \cdots \end{array}\end{array}\right.$$

(22)

$$T_{012}{l}_{012}\left\{\begin{array}{c}{T}_{012}^{\prime }{l}_{012}=l_{012}^{\prime }=\left[\begin{array}{rrr}\hfill \mathrm{guarantee},& \hfill dominating object,& \hfill \mathrm{agricultural} \mathrm{orders}\\ \hfill & \hfill \mathrm{methodology},& \hfill \mathrm{customer} \mathrm{service} \mathrm{level}\\ \hfill & \hfill \mathrm{missing} \mathrm{order} \mathrm{rate},& \hfill v_{012}^{\prime }\end{array}\right]\\ \begin{array}{l}{T}_{012}^{″}{l}_{012}=l_{012}^{″}=\left[\begin{array}{rrr}\hfill \mathrm{guarantee},& \hfill dominating object,& \hfill \mathrm{agricultural} \mathrm{orders}\\ \hfill & \hfill \mathrm{methodology},& \hfill \mathrm{order} \mathrm{process}\\ \hfill & \hfill \mathrm{missing} \mathrm{order} \mathrm{rate},& \hfill v_{012}^{″}\end{array}\right]\\ \cdots \end{array}\end{array}\right.$$

(23)

Combine the new conditions of the extension transformation to form a transformation of the condition-based product supply chain efficiency, as follows:

$$T_{01}{l}_{01}=\left\{\begin{array}{l}{l}_{01}^{\prime }=T_{01}^{\prime }{l}_{01}\Leftarrow \{T_{011}^{\prime }{l}_{011}\wedge T_{012}^{\prime }{l}_{012}\\ l_{01}^{″}=T_{01}^{″}{l}_{01}\Leftarrow \{T_{011}^{″}{l}_{011}\wedge T_{012}^{\prime }{l}_{012}\\ l_{01}^{‴}=T_{01}^{‴}{l}_{01}\Leftarrow \{T_{011}^{\prime }{l}_{011}\wedge T_{012}^{″}{l}_{012}\\ l_{01}^{⁗}=T_{01}^{⁗}{l}_{01}\Leftarrow \{T_{011}^{″}{l}_{011}\wedge T_{012}^{″}{l}_{012}\\ \dots \end{array}\right.$$

(24)

After the transformation conduction is the following:

$$T_{01}{l}_{01}=\left\{\begin{array}{l}(T_{011}^{\prime }{l}_{011}\wedge T_{012}^{\prime }{l}_{012})T_{01}^{\prime }{l}_{01}=l_{01}^{\prime }[\begin{array}{ccc}\mathrm{product} \mathrm{supply} \mathrm{efficiency},& \mathrm{rate},& 70\end{array}]\\ (T_{011}^{″}{l}_{011}\wedge T_{012}^{\prime }{l}_{012})T_{01}^{″}{l}_{01}=l_{01}^{″}[\begin{array}{ccc}\mathrm{product} \mathrm{supply} \mathrm{efficiency},& \mathrm{rate},& 75\end{array}]\\ (T_{011}^{\prime }{l}_{011}\wedge T_{012}^{″}{l}_{012})T_{01}^{‴}{l}_{01}=l_{01}^{‴}[\begin{array}{ccc}\mathrm{product} \mathrm{supply} \mathrm{efficiency},& \mathrm{rate},& 68\end{array}]\\ (T_{011}^{″}{l}_{011}\wedge T_{012}^{″}{l}_{012})T_{01}^{⁗}{l}_{01}=l_{01}^{⁗}[\begin{array}{ccc}\mathrm{product} \mathrm{supply} \mathrm{efficiency},& \mathrm{rate},& 78\end{array}]\end{array}\right.$$

(25)

In this case, if there exists the dependent function $k\left(v\left(T_{01}{l}_{01}\right)\right)\ge 0$ of the conditional basic-elements after the extension transformation, then it means that the transformation is feasible. By calculating $k\left(v\left(T_{01}{l}_{01}\right)\right)\max$ = 0.77.

