Search Results (389)

To address the challenges of high-dimensional complexity and increasing heterogeneity in expert opinions, this study proposes a novel numerical aggregation model for multi-expert decision making based on triangular intuitionistic fuzzy numbers (TIFNs) and the Plant Growth Simulation Algorithm (PGSA). The proposed framework transforms experts’ fuzzy preference information into five-dimensional geometric vectors and employs the PGSA to perform global optimization, thereby yielding an optimized collective decision matrix. To comprehensively evaluate the aggregation performance, several quantitative indicators—such as weighted Hamming distance, correlation sum, information intuition energy, and weighted correlation coefficient—are introduced to assess the results from the perspectives of consensus, stability, and informational strength. Extensive numerical experiments and comparative analyses demonstrate that the proposed method significantly improves expert consensus reliability and aggregation robustness, achieving higher decision accuracy than conventional approaches. This framework provides a scalable and generalizable tool for high-dimensional fuzzy group decision making, offering promising potential for complex real-world applications. Full article

Traditional multi-criteria decision-making (MCDM) methods face problems in sustainable product design evaluation, including weak semantic expression, single weight modeling, and insufficient ranking robustness. To address these issues, this paper proposes an evaluation framework based on Trapezoidal Intuitionistic Fuzzy (TrIF), named TrIF-DEC, which integrates Decision-Making Trial and Evaluation Laboratory (DEMATEL), Entropy, and Combined Compromise Solution (CoCoSo). Firstly, design criteria across four dimensions—social, economic, technological, and environmental—are identified based on sustainability considerations. Then, TrIF is used to capture the fuzziness and hesitation in expert judgments. The DEMATEL and Entropy methods are combined to extract causal relationships between criteria and quantify data variation, enabling the collaborative weighting of subjective and objective factors. Finally, multi-strategy integrated ranking is performed through TrIF-CoCoSo to enhance decision stability. An empirical case study on nursing bed design demonstrates the effectiveness of the proposed framework. Results demonstrate that TrIF-DEC can systematically integrate uncertainty information with multidimensional sustainability goals, providing reliable support for complex product design evaluation. Full article

Slope instability may cause severe casualties, property losses, and ecological damage. To accurately evaluate slope stability grades and mitigate geological hazards, a dynamic stability assessment method based on variable weight theory and trapezoidal cloud model is proposed. First, an evaluation index system for slope stability is established following the principles of uniqueness, purposefulness, and scientific validity. Then, to improve the accuracy of subjective constant weights, the intuitionistic fuzzy analytic hierarchy process (IFAHP) is employed to calculate subjective constant weights. Considering the contrast intensity and conflict among indicators, an improved CRITIC method is applied to determine objective constant weights. To balance subjective and objective factors and avoid constant weight imbalance, the optimal comprehensive constant weights are computed based on game theory, effectively reducing bias caused by single weighting methods. Furthermore, to fully account for the influence of indicator state values on their weights, variable weight theory is introduced to dynamically adjust the comprehensive constant weights. Finally, based on the variable weights of evaluation indicators, a trapezoidal cloud model is utilized to construct the slope stability evaluation model, which is validated through an engineering case study. The results indicate that the stability grade of Stage 1 is assessed as basically stable, while Stages 2 and 3 are evaluated as stable. Numerical simulations show the safety factors of the three stages are 1.36, 1.83, and 2.36, respectively, verifying the correctness of the proposed model. The proposed model demonstrates practical engineering value in slope stability assessment and can be referenced for slope reinforcement and hazard prevention in later stages. Full article

The main focus of this paper is to introduce an algorithm that enhances the outcomes of multiple-attribute decision making by harnessing the adaptability of interval-valued intuitionistic fuzzy ($IVIF$) sets ($IVIFS$s). This algorithm utilizes $IVIF$ numbers ($IVIFN$s) to represent attribute values and attribute weights, enabling the decision maker to account for the intricate nuances and uncertainties that are inherent in the decision-making process. We introduce a novel generalized score function ($GSF$) designed to overcome the limitations of previous functions. This function incorporates two parameters, denoted as ${\gamma }_1\mathrm{and}{\gamma }_2({\gamma }_1+{\gamma }_2=1)$ with ${\gamma }_1\in (0,0.5)$. The core concept of this algorithm centers around the computation of the p-distance for each alternative relative to the positive ideal alternative. The p-distance is derived from the p-norm associated with each alternative’s score matrix, providing the decision maker ($DM$) with a tool to rank the available alternatives. Various examples are given to demonstrate the practicality and effectiveness of the proposed algorithm. Additionally, we apply the algorithm to a real event-based multiple-attribute decision-making ($MADM$) problem—the investment company problem—to identify the optimal alternatives through a comparative analysis. Full article

