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This paper investigates the potential impact of green fuel adoption on the Saudi Arabian maritime industry using fuzzy set theory. We will examine the cost-profitability of green fuel adoption and its implications for the Saudi Arabian economy. By employing fuzzy set theory, we can more accurately predict and analyze the potential impacts of green shipping. This paper will present case studies from the shipping industry that have successfully used fuzzy set theory to optimize green fuel usage and profitability. Moreover, this paper will focus on the use of green fuels as a way of reducing the environmental impacts of the shipping industry in Saudi Arabia. This paper will explore the impact of fueling ships with green fuel in Saudi Arabia and use fuzzy set theory to analyze the cost-profitability of this action. [ABSTRACT FROM AUTHOR]

The design for large-scale offshore systems like renewable energy systems as well as ship structures represents the key factor for the investigation and application of such devices. The existing guide for design schemes of offshore systems cannot cover novel large-scale design demand for recent offshore systems, as a result of the fast-growing scale of offshore systems but the late update of guides. To this end, this paper proposes a novel risk estimation approach of alternative design schemes for large-scale offshore systems as a basis to support the design scheme determinations. Initially, the risks of design schemes are analyzed by fault tree analysis. Subsequently, Bayesian networks and fuzzy sets are employed to calculate the reliability of alternative designs that comply with, or deviate from, the existing guides. The risk level of alternative designs is assessed to ensure the better performance of alternative design schemes in terms of safety. The Bayesian network approach proposed also accretions the weak links in the alternative designs. The results of this paper contribute to enhancing the survivability of offshore systems, such as renewable energy systems as well as ship structures. [ABSTRACT FROM AUTHOR]

With the rapid development of China's economy and society, the innovation of grassroots social governance has become increasingly important. This paper constructs 35 grassroots social governance innovation samples. Using the TOE theoretical framework and a fuzzy set qualitative comparative analysis (fsQCA), this paper analyzes the joint effects and interactive relationships of multiple factors on grassroots social governance innovation performance from three dimensions: technology, organization, and environment. The research reveals that internal environmental openness is a necessary condition for achieving high innovation performance in grassroots social governance, and proposes four grouping models that affect the performance of grassroots social governance innovation. This paper explores the inner logic of grassroots social governance innovation from a histological perspective, and on this basis proposes an adaptive path to enhance the performance of grassroots social governance innovation. [ABSTRACT FROM AUTHOR]

Relieving the emotions of the public through government response is an important part of government emergency management. How governments respond in different situations can avoid stimulating negative emotions during emergencies? This paper analyzes the problem from the perspective of configuration; that is, this paper explores the combined effects of multiple factors on emotions. We construct the theoretical framework "Situation-Responder-Content" from situation, responder and response content, and use the government microblogs (n= 1517) from 23 major production accidents in China for the discussion with the use of fuzzy set qualitative comparison analysis (fsQCA). According to the results, the effective response types of different agencies in emergencies are summarized. Local authorities can respond in ways that include "Measures type" and "Measures-Emotion type". Functional agencies can respond through "Measures type", "Measures-Emotion type" and "Government feature-Driven" type. This study emphasizes that government response in emergencies is a systematic process. Responsive agencies need to release effective information on the basis of fully considering the situation and other factors. Configuration analysis should also be an important direction in government response research, which is helpful to the practice of government response in emergencies. [ABSTRACT FROM AUTHOR]

Infrastructure networks are critical components of contemporary society, and numerous approaches have been suggested for the selection of strategies to protect these networks. However, for uncertain environments, research on attack and defense game models for infrastructure networks is limited. Therefore, after reviewing the existing approaches, a method based on interval-valued intuitionistic fuzzy set (IVIFS) theory is proposed for attack and defense games in critical infrastructure networks. First, we present the process of constructing the game model proposed in this paper, which mainly includes the formulation of the cost model, the strategies, and the method of generating IVIFS payoffs. Next, the Nash equilibria of the game are identified by a pair of nonlinear programming models based on IVIFS theory. Finally, experiments are conducted on a target scale-free network, and an investigation into the variation patterns of the Nash equilibria under different circumstances is also conducted. We provide explanations for these variation patterns by considering payoffs from the perspective of mathematical programming models. Furthermore, we find that compared to the existing attack and defense game model with crisp payoffs, the model proposed in this paper leads to superior Nash equilibria. Our work is a preliminary attempt to analyse attack and defense games for infrastructure networks based on IVIFS theory, providing a method for assessing payoffs in uncertain environments for the attacker and defender. This topic deserves further study. [ABSTRACT FROM AUTHOR]