(2)

Divergence analysis of $l_{021}$ information statistics and $l_{022}$ funding source obtained from the analysis of the $l_{02}$ financing capacity correlation of the conditional basic-elements, resulting in the following:

$$l_{02}\sim \left\{\begin{array}{c}{l}_{021}=\left[\begin{array}{rrr}\hfill information statistics,& \hfill acting object,& \hfill \mathrm{enterprise} \mathrm{M} \mathrm{employees}\\ \hfill & \hfill \mathrm{credibility},& \hfill \mathrm{moderate}\\ \hfill & \hfill \mathrm{volume} \mathrm{of} \mathrm{information},& \hfill v_{021}\end{array}\right]\\ l_{052}=\left[\begin{array}{ccc}\mathrm{capital},& \mathrm{source},& \mathrm{enterprise} \mathrm{M}\\ & \mathrm{sum},& v_{022}\end{array}\right]\end{array}\right.$$

(26)

Similarly, the associated basic-elements $l_{021}$ and $l_{022}$ of $l_{02}$ can be extension transformed as:

$$T_{021}{l}_{021}\left\{\begin{array}{c}{T}_{021}^{\prime }{l}_{021}=l_{021}^{\prime }=\left[\begin{array}{rrr}\hfill information statistics,& \hfill \mathrm{a}cting object,& \hfill \mathrm{information} \mathrm{commissioners}\\ \hfill & \hfill \mathrm{credibility},& \hfill \mathrm{high}\\ \hfill & \hfill \mathrm{volume} \mathrm{of} \mathrm{information},& \hfill v_{021}^{\prime }\end{array}\right]\\ \begin{array}{l}{T}_{021}^{″}{l}_{021}=l_{021}^{″}=\left[\begin{array}{rrr}\hfill information statistics,& \hfill \mathrm{a}cting object,& \hfill \mathrm{intelligent} \mathrm{platforms}\\ \hfill & \hfill \mathrm{credibility},& \hfill \mathrm{high}\\ \hfill & \hfill \mathrm{volume} \mathrm{of} \mathrm{information},& \hfill v_{021}^{″}\end{array}\right]\\ \cdots \end{array}\end{array}\right.$$

(27)

$$T_{022}{l}_{022}\left\{\begin{array}{c}{T}_{022}^{\prime }{l}_{022}=l_{022}^{\prime }=\left[\begin{array}{ccc}\mathrm{capital},& \mathrm{source},& \mathrm{enterprise} \mathrm{M}\\ & \mathrm{sum},& v_{022}^{\prime }\end{array}\right]\\ \begin{array}{l}{T}_{022}^{″}{l}_{022}=l_{022}^{″}=\left[\begin{array}{ccc}\mathrm{capital},& \mathrm{source},& \mathrm{enterprise} \mathrm{M}\\ & \mathrm{sum},& v_{022}^{″}\end{array}\right]\\ \cdots \end{array}\end{array}\right.$$

(28)

Combining and transforming the new conditional basic-elements produced by extension transformations, the following occurs:

$$T_{02}{l}_{02}=\left\{\begin{array}{l}{l}_{02}^{\prime }=T_{02}^{\prime }{l}_{02}\Leftarrow \{T_{021}^{\prime }{l}_{021}\wedge T_{022}^{\prime }{l}_{022}\\ l_{02}^{″}=T_{02}^{″}{l}_{02}\Leftarrow \{T_{021}^{″}{l}_{021}\wedge T_{022}^{\prime }{l}_{022}\\ l_{02}^{‴}=T_{02}^{‴}{l}_{02}\Leftarrow \{T_{021}^{\prime }{l}_{021}\wedge T_{022}^{″}{l}_{022}\\ l_{02}^{⁗}=T_{02}^{⁗}{l}_{02}\Leftarrow \{T_{021}^{″}{l}_{021}\wedge T_{022}^{″}{l}_{022}\\ \dots \end{array}\right.$$

(29)