In a dynamic and uncertain environment, maintaining a high level of business process (BP) reliability represents a key long-term objective for organizations. The manufacturing process, as the most critical business process in manufacturing enterprises, is emphasized due to its potential to cause significant disruptions across other BPs if it fails. This paper proposes a two-stage model. In the first stage, failures leading to lean waste are evaluated and ranked using the Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) combined with interval-valued intuitionistic fuzzy numbers (IVIFNs), referred to as IF-TOPSIS. The model is grounded in the Failure Mode and Effect Analysis (FMEA) framework. In the second stage, a modified fuzzy logic system with IVIFN-based rules is applied to determine the risk level of the manufacturing process. This approach is based on the property of symmetry in the decision-making process, ensuring that criteria are treated in a balanced manner and inference rules are applied consistently. A case study based on real-life data demonstrates that the obtained results identify measures that can enhance business strategy and reduce failure rates. Thus, the model is validated and shown to contribute to lean waste reduction. It can be concluded that the proposed methodology provides clear and practical guidance to enterprise management, as well as to all sectors and individuals involved in ensuring a reliable manufacturing process, for defining failure priorities and implementing preventive measures. Full article

The specificity of the business of agro-food companies is that their products have little or no impact on the environment. However, environmental pollution of these products is caused by the use of packaging. Therefore, it is necessary to apply the principles of the circular economy in the business of companies. Applying green packaging that has little or no impact on the environment helps in preserving the environment. Companies usually purchase packaging from suppliers and therefore, it is necessary to choose the right supplier from which to purchase green packaging to support the implementation of the circular economy. The aim of this research is to select a green packaging supplier for company X in order to influence the development of a circular economy in the company’s business. Based on this, the following research question is considered in this paper: how can the selection of a green packaging supplier influence the implementation of a circular economy at company X? The research covers ten criteria used in this selection, with which eight suppliers were observed. Because every decision-making process in the economy is characterized by risk and insecurity that affects the uncertainty in decision-making, an intuitionistic fuzzy set (IFS) was used. Determining the importance of weights was performed directly based on the ratings of the decision-maker (DM) and the steps of the SiWeC (Simple Weight Calculation) method, as well as using the Entropy method. The compromise results of these methods showed that the most important criteria for assessing the life cycle of packaging are transparency and ethics in business. The ranking of suppliers was carried out using the TOPSIS (Technique for Order of Preference by Similarity to Ideal Solution) method and its results showed that supplier 5 is the first choice for establishing long-term cooperation in the procurement of green packaging. Full article

The principles of least effort and the illusion of control may influence the decision-making process. It is challenging for a decision-maker to maintain complete independence when assessing the membership and non-membership degrees of indicators. However, existing neutrosophic sets and q-rung orthopair fuzzy sets assume full independence of such information. In view of this, this paper proposes a new neutrosophic set, namely the q-type semi-dependent neutrosophic set (QTSDNS), based on the classical neutrosophic set, whose membership and non-membership degrees are interrelated. QTSDNS is a generalized form of classical semi-dependent fuzzy sets, such as the intuitionistic neutrosophic set. It contains a regulatory parameter, which allows for decision-makers to flexibly adjust the model. Furthermore, a multi-attribute group decision-making (MAGDM) algorithm is proposed by integrating QTSDNS with evidence theory to solve the supplier selection problem. The algorithm first utilizes QTSDNS to represent the preference information of experts, then employs the q-TSDNWAA (or q-TSDNWGA) operator to aggregate the evaluation information of individual experts. Following the analysis of the mathematical relationship between QTSDNS and evidence theory, evidence theory is used to aggregate the evidence from each expert to obtain the group trust interval. Then, the best supplier is determined using interval number ranking methods. Finally, a numerical example is provided to demonstrate the feasibility of the proposed method. Full article

