Search Results (455)

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

To offer a viewpoint on convexity and connectedness inside intuitionistic fuzzy graphs (IFGs), the paper is devoted to the study of intuitionistic fuzzy geodetic convexity. The paper introduces an algorithm for precise identification and characterization of geodetic pathways in IFGs, supported by a Python program. Various properties of IF-geodetic convex sets such as IF-internal and IF-boundary vertices are obtained. Furthermore, this work introduces and characterizes the concepts of geodetic IF-cover, geodetic IF-basis, and geodetic IF-number. Additionally, the study develops the IF-geodetic Wiener index. The scope of the work explores the application of IF-geodetic cover in wireless mesh networks, focusing on the identification of gateway nodes, where symmetry in connectivity patterns enhances network efficiency. A practical implementation of the IF-geodetic Wiener index method in global human trading analysis underscores the real-world implications of the developed concepts, where the efficiency and interpretability of fuzzy geodetic measures are improved by symmetry in network topologies and trade patterns. 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

Instead of measuring the distance between two points with a positive real number, determining the degree to which the distance between these two points is close, not close, or uncertain allows for more detailed measurement. Recently, researchers have overcome this grading problem by using probability distribution functions, along with fuzzy, intuitionistic fuzzy, and neutrosophic sets. This study pioneers neutrosophic quadruple metric spaces as a powerful new tool for quantifying distances under complex, multi-dimensional uncertainty. It provides a comprehensive mathematical structure, including topology, convergence theory, and completeness, and handles both symmetric and asymmetric cases, generalising previous neutrosophic metric results. For this purpose, neutrosophic quadruple metric spaces were derived from neutrosophic metric spaces in order to better model situations involving uncertainty. Also, we generalised the findings obtained with the neutrosophic metric to the quadruple neutrosophic metric. 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

Heightened environmental policies along with the necessity for a resilient supply chain (SC) network have driven companies to adopt circular economy (CE) strategies. Although CE initiatives have shown significant effects on SC operations, the advent of digital technologies is encouraging businesses to digitize their SCs. However, the relationship connecting SC digitalization with CE practices remains underexplored. This study presents a novel framework that bridges the gap between CE principles and SC digitalization by identifying and prioritizing critical success factors (CSFs) for implementing SC4.0 in a circular economy context. We conducted a comprehensive literature review to determine CSFs and approaches relevant to Supply Chain 4.0 (SC4.0), and expert insights were gathered using the Delphi method for final validation. To capture the complex interrelationships among these factors, the study employed a combined approach using Intuitionistic Fuzzy Set (IFS), Analytic Network Process (ANP), decision-making trial and evaluation laboratory, and the Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) techniques to assess the CSFs and strategies. The findings highlight that an intelligent work environment, performance tracking, and data accuracy and pertinence are the top three critical CSFs for SC digitalization. Furthermore, enhancing analytical capabilities, optimizing processes through data-driven methods, and developing a unified digital platform were identified as key strategies for transitioning to SC4.0. By embedding CE principles into the evaluation of digital SC transformation, this research contributes a novel interdisciplinary perspective and offers practical guidance for industries aiming to achieve both digital resilience and environmental sustainability. The study delivers a comprehensive evaluation of CSFs for SC4.0, applicable to a variety of sectors aiming for digital and sustainable transformation. Full article

Intuitionistic fuzzy sets (IFSs), proposed in 1983, are one of the most viable and widely explored extensions of Zadeh’s fuzzy sets. In the decade following their introduction, they were extended to interval-valued IFSs (IVIFSs), temporal IFSs, IFSs of the second type (incorrectly called “Pythagorean fuzzy sets” by some authors) IFSs of n-th type, and IFSs over different universes. For each of these extensions, at least one geometrical interpretation has been defined, and for IVIFSs, at least seven different interpretations are known. In the present paper, revisiting some existing results on IVIFSs, some necessary modifications, additions, and corrections to the planar and spatial geometrical interpretations are introduced here for the first time. A new, eighth, geometrical interpretation of IVIFSs is proposed. A basic logic operation and two modal operators are illustrated and a comparison is made between the planar and the new “two-rods” geometrical interpretations of identical IVIFS elements. Finally, a new operator over IVIFSs is proposed for the first time, some of its properties are proven, and its geometrical interpretations are described. 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