After the transformation conduction is the following:

$$T_{02}{l}_{02}=\left\{\begin{array}{l}{T}_{021}^{\prime }{l}_{021}\wedge T_{022}^{\prime }{l}_{022}{T}_{02}^{\prime }{l}_{02}=l_{02}^{\prime }\left[\begin{array}{ccc}financing capacity,& rate,& 77\end{array}\right]\\ T_{021}^{″}{l}_{021}\wedge T_{022}^{\prime }{l}_{022}{T}_{02}^{″}{l}_{02}=l_{02}^{″}\left[\begin{array}{ccc}financing capacity,& rate,& 72\end{array}\right]\\ T_{021}^{\prime }{l}_{021}\wedge T_{022}^{″}{l}_{022}{T}_{02}^{‴}{l}_{02}=l_{02}^{‴}\left[\begin{array}{ccc}financing capacity,& rate,& 70\end{array}\right]\\ T_{021}^{″}{l}_{021}\wedge T_{022}^{″}{l}_{022}{T}_{02}^{⁗}{l}_{02}=l_{02}^{⁗}\left[\begin{array}{ccc}financing capacity,& rate,& 74\end{array}\right]\\ \dots \end{array}\right.$$

(30)

In this case, if there exists the dependent function $k\left(v\left(T_{02}{l}_{02}\right)\right)\ge 0$ of the conditional basic-elements after the extension transformation, then it means that the transformation is feasible. By calculating $k\left(v\left(T_{02}{l}_{02}\right)\right)\max$=0.33.

(3)

Divergence analysis of $l_{031}$ marketing approach obtained from the $l_{03}$ enterprise visibility correlation analysis of the conditional basic-elements, resulting in the following:

$$l_{03}\sim l_{031}=\left[\begin{array}{rrr}\hfill \mathrm{marketing} \mathrm{approach},& \hfill \mathrm{executing} \mathrm{entity},& \hfill \mathrm{enterprise} \mathrm{M}\\ \hfill & \hfill \mathrm{typology},& \hfill telemarketing\\ \hfill & \hfill \mathrm{degree} \mathrm{of} \mathrm{influence},& \hfill v_{031}\end{array}\right]$$

(31)

Similarly, the associated basic-elements $l_{031}$ of $l_{03}$ can be extension transformed as follows:

$$T_{031}{l}_{031}\left\{\begin{array}{l}{T}_{031}^{\prime }{l}_{031}=l_{031}^{\prime }=\left[\begin{array}{rrr}\hfill \mathrm{marketing} \mathrm{approach},& \hfill \mathrm{executing} \mathrm{entity},& \hfill \mathrm{advertisers}\\ \hfill & \hfill \mathrm{typology},& \hfill \mathrm{online} \mathrm{advertising}\\ \hfill & \hfill \mathrm{degree} \mathrm{of} \mathrm{influence},& \hfill v_{031}^{’}\end{array}\right]\\ T_{031}^{″}{l}_{031}=l_{031}^{″}=\left[\begin{array}{rrr}\hfill \mathrm{marketing} \mathrm{approach},& \hfill \mathrm{executing} \mathrm{entity},& \hfill \mathrm{operator}\\ \hfill & \hfill \mathrm{typology},& \hfill \mathrm{search} \mathrm{engine} \mathrm{exposure}\\ \hfill & \hfill \mathrm{degree} \mathrm{of} \mathrm{influence},& \hfill v_{031}^{″}\end{array}\right]\\ T_{031}^{‴}{l}_{031}=l_{031}^{‴}=\left[\begin{array}{rrr}\hfill \mathrm{marketing} \mathrm{approach},& \hfill \mathrm{executing} \mathrm{entity},& \hfill \mathrm{associate}\\ \hfill & \hfill \mathrm{typology},& \hfill \mathrm{exhibition} \mathrm{promotion}\\ \hfill & \hfill \mathrm{degree} \mathrm{of} \mathrm{influence},& \hfill v_{031}^{‴}\end{array}\right]\\ T_{031}^{⁗}{l}_{031}=l_{031}^{⁗}=\left[\begin{array}{rrr}\hfill \mathrm{marketing} \mathrm{approach},& \hfill \mathrm{executing} \mathrm{entity},& \hfill \mathrm{enterprise} \mathrm{H}\\ \hfill & \hfill \mathrm{typology},& \hfill \text{product co-branding}\\ \hfill & \hfill \mathrm{degree} \mathrm{of} \mathrm{influence},& \hfill v_{031}^{⁗}\end{array}\right]\end{array}\right.$$