It is widely known that symmetry does exist in management systems, such as economics, management, and even daily life. In addition, effective and qualified decision-making methods can enhance the performance and symmetry of management systems. Hence, this paper focuses on a decision-making method. Linguistic interval-valued q-rung orthopair fuzzy sets (LIVq-ROFSs) have recently been proposed as being effective in describing decision-makers' evaluation values in complex situations. This paper proposes a novel multi-attribute group decision-making (MAGDM) method with LIVq-ROFSs to handle realistic decision-making problems. The main contributions of this study are three-fold. First, a new method for determining the weight information of attributes based on decision makers' evaluation values is proposed. Second, the classical TODIM is extended into LIVq-ROFSs and a new decision-making method is proposed. Third, our proposed MAGDM method is applied to a real decision-making problem to reveal its effectiveness. [ABSTRACT FROM AUTHOR]

Fuzzy sets possess remarkable abilities in expressing and handling information uncertainty, which has resulted in their widespread application in various fields. Nevertheless, distance measurement between IFSs for quantitating their differences and levels of differentiation has remained an open problem that deserves attention. Despite the development of various metrics, they either lack intuitive insight or do not satisfy the axioms of distance measurement, leading to counterintuitive results. To address these issues, this paper proposed a distance measurement method based on Clark divergence, which satisfies the distance measurement axioms and exhibits nonlinearity. Numerical examples demonstrate that our method effectively distinguishes different indicators, yielding more reasonable results. Moreover, when comparing relative differences of the results, our method demonstrated superior adaptability to complex environmental decision-making, providing decision-makers with more accurate and confidential judgments. In our numerical and pattern classification application tests, we achieve an accuracy of 98%, a 40% increase in computing time efficiency and a relative diversity improvement of 35%. The pattern classification algorithm designed in this paper will offer a promising solution to inference problems. [ABSTRACT FROM AUTHOR]

China is at a critical moment of transforming high-speed development to high-quality development, and it is significant to improve the efficiency of green technological innovation. In this paper, under the perspective of two-stage innovation value chain, we construct the evaluation index system of green technology innovation efficiency, adopt the super efficiency SBM model to measure the green technology innovation efficiency of China's high-tech industries, and based on the results obtained, we assume the fuzzy set qualitative comparative analysis method (fs-QCA) based on the group theory to explore the complex causal mechanism and grouping paths of the interaction between enterprises, government and market that affects the green technology innovation efficiency Mechanism and group path. The study results show that (1) enterprise, government, and market are not necessary conditions to influence the efficiency of green technological innovation, and even if a particular party plays a central role, it needs the assistance of other parties. (2) The improvement of green technological innovation efficiency requires the interaction of enterprises, government, and market, and even if any party does not have the core conditions, it can still produce high green technological innovation efficiency. (3) The path of the "innovative compensation" effect is identified, which indicates that enterprises will generate a high level of green innovation efficiency under sufficient investment brought about by the enterprise scale effect and matched with a good level of economic development. (4) The market economy-led pathway suggests that when the market economy is highly developed, firms do not need environmental regulation and government support to generate efficient levels of green technological innovation. [ABSTRACT FROM AUTHOR]

The rapid development of renewable energy presents challenges to the security and stability of power systems. Aiming at addressing the power system scheduling problem with load demand and wind power uncertainty, this paper proposes the establishment of different error fuzzy sets based on the Wasserstein probability distance to describe the uncertainties of load and wind power separately. Based on these Wasserstein fuzzy sets, a distributed robust chance-constrained scheduling model was established. In addition, the scheduling model was transformed into a linear programming problem through affine transformation and CVaR approximation. The simplex method and an improved differential evolution algorithm were used to solve the model. Finally, the model and algorithm proposed in this paper were applied to model and solve the economic scheduling problem for the IEEE 6-node system with a wind farm. The results show that the proposed method has better optimization performance than the traditional method. [ABSTRACT FROM AUTHOR]