Trapezoidal-valued intuitionistic fuzzy numbers (TrVIFNs) are the real generalizations of intuitionistic fuzzy numbers, interval-valued intuitionistic fuzzy numbers, and triangular intuitionistic fuzzy numbers, which effectively model real-life problems that consist of imprecise and incomplete data. This study incorporates the Aczel-Alsina aggregation operators (which consist of parameter-based flexibility) for solving any group of decision-making problems modeled in a trapezoidal-valued intuitionistic fuzzy (TrVIF) environment. In this study, we first define new operations on TrVIFNs based on the Aczel-Alsina operations. Secondly, we introduce new trapezoidal-valued intuitionistic fuzzy aggregation operators, such as the TrVIF Aczel-Alsina weighted averaging operator, the TrVIF Aczel-Alsina ordered weighted averaging operator, and the TrVIF Aczel-Alsina hybrid averaging operator, and we discuss their fundamental mathematical properties by examining various theorems. This study also includes a new algorithm named ‘three-stage multi-criteria group decision-making’, where we obtain the criteria weights using the newly proposed TrVIF-MEREC method. Additionally, we introduce a new modified algorithm called TrVIF-WASPAS to solve the multi-criteria decision-making (MCDM) problem in the trapezoidal-valued intuitionistic fuzzy environment. Then, we apply this proposed method to solve a model case study problem involving location selection for a wind power plant project. Then, we discuss the proposed algorithm’s sensitivity analysis by changing the criteria weights concerning different parameter values. Finally, we compare our proposed methods with various existing methods, like some subclasses of TrVIFNs such as IVIFWA, IVIFWG, IVIFEWA, and IVIFEWG, and also with some MCGDM methods of TrVIFNs, such as the Dombi aggregation operator-based method in TrVIFNs and the TrVIF-Topsis method-based MCGDM, to show the efficacy of our proposed algorithm. This study has many advantages, as it consists of a total ordering principle in ranking alternatives in the newly proposed TrVIF-MCGDM techniques and TrVIF-WASPAS MCDM techniques for the first time in the literature. Full article

The theoretical reliability of complex equipment often significantly deviates from real-world performance due to the inherent influence of diverse environmental and operational factors, making scientific reliability evaluation particularly challenging. This study proposes a multi-attribute group decision-making (MAGDM) evaluation framework based on a strict intuitionistic fuzzy distance and an improved TOPSIS approach. First, an improved strict intuitionistic fuzzy distance measure (ISIFDisM) is rigorously developed to overcome the limitations of existing methods, exhibiting high robustness, monotonicity, and discriminability. Second, building upon ISIFDisM, a systematic MAGDM evaluation model is constructed, comprising three key steps: (1) data acquisition through structured questionnaire surveys; (2) attribute weights determined using the entropy weight method; and (3) alternative ranking through normalized priority coefficients derived from intuitionistic fuzzy distance calculations. Third, the proposed framework is applied to a practical case study focused on reliability assessment of ship equipment, enabling effective ranking of various marine engines. Finally, through static comparative analyses and dynamic scenario simulations, the feasibility, robustness, and methodological superiority of the proposed framework are thoroughly validated. Full article

For interval-valued intuitionistic fuzzy sets featuring complementary symmetry in evaluation relations, this paper proposes a novel, complete fuzzy multi-attribute group decision-making (MAGDM) method that optimizes both expert weights and attribute weights. First, an optimization model is constructed to determine expert weights by minimizing the cumulative difference between individual evaluations and the overall consistent evaluations derived from all experts. Second, based on the Technique for Order Preference by Similarity to an Ideal Solution (TOPSIS), the improved closeness index for evaluating each alternative is obtained. Finally, leveraging entropy theory, a concise and interpretable optimization model is established to determine the attribute weight. This weight is then incorporated into the closeness index to enable the ranking of alternatives. Integrating these features, the complete fuzzy MAGDM algorithm is formulated, effectively combining the strengths of subjective and objective weighting approaches. To conclude, the feasibility and effectiveness of the proposed method are thoroughly verified and compared through detailed examination of two real-world cases. Full article

Rough sets and fuzzy sets are two complementary approaches for modeling uncertainty and imprecision. Their integration enables a more comprehensive representation of complex, uncertain systems. However, existing rough fuzzy sets models lack the expressive power to fully capture the interactions among structural uncertainty, cognitive hesitation, and multi-level granular information. To address these limitations, we achieve the following: (1) We propose intuitionistic fuzzy covering rough membership and non-membership degrees based on maximal description and construct a new single-granulation model that more effectively captures both the structural relationships among elements and the semantics of fuzzy information. (2) We further extend the model to a multi-granulation framework by defining optimistic and pessimistic approximation operators and analyzing their properties. Additionally, we propose a neutral multi-granulation covering rough intuitionistic fuzzy sets based on aggregated membership and non-membership degrees. Compared with single-granulation models, the multi-granulation models integrate multiple levels of information, allowing for more fine-grained and robust representations of uncertainty. Finally, a case study on real estate investment was conducted to validate the effectiveness of the proposed models. The results show that our models can more precisely represent uncertainty and granularity in complex data, providing a flexible tool for knowledge representation in decision-making scenarios. Full article