(32)

Based on the properties of the transformation, transformation $\left(T_m\wedge T_n\cdots \wedge T_{\mathrm{i}}\cdots \right)\Rightarrow T_{03}$ will occur, such that $T_{03}{l}_{031}=l_{03}^{\prime }$.

$$T_{03}{l}_{03}=\left\{\begin{array}{l}{T}_{03}{l}_{031}^{\prime }=l_{03}^{\prime }\\ T_{03}{l}_{031}^{″}=l_{03}^{″}\\ T_{03}{l}_{031}^{‴}=l_{03}^{‴}\\ T_{03}{l}_{031}^{⁗}=l_{03}^{⁗}\\ \cdots \end{array}\right.$$

(33)

After the transformation conduction is the following:

$$T_{03}{l}_{03}==\left\{\begin{array}{c}{l}_{03}^{\prime }[\begin{array}{ccc}\mathrm{enterprise} \mathrm{visibility},& \mathrm{rate},& 71\end{array}]\\ l_{03}^{″}[\begin{array}{ccc}\mathrm{enterprise} \mathrm{visibility},& \mathrm{rate},& 77\end{array}]\\ l_{03}^{‴}[\begin{array}{ccc}\mathrm{enterprise} \mathrm{visibility},& \mathrm{rate},& 68\end{array}]\\ l_{03}^{⁗}[\begin{array}{ccc}\mathrm{enterprise} \mathrm{visibility},& \mathrm{rate},& 75\end{array}]\end{array}\right.$$

(34)

In this case, if there exists the dependent function $k\left(v\left(T_{03}{l}_{03}\right)\right)\ge 0$ of the conditional basic-elements after the extension transformation, then it means that the transformation is feasible. By calculating $k\left(v\left(T_{03}{l}_{03}\right)\right)\max$=0.85.

(4)

Divergence analysis of $l_{041}$ production equipment inputs obtained from the $l_{04}$ production and processing equipment correlation analysis of the conditional basic-elements, resulting in the following:

$$l_{04}\sim l_{041}=\left[\begin{array}{rrr}\hfill \mathrm{equipment} \mathrm{inputs},& \hfill \mathrm{executing} \mathrm{entity},& \hfill \mathrm{enterprise} \mathrm{M}\\ \hfill & \hfill \mathrm{typology},& \hfill \mathrm{artificial} \mathrm{traditional} \mathrm{production} \mathrm{equipment}\\ \hfill & \hfill \mathrm{sum} \mathrm{of} \mathrm{money},& \hfill v_{041}\end{array}\right]$$

(35)

Similarly, the associated basic-elements $l_{041}$ of $l_{04}$ can be extension transformed as follows:

$$T_{041}{l}_{041}\left\{\begin{array}{l}{T}_{041}^{\prime }{l}_{041}=l_{041}^{\prime }=\left[\begin{array}{rrr}\hfill \mathrm{equipment} \mathrm{inputs},& \hfill \mathrm{executing} \mathrm{entity},& \hfill \mathrm{enterprise} \mathrm{M}\\ \hfill & \hfill \mathrm{typology},& \hfill \mathrm{automated} \mathrm{production} \mathrm{equipment}\\ \hfill & \hfill \mathrm{sum} \mathrm{of} \mathrm{money},& \hfill v_{041}^{’}\end{array}\right]\\ T_{041}^{″}{l}_{041}=l_{041}^{″}=\left[\begin{array}{rrr}\hfill \mathrm{equipment} \mathrm{inputs},& \hfill \mathrm{executing} \mathrm{entity}& \hfill \mathrm{enterprise} \mathrm{M}\\ \hfill & \hfill \mathrm{typology},& \hfill \mathrm{customised} \mathrm{production} \mathrm{equipment}\\ \hfill & \hfill \mathrm{sum} \mathrm{of} \mathrm{money},& \hfill v_{041}^{″}\end{array}\right]\\ T_{041}^{‴}{l}_{041}=l_{041}^{‴}=\left[\begin{array}{rrr}\hfill \mathrm{equipment} \mathrm{inputs},& \hfill \mathrm{executing} \mathrm{entity}& \hfill \mathrm{enterprise} \mathrm{M}\\ \hfill & \hfill \mathrm{typology},& \hfill \text{environmental protection and energy-saving production equipment}\\ \hfill & \hfill \mathrm{sum} \mathrm{of} \mathrm{money},& \hfill v_{041}^{‴}\end{array}\right]\\ T_{041}^{⁗}{l}_{041}=l_{041}^{⁗}=\left[\begin{array}{rrr}\hfill \mathrm{equipment} \mathrm{inputs},& \hfill \mathrm{executing} \mathrm{entity}& \hfill \mathrm{enterprise} \mathrm{M}\\ \hfill & \hfill \mathrm{typology},& \hfill \mathrm{intelligent} \mathrm{production} \mathrm{equipment}\\ \hfill & \hfill \mathrm{sum} \mathrm{of} \mathrm{money},& \hfill v_{041}^{⁗}\end{array}\right]\end{array}\right.$$

(36)

Based on the properties of the transformation, transformation $\left(T_m\wedge T_n\cdots \wedge T_{\mathrm{i}}\cdots \right)\Rightarrow T_{04}$ will occur, such that $T_{04}{l}_{041}=l_{04}^{\prime }$.

$$T_{04}{l}_{04}=\left\{\begin{array}{l}{T}_{04}{l}_{041}^{\prime }=l_{04}^{\prime }\\ T_{04}{l}_{041}^{″}=l_{04}^{″}\\ T_{04}{l}_{041}^{‴}=l_{04}^{‴}\\ T_{04}{l}_{041}^{⁗}=l_{04}^{⁗}\\ \cdots \end{array}\right.$$

(37)

After the transformation conduction is the following:

$$T_{04}{l}_{04}==\left\{\begin{array}{c}{l}_{04}^{\prime }[\begin{array}{ccc}\mathrm{production} \mathrm{and} \mathrm{processing} \mathrm{equipment},& \mathrm{rate},& 77\end{array}]\\ l_{04}^{″}[\begin{array}{ccc}\mathrm{production} \mathrm{and} \mathrm{processing} \mathrm{equipment},& \mathrm{rate},& 71\end{array}]\\ l_{04}^{‴}[\begin{array}{ccc}\mathrm{production} \mathrm{and} \mathrm{processing} \mathrm{equipment},& \mathrm{rate},& 78\end{array}]\\ l_{04}^{⁗}[\begin{array}{ccc}\mathrm{production} \mathrm{and} \mathrm{processing} \mathrm{equipment},& \mathrm{rate},& 73\end{array}]\end{array}\right.$$

(38)

In this case, if there exists the dependent function $k\left(v\left(T_{04}{l}_{04}\right)\right)\ge 0$ of the conditional basic-elements after the extension transformation, then it means that the transformation is feasible. By calculating $k\left(v\left(T_{04}{l}_{04}\right)\right)\max$=0.44.