The Circular Economy (CE) is receiving more attention, especially in Industry 4.0 (I4.0). In the face of several ambiguous and uncertain information, fuzzy techniques based on Fuzzy Set Theory (FST) are essential for developing CE strategies. This paper uses bibliometric methods to analyze the characteristics of the authors, nations/regions, institutions of the literature of FST and CE, and the collaborations relations between them, and then summarize the literature on fuzzy techniques in the CE and identify the specific role that FST can play in each stage of CE, its primary effects on the CE's pre-preparation stage, design and production stage, and recycling and reuse stage. Meanwhile, the paper explores the advantages of I4.0 technologies for CE and analyzes the research on the role of fuzzy techniques based on FST for CE and I4.0 technologies. Last but not least, this paper is concluded by summarizing the knowledge gained from the bibliometric and content analyses of the literature and suggesting further research directions of investigation. This research will draw attention to FST's contribution and encourage its advancement in CE and I4.0 technologies. [ABSTRACT FROM AUTHOR]

Large-scale group decision-making (LSGDM) involves aggregating the opinions of participating decision-makers into collective opinions and selecting optimal solutions, addressing challenges such as a large number of participants, significant scale, and a low consensus. In real-world scenarios of LSGDM, various challenges are often encountered due to factors such as fuzzy uncertainties in decision information, the large size of decision groups, and the diverse backgrounds of participants. This paper introduces a dual fine-tuning-based LSGDM method using an online review. Initially, the sentiment analysis is conducted on online review data, and the identified sentiment words are graded and quantified into a fuzzy data set to understand the emotional tendencies of the text. Then, the Louvain algorithm is used to cluster the decision-makers. Meanwhile, a method combining Euclidean distances with Wasserstein distances is introduced to accurately measure data similarities and improve clustering performances. During the consensus-reaching process (CRP), a two-stage approach is employed to adjust the scores: to begin with, by refining the scores of the decision representatives via minor-scale group adjustments to generate a score matrix. Then, by identifying the scores corresponding to the minimum consensus level in the matrix for adjustment. Subsequently, the final adjusted score matrix is integrated with the prospect–regret theory to derive the comprehensive brand scores and rankings. Ultimately, the practicality and efficiency of the proposed model are demonstrated using a case study focused on the purchase of solar lamps. In summary, not only does the model effectively extract the online review data and enhance decision efficiency via clustering, but the dual fine-tuning mechanism in the model to improve consensus attainment also reduces the number of adjustment rounds and avoids multiple cycles without achieving the consensus. [ABSTRACT FROM AUTHOR]

When information is incomplete or uncertain, Fermatean hesitant fuzzy sets (FHFSs) can provide more information to help decision-makers deal with more complex problems. Typically, determining attribute weights assumes that each attribute has a fixed influence. Introducing probability information can enable one to consider the stochastic nature of evaluation data and better quantify the importance of the attributes. To aggregate data by considering the location and importance degrees of each attribute, this paper develops a Fermatean hesitant fuzzy multi-attribute decision-making (MADM) method with probabilistic information and an ordered weighted averaging (OWA) method. The OWA method combines the concepts of weights and sorting to sort and weigh average property values based on those weights. Therefore, this novel approach assigns weights based on the decision-maker's preferences and introduces probabilities to assess attribute importance under specific circumstances, thereby broadening the scope of information expression. Then, this paper presents four probabilistic aggregation operators under the Fermatean hesitant fuzzy environment, including the Fermatean hesitant fuzzy probabilistic ordered weighted averaging/geometric (FHFPOWA/FHFPOWG) operators and the generalized Fermatean hesitant fuzzy probabilistic ordered weighted averaging/geometric (GFHFPOWA/GFHFPOWG) operators. These new operators are designed to quantify the importance of attributes and characterize the attitudes of decision-makers using a probabilistic and weighted vector. Then, a MADM method based on these proposed operators is developed. Finally, an illustrative example of selecting the best new retail enterprise demonstrates the effectiveness and practicality of the method. [ABSTRACT FROM AUTHOR]