Complex Intuitionistic Fuzzy Sets (CIFSs) are an advanced form of intuitionistic fuzzy sets that utilize complex numbers to effectively manage uncertainty and hesitation in multi-criteria decision making (MCDM). This paper introduces the Shapley Choquet integral (SCI), which is a powerful tool for integrating information from various sources while considering the importance and interactions among criteria. To address ambiguity and inconsistency, we apply the Aczel–Alsina (AA) t-norm and t-conorm, which offer greater flexibility than traditional norms. We propose two novel aggregation operators within the CIFS framework using the Aczel–Alsina Generalized Shapley Choquet Integral (AAGSCI): the Complex Intuitionistic Fuzzy Aczel–Alsina Weighted Average Generalized Shapley Choquet Integral (CIFAAWAGSCI) and the Complex Intuitionistic Fuzzy Aczel–Alsina Weighted Geometric Generalized Shapley Choquet Integral (CIFAAWGGSCI), along with their special cases. The properties of these operators, including idempotency, boundedness, and monotonicity, are thoroughly investigated. These operators are designed to evaluate complex and asymmetric information in real-life problems. A case study on selecting the optimal bridge design based on structural and aesthetic criteria demonstrates the applicability of the proposed method. Our results indicate that the proposed method yields more consistent and reliable outcomes compared to existing approaches. Full article

Natural disasters and emergencies continue to increase in frequency and severity worldwide, necessitating robust emergency management (EM) systems and evaluation methodologies. This study addresses critical gaps in current emergency response capacity (ERC) evaluation frameworks by developing a comprehensive quantitative decision-making model to assess ERC more effectively. This research constructs a systematic ERC assessment framework based on the four phases of the disaster management cycle (DMC): prevention, preparedness, response, and recovery. The methodology employs multi-criteria decision analysis to evaluate ERC using three distinct information representation environments: intuitionistic fuzzy (IF) sets, linguistic variables (LV), and a novel mixed IF-LV environment. For each environment, we derive appropriate aggregation operators, weight determination methods, and information fusion mechanisms. The proposed model was empirically validated through a case application to emergency plan selection in Shenzhen, China. A statistical analysis of results demonstrates high consistency across all three decision environments (IF, LV, and mixed IF-LV), confirming the model’s robustness and reliability. A sensitivity analysis of key parameters further validates the model’s stability. Results indicate that the proposed decision-making approach provides significant value for EM by enabling more objective, comprehensive, and flexible ERC assessment. The indicator system and evaluation methodology offer decision-makers (DMs) tools to quantitatively analyze ERC using various information expressions, accommodating both subjective judgments and objective metrics. This framework represents an important advancement in emergency preparedness assessment, supporting more informed decision-making in emergency planning and response capabilities. Full article

Aiming at the limitations of existing multisensor fault diagnosis methods for rolling bearings in real industrial scenarios, this paper proposes an innovative intuitionistic fuzzy weighted least squares twin support higher-order tensor machine (IFW-LSTSHTM) model, which realizes a breakthrough in the noise robustness, adaptability to the working conditions, and the class imbalance processing capability. First, the multimodal feature tensor is constructed: the fourier synchro-squeezed transform is used to convert the multisensor time-domain signals into time–frequency images, and then the tensor is reconstructed to retain the three-dimensional structural information of the sensor coupling relationship and time–frequency features. The nonlinear feature mapping strategy combined with Tucker decomposition effectively maintains the high-order correlation of the feature tensor. Second, the adaptive sample-weighting mechanism is developed: an intuitionistic fuzzy membership score assignment scheme with global–local information fusion is proposed. At the global level, the class contribution is assessed based on the relative position of the samples to the classification boundary; at the local level, the topological structural features of the sample distribution are captured by K-nearest neighbor analysis; this mechanism significantly improves the recognition of noisy samples and the handling of class-imbalanced data. Finally, a dual hyperplane classifier is constructed in tensor space: a structural risk regularization term is introduced to enhance the model generalization ability and a dynamic penalty factor is set to set adaptive weights for different categories. A linear equation system solving strategy is adopted: the nonparallel hyperplane optimization is converted into matrix operations to improve the computational efficiency. The extensive experimental results on the two rolling bearing datasets have verified that the proposed method outperforms existing solutions in diagnostic accuracy and stability. Full article

Influence graphs are essential tools for analyzing interactions and relationships in social networks. However, real-world networks often involve uncertainty due to incomplete, vague, or dynamic information. The structure of influence graphs often exhibits natural symmetries, which play a crucial role in optimizing covering and matching strategies by decreasing redundancy and enhancing efficiency. Traditional influence graph models struggle to address such complexities. To address this gap, we present the novel concepts of covering and matching in intuitionistic fuzzy influence graphs (IFIGs) for modeling academic social networks. These graphs incorporate degrees of membership and non-membership to better reflect uncertainty in influence patterns. Thus, the main aim of this study is to initiate the concepts of covering and matching within the IFIG paradigm and provide its application in social networks. Initially, we establish some basic terms related to covering and matching with illustrative examples. We also investigate complete and complete bipartite IFIGs. To verify the practicality of this study, student interactions across subjects are analyzed using strong paths and strong independent sets. The proposed model is then evaluated using the TOPSIS method to rank participants based on their influence. Moreover, a comparative study is conducted to demonstrate that the proposed model not only handles uncertainty effectively but also performs better than the existing approaches. Full article