5. Discussion

Through an extensive analysis of the elemental conditions within incompatibility problems, we employed the extension transformation method to generate a substantial set of resilience enhancement strategy elements with positive impacts. These elements were further combined to form a multidimensional extension strategy set for resilience enhancement. We initially calculated the correlation function for the different strategy combinations used to enterprise M’s supply chain in order to identify an optimal set of resilience enhancement strategies. The combination that produced the highest positive correlation value was then chosen as enterprise M’s best course of action for enhancing resilience. There exists a total compatibility function, as follows:

$$K\left(p_0\right)=\underset{i=1}{\overset{4}{{\displaystyle \wedge }}}k\left(x_i\right)=k_{\max }\left(x_1\right)\wedge k_{\max }\left(x_2\right)\wedge k_{\max }\left(x_3\right)\wedge k_{\max }\left(x_4\right)>0$$

By addressing the resilience-related challenges within Enterprise M’s fresh produce supply chain and formulating a novel set of enhancement strategies, we apply our expertise in calculation and screening to identify the most effective solutions. This process has resulted in the development of targeted resilience enhancement strategies specifically tailored to the fresh produce supply chain. These strategies are designed to tackle the primary challenges faced by Company M across four critical areas: inefficient supply, inadequate financing capacity, limited business visibility, and suboptimal production equipment.

(1)

Ensure an adequate supply of fresh produce. First of all, it is important to optimize supply chain management. Strengthen the integration and coordination between all links in the supply chain, and streamline intermediate links to improve overall operational efficiency. By establishing a unified information platform that facilitates information sharing across the supply chain, real-time data transmission can not only reduce information delays and errors but also significantly improve supply chain transparency and its responsiveness to market changes. Secondly, improve logistics and transportation. Develop efficient logistics and distribution networks, optimize transportation route planning and scheduling systems to minimize transportation times, and reduce logistics costs. Specifically, it is crucial to strengthen cold chain logistics capacity to ensure the maintenance of appropriate low-temperature conditions during transportation, thereby safeguarding the quality and freshness of fresh produce and minimizing wastage. Furthermore, it is essential to establish solid strategic alliances with both upstream and downstream enterprises in the supply chain. These initiatives will enhance the overall stability and dependability of the supply chain as well as its operational efficiency and competitiveness by putting collaborative supply chain concepts into practice and encouraging close cooperation at all stages.

(2)

To enhance the financing capabilities of the fresh produce supply chain, several strategic measures can be implemented. First, optimizing the supply chain structure can significantly improve financing capacity. For instance, reducing information asymmetry by promoting transparency can foster greater trust among enterprises within the supply chain. This, in turn, enhances the liquidity across the entire chain by improving transaction information sharing among the companies involved. Second, the adoption of information technology can further boost the financial efficiency of the fresh agricultural product supply chain. For example, blockchain technology can be leveraged to establish an electronic transaction document identification system, thereby increasing the transparency of business operations. Additionally, big data analytics can be employed to identify high-quality partners and mitigate trade risks. Finally, it is imperative to strengthen the risk management mechanisms for the fresh agricultural product supply chain. This includes, but is not limited to, improving the pre-loan review process, implementing dynamic monitoring systems, and developing comprehensive post-disposal plans. These measures will help ensure effective control of financing risks within the supply chain.

(3)

Improve the visibility of fresh produce business. First, fresh produce companies can improve their business visibility by enhancing supply chain visibility. Blockchain technology allows companies to share trusted information sources, which not only strengthens the trust relationship between partners, but also facilitates the smooth operation of the entire fresh produce supply chain system. Second, processes can be automated and visibility can be improved. Automation can help businesses reduce repetitive work and increase work efficiency. When processes are automated, they can take a closer look at the process and identify areas for improvement. With advanced synchronization and integration capabilities, fresh produce companies can eliminate redundant work in business processes while increasing visibility into the processes themselves. Finally, the security and visibility of the cloud platform can be strengthened. This is due to the increasing maturity of cloud platforms, which enable fresh produce companies to eliminate potential blind spots and enhance the overall efficiency of the supply chain.