Based on the configuration theory, this paper discusses the multiple concurrent causes and causal complex mechanisms affecting the performance differences among different new farmers. Using the fuzzy set qualitative comparative analysis method, taking 40 cases of CCTV’s “ZHI FU JING” column as samples, the paper analyzes the necessary conditions for new farmers to produce high performance by the anthefactory-variable configuration composed of human capital, social capital, psychological capital, entrepreneurial learning and entrepreneurial opportunity identification. The results show that: (1) high human capital is the necessary core condition for new farmers to produce high entrepreneurial performance, lack of high entrepreneurial learning and lack of high entrepreneurial opportunity identification is the core necessary condition for low entrepreneurial performance; (2) the driving mechanism of new farmers’ high entrepreneurial performance is divided into three paths, and the driving mechanism of new farmers’ low entrepreneurial performance is divided into two paths; and (3) the ways of inhibiting new farmers’ performance and promoting their performance are asymmetrical. [ABSTRACT FROM AUTHOR]

The integration of Distributed Energy Resources utilizing Renewable Energy Sources, Energy Storage Systems, and Information and Communication Technologies is transforming traditional energy systems into adaptable, flexible, and sustainable systems, with the Smart Grid concept playing a pivotal role. This paper surveys intelligent techniques and methods applied in various markets and applications, particularly focusing on their potential adaptation for negotiation processes in Smart Grid contexts. The negotiation mechanisms, crucial for prosumers who engage in real-time transactions, are analyzed with a focus on fuzzy logic tools, specifically q-Rung Orthopair Fuzzy Sets. These tools are evaluated for their capability to handle negotiation tasks and Multi-Criteria Decision-Making problems. The paper proposes a negotiation schema for healthcare buildings, especially hospitals, given their significant environmental impact, providing insight for future research. [ABSTRACT FROM AUTHOR]

Featured Application: The research in this paper can provide a feasible technical means for the assembly sequence optimization of aviation reducers with complex structures, effectively promote the progress of the complex assembly sequence optimization technology of aviation reducers, and realize the comprehensive evaluation of the overall assembly quality and performance index of aviation reducer products. It can be applied to the assembly control of tanks, armored vehicles, ships, and other complex equipment to improve their assembly quality. An assembly sequence evaluation is one of the most important research directions of assembly sequence planning (ASP) for complex mechanical transmission products. Currently, aviation reducers lack a multi-perspective and multi-level evaluation of their assembly sequence. The existing evaluation indicators vary. The evaluation methods have low effectiveness and poor practicability. Therefore, a comprehensive multidimensional evaluation method for complex assembly sequences is proposed in this paper. A multidimensional comprehensive evaluation of the overall assembly quality and performance indices of aviation reducer products is realized. Firstly, the main factors affecting assembly sequence planning are considered: the attributes of the basic unit parts and the cost control of the assembly process. An evaluation index system of assembly sequence planning based on the two dimensions of assembly cost and ontology is constructed. Then, according to the multidimensional evaluation index, fuzzy evaluation theory is used to establish a fuzzy set and a matrix for each dimensional evaluation index. The index weight is divided. A comprehensive evaluation model and the function of each dimension are established. After a comprehensive evaluation, the multidimensional assembly sequence evaluation method for aviation reducers is formed. Finally, the method is applied to the assembly process of the primary reducer of a helicopter's main reducer, and a comprehensive evaluation of its assembly sequence scheme is completed to verify the feasibility of the proposed method. This article constructs a complex assembly sequence evaluation method that includes 12 evaluation indicators, improves the assembly sequence planning evaluation index system of aviation reducers, and can effectively promote the progress of optimization technology for complex assembly sequences of aviation reducers. [ABSTRACT FROM AUTHOR]

Multispectral image registration is the process of aligning the spatial regions of two images with different distributions. One of the main challenges it faces is to resolve the severe inconsistencies between the reference and target images. This paper presents a novel multispectral image registration network, Multi-scale Intuitionistic Fuzzy Set Feature-guided Registration Network (IFSrNet), to address multispectral image registration. IFSrNet generates pseudo-infrared images from visible images using Cycle Generative Adversarial Network (CycleGAN), which is equipped with a multi-head attention module. An end-to-end registration network encodes the input multispectral images with intuitionistic fuzzification, which employs an improved feature descriptor—Intuitionistic Fuzzy Set–Scale-Invariant Feature Transform (IFS-SIFT)—to guide its operation. The results of the image registration will be presented in a direct output. For this task we have also designed specialised loss functions. The results of the experiment demonstrate that IFSrNet outperforms existing registration methods in the Visible–IR dataset. IFSrNet has the potential to be employed as a novel image-to-image translation paradigm. [ABSTRACT FROM AUTHOR]