The rapid advancement of artificial intelligence is transforming agriculture by enabling data-driven plant disease monitoring and decision support. Soil-borne mosaic wheat virus (SBWMV) is a soil-transmitted virus disease that poses a serious threat to wheat production across multiple ecological zones. Due to the regional variability in environmental conditions and symptom expressions, accurately evaluating the severity of wheat soil-borne mosaic (WSBM) infections remains a persistent challenge. To address this, the problem is formulated as large-scale group decision-making process (LSGDM), where each planting plot is treated as an independent virtual decision maker, providing its own severity assessments. This modeling approach reflects the spatial heterogeneity of the disease and enables a structured mechanism to reconcile divergent evaluations. First, for each site, field observation of infection symptoms are recorded and represented using intuitionistic fuzzy numbers (IFNs) to capture uncertainty in detection. Second, a Bayesian graph convolutional networks model (Bayesian-GCN) is used to construct a spatial trust propagation mechanism, inferring missing trust values and preserving regional dependencies. Third, an enhanced spectral clustering method is employed to group plots with similar symptoms and assessment behaviors. Fourth, a feedback mechanism is introduced to iteratively adjust plot-level evaluations based on a set of defined agricultural decision indicators sets using a multi-granulation rough set (ADISs-MGRS). Once consensus is reached, final rankings of candidate plots are generated from indicators, providing an interpretable and evidence-based foundation for targeted prevention strategies. By using the WSBM dataset collected in 2017–2018 from Walla Walla Valley, Oregon/Washington State border, the United States of America, and performing data augmentation for validation, along with comparative experiments and sensitivity analysis, this study demonstrates that the AI-driven LSGDM model integrating enhanced spectral clustering and ADISs-MGRS feedback mechanisms outperforms traditional models in terms of consensus efficiency and decision robustness. This provides valuable support for multi-party decision making in complex agricultural contexts. Full article

The development of technology has influenced agricultural production and the establishment of the Agriculture 4.0 system in practice. This research is focused on the selection of equipment and machinery suppliers for the needs of the MAMEX Company. When selecting suppliers, an approach based on the application of an intuitionistic fuzzy set for decision-making was used. This approach allows the uncertainty present in decision-making to be incorporated, considered, and, hopefully, reduced in order to make a final decision on which of the observed suppliers is the most suitable for this company. Ten criteria were used that enable the application of sustainability in the supply chain. Eight local suppliers of equipment and machinery were observed with these criteria. The results obtained by applying the SWARA (Step-wise Weight Assessment Ratio Analysis) method showed that the most important criterion for selecting suppliers is the reliability and quality of equipment and machinery, while the results of the CORASO (COmpromise Ranking from Alternative Solutions) method showed that the SUP2 supplier is the best choice for establishing partnership relations with the MAMEX company. This supplier should help the MAMEX company improve its business and achieve better results in the market. The contribution of this research is to improve the application of intuitionistic fuzzy sets in decision-making, and to emphasize the importance of equipment and machinery in agricultural production in the Agriculture 4.0 system. Full article

Hydrogen is a potential source of imminent clean energy in the future, with its transportation playing a crucial role in allowing large-scale deployment. The challenge lies in selecting an effective, sustainable, and scalable transportation alternative. This study develops a multi-criteria decision-making (MCDM) framework based on the intuitionistic fuzzy analytic hierarchy process (IF-AHP) to evaluate land-based hydrogen transportation alternatives across Canada. The framework includes uncertainty and decision-maker hesitation through the application of triangular intuitionistic fuzzy numbers (TIFNs). Seven factors, their subsequent thirty-three subfactors, and three alternatives to hydrogen transportation were identified through a literature review. Pairwise comparison was aggregated among factors, subfactors, and alternatives from three decision makers using an intuitionistic fuzzy weighted average, and priority weights were computed using entropy-based weight. The results show that safety and economic efficiency emerged as the most influential factors in the evaluation of hydrogen transportation alternatives, followed by environmental impact, security, and social impact and public health in ascending order. Among the alternatives, tube truck transport obtained the highest overall weight (0.3551), followed by pipelines (0.3272) and rail lines (0.3251). The findings suggest that the tube ruck is currently the most feasible transport option for land-based hydrogen distribution that aims to provide a transition of Canada’s energy mix. Full article

An artificial neural network (ANN)-based decision support system model, which aggregates intuitionistic fuzzy matrix data using a recently introduced operator, is developed in this work. Several desirable features related to distance measures of aggregation operators and artificial neural networks, including the backpropagation method, are investigated to support the application of the proposed methodologies to multiple attribute group decision-making (MAGDM) problems using intuitionistic fuzzy information. A novel and enhanced aggregation operator—the Hamming–Intuitionistic Fuzzy Power Generalized Weighted Averaging (H-IFPGWA) operator—is proposed for weight determination in MAGDM situations. Numerical examples are provided, and various ranking techniques are used to demonstrate the effectiveness of the suggested strategy. Subsequently, an identical numerical example is solved without bias using the ANN backpropagation approach. Additionally, a novel algorithm is created to address MAGDM problems using the proposed backpropagation model in an unbiased manner. Several defuzzification operators are applied to solve the numerical problems, and the efficacy of the solutions is compared. For MAGDM situations, the novel approach works better than the previous ANN approaches. Full article