(4)

Optimizing production equipment is essential to ensure the efficient production of fresh products. First, the introduction of advanced production equipment can achieve automation and intelligence in the production process, significantly reducing manual intervention and operator errors. This leads to substantial improvements in both productivity and product quality. By incorporating advanced production equipment and flexible manufacturing systems, companies can swiftly adjust equipment configurations and production processes to meet the specific demands of different products. This not only enhances equipment utilization but also increases production flexibility, allowing companies to better respond to the diverse needs of the market. Second, developing a comprehensive preventive maintenance plan for equipment is crucial. Regular inspections and maintenance help prevent potential failures and ensure the longevity of production equipment. The integration of Internet of Things (IoT) technology and big data analysis enables real-time monitoring of equipment status, allowing companies to predict potential issues and take proactive measures to address them. This predictive maintenance approach not only detects and resolves problems early but also prevents unplanned downtime, thus ensuring continuous and stable production. Finally, promoting green production practices is vital in optimizing production equipment. While focusing on improving equipment efficiency, it is equally important to adopt energy-saving equipment and environmentally friendly processes. These practices minimize energy consumption and waste emissions during production, contributing to environmental protection and aligning with global trends in sustainable development. By integrating these strategies, the efficiency and reliability of production equipment will be greatly enhanced, while supporting environmental sustainability and promoting green production practices, thereby ensuring the consistent production of fresh products.

6. Summary

6.1. Conclusions

Fresh produce plays a vital role as the main source of nutrition for residents and occupies an important place in daily consumption. The unique characteristics of fresh produce, such as perishability, dispersion, short shelf life, long lead times, high uncertainty in supply and demand, and low margins, make its supply chain more susceptible to disruptions. These disruptions can impact daily life and severely impact business operations. By enhancing the fresh produce supply chain resilience, companies can more effectively manage risks and challenges, thereby ensuring product quality and maintaining supply chain stability. The contribution of this paper lies in its application of matter-element extension theory to the current context of fresh agricultural product enterprises. Specifically, it introduces a resilience evaluation method for fresh agricultural product supply chains based on the matter-element extension model. Additionally, by utilizing the extension transformation method, the paper proposes a mechanism for generating resilience improvement strategies. This approach not only outlines the specific process for developing resilience strategies but also validates the feasibility of the proposed solutions by examining the fresh produce supply chain of M enterprises. The main conclusions of this paper are as follows:

(1)

From both quantitative and qualitative perspectives, this paper classifies the evaluation indicators of supply chain resilience and establishes a comprehensive evaluation system tailored to fresh agricultural product enterprises. The supply chain resilience evaluation index is categorized into three dimensions: product evaluation, capital evaluation, and enterprise internal evaluation, encompassing a total of 12 indicators. These indicators collectively form a robust evaluation framework for supply chain resilience, providing a foundation for its comprehensive assessment, enhancement, and development. Moreover, the paper adopts the matter-element analysis method as the evaluation approach for supply chain resilience, enabling a multi-level, multi-dimensional assessment. By systematically evaluating resilience levels using the self-constructed index system, weight system, and matter-element analysis model, the paper also outlines a process for deriving supply chain resilience improvement strategies. These strategies are generated through the integration of the extension transformation method, offering a targeted approach to enhancing resilience within the supply chain.

(2)

The research object is to take enterprise M in the supply chain of fresh agricultural products as the research object. It is obtained by the correlation degree function. In this case, the resilience level of enterprise M corresponds to the third level, that is $K_3=0.1374>K_1>0$. The resilience level of the supply chain represents “good”. Further analysis shows that product supply efficiency $C_4=47$, financing capacity $C_5=52$, enterprise visibility $C_9=42$, and production and processing equipment $C_{12}=39$ belong to the extensible domain [0, 59]. This means that the product supply efficiency, financing ability, enterprise reputation, and production and processing equipment are all in poor grades. This shows that the key to restricting the improvement of the resilience of enterprise M lies in four aspects: improving product supply efficiency, financing ability, corporate visibility, and production and processing equipment. And since the total compatibility function is $K\left(p_0\right)=-2.11\wedge -0.53\wedge -1.71\wedge -3<0$, this indicates that, to enhance the resilience of Enterprise M under the current conditions, it is essential to implement an extension transformation. This transformation involves adjusting the goal or conditions in order to address and resolve the existing incompatibility issues.

(3)

In the solution of the incompatibility problem, it is necessary to carry out the extension transformation of the four indicators of product supply efficiency, financing ability, enterprise popularity, and production and processing equipment. Finally, the compatibility function of product supply efficiency is 0.77, and the compatibility function of financing capacity is 0.33. The compatibility function of corporate awareness is 0.85. The compatibility function of production and processing equipment is 0.44. They are all greater than 0, which indicates that their toughness level has been increased by the extension transformation. According to the criterion primitive transformation, the compatibility function is calculated as $K\left(p_0\right)=\underset{i=1}{\overset{4}{{\displaystyle \wedge }}}k\left(x_i\right)=0.77\wedge 0.33\wedge 0.85\wedge 0.44>0$, which indicates that the extended transformation strategy is the optimal supply chain resilience improvement strategy for fresh agricultural product enterprises, which can solve the problems of low product supply efficiency, poor financing ability, low corporate visibility, and backward production and processing equipment.

6.2. Implications

While supply chain resilience has gained considerable attention in academic research, studies specifically focusing on resilience within the fresh produce supply chain remain relatively scarce. Through a comprehensive analysis of the unique characteristics of fresh produce supply chain resilience, this paper develops a specialized resilience index system, providing a novel research perspective and a solid theoretical foundation for this field. Additionally, existing literature often relies on oversimplified evaluation methods that lack sufficient explanatory power. To address this limitation, this paper introduces extension theory as a framework to systematically and quantitatively assess the various dimensions of resilience in fresh produce supply chains. The adoption of this method not only enriches current resilience evaluation models but also enhances the scientific rigor and explanatory depth of the results. Although the primary focus of this paper is on strategies for improving resilience within the fresh produce supply chain, the methodologies applied offer valuable insights that can be adapted to resilience improvement strategies in other supply chain contexts.

The direct beneficiaries of this study are SMEs, consumers, and stakeholders of fresh produce. By improving the supply chain resilience, small and medium-sized fresh produce companies can better withstand the negative impact of market fluctuations and reduce cost increases and revenue losses caused by emergencies. For consumers, a stable supply chain ensures a safe and continuous supply of fresh produce. For stakeholders, including investors, partners, local governments, and others, they will all benefit from a healthier business environment. It can also serve as a reference for other businesses and ultimately drive the entire fresh produce industry towards a more resilient and sustainable direction.

In the context of a globalized, complex, and volatile economic environment, small and medium-sized fresh produce enterprises—key contributors to the national economy—face a range of risks, including natural disasters, public health crises such as the COVID-19 pandemic, and social unrest like strikes. These disruptions can severely affect their long-term sustainability and the stability of fresh produce supply chains. For example, the COVID-19 pandemic led to labor shortages, a sharp decline in market demand, logistical bottlenecks, and overall supply chain instability. Consequently, enhancing supply chain resilience in the face of such disruptive risks is vital for the continued operation of small and medium-sized fresh produce enterprises. By implementing resilience improvement strategies based on extension theory, these enterprises can better optimize their resources, improving their ability to adapt to market fluctuations and respond flexibly to disruptions. This approach not only strengthens overall supply chain resilience but also ensures that the supply chain can withstand external shocks, maintaining stability even during times of uncertainty.

6.3. Research Limitations and Perspectives

The scores and comprehensive weights of the indicators in this study were primarily obtained through expert evaluations. Although efforts were made to ensure fairness and objectivity during the scoring process, the inherent subjectivity of expert assessments remains unavoidable. Additionally, this study focuses on the fresh produce supply chain and offers findings with a certain degree of generalizability, but it lacks targeted research on specific sectors within the fresh produce industry.

Future research could benefit from collecting more data and employing more objective methods, such as the entropy method, CRITIC weighting method, and game theory-based weighting methods, to calculate the comprehensive weights of the indicators, thereby enhancing the scientific rigor and rationality of the results. Furthermore, focusing on specific sectors within the fresh produce industry, researchers could extract key elements of supply chain resilience and develop a more detailed and refined comprehensive evaluation system.