Convolutional Neural Networks (CNNs) are a kind of artificial neural network designed to extract features and find out patterns for tasks such as segmentation, recognizing objects, and drawing up classification. Within a CNNs architecture, pooling operations are used until the number of parameters and the computational complexity are reduced. Numerous papers have focused on investigating the impact of pooling on the performance of Convolutional Neural Networks (CNNs), leading to the development of various pooling models. Recently, a fuzzy pooling operation based on type-1 fuzzy sets was introduced to cope with the local imprecision of the feature maps. However, in fuzzy set theory, it is not always accurate to assume that the degree of non-membership of an element in a fuzzy set is simply the complement of the degree of membership. This is due to the potential existence of a hesitation degree, which implies a certain level of uncertainty. To overcome this limitation, intuitionistic fuzzy sets (IFS) were introduced to incorporate the concept of a degree of hesitation. In this paper, we introduce a novel pooling operation based on intuitionistic fuzzy sets to incorporate the degree of hesitation heretofore neglected by a fuzzy pooling operation based on classical fuzzy sets, and we investigate its performance in the context of image classification. Intuitionistic pooling is performed in four steps: bifuzzification (by the transformation of data through the use of membership and non-membership maps), first aggregation (through the transformation of the IFS into a standard fuzzy set, second aggregation (through the transformation and use of a sum operator), and the defuzzification of feature map neighborhoods by using a max operator. IFS pooling is used for the construction of an intuitionistic pooling layer that can be applied as a drop-in replacement for the current, fuzzy (type-1) and crisp, pooling layers of CNN architectures. Various experiments involving multiple datasets demonstrate that an IFS-based pooling can enhance the classification performance of a CNN. A benchmarking study reveals that this significantly outperforms even the most recent pooling models, especially in stochastic environments. [ABSTRACT FROM AUTHOR]

A new methodology for solving the fuzzy multiobjective optimization problems is proposed in this paper by considering the fusion of cooperative game theory and genetic algorithm. The original fuzzy multiobjective optimization problem needs to be transformed into a scalar optimization problem, which is a conventional optimization problem. Usually, the assignments of suitable coefficients to the corresponding scalar optimization problem are subjectively determined by the decision makers. However, these assignments may cause some biases by their subjectivity. Therefore, this paper proposes a mechanical procedure to avoid this subjective biases. We are going to formulate a cooperative game using the α -level functions of the multiple fuzzy objective functions. Under this setting, the suitable coefficients can be determined mechanically by involving the core values of the cooperative game, which is formulated using the multiple fuzzy objective functions. We shall prove that the optimal solutions of the transformed scalar optimization problem are indeed the nondominated solutions of fuzzy multiobjective optimization problem. Since the core-nondominated solutions will depend on the coefficients that are determined by the core values of cooperative game, there will be a lot of core-nondominated solutions that will also depend on the corresponding coefficients. In order to obtain the best core-nondominated solution, we shall invoke the genetic algorithms by evolving the coefficients. [ABSTRACT FROM AUTHOR]

This paper investigates the complex causal relationships between various types of environmental regulatory instruments (ERI) and agri-firms' technological innovation employing fuzzy set qualitative comparative analysis (fsQCA). The study finds a well-designed set of ERI can promote technological innovation in agribusiness; control-command ERI cannot promote technological innovation in agribusiness solely, market-incentivized ERI is indispensable in promoting firms' innovation performance, implicit ERI plays an important role in promoting firms' innovation and voluntary ERI does not play a significant role in promoting firms' technological innovation. The government should coordinate among various types of ERI and improve the design of ERI to achieve a win-win situation for both economic and environmental performance in the agriculture sector. [ABSTRACT FROM AUTHOR]

This paper investigates the performance of a two-stage multi-criteria decision-making procedure for order scheduling problems. These problems are represented by a novel nonlinear mixed integer program. Hybridizations of three Multi-Objective Evolutionary Algorithms (MOEAs) based on dominance relations are studied and compared to solve small, medium, and large instances of the joint order batching and picking problem in storage systems with multiple blocks of two and three dimensions. The performance of these methods is compared using a set of well-known metrics and running an extensive battery of simulations based on a methodology widely used in the literature. The main contributions of this paper are (1) the hybridization of MOEAs to deal efficiently with the combination of orders in one or several picking tours, scheduling them for each picker, and (2) a multi-criteria approach to scheduling multiple picking teams for each wave of orders. Based on the experimental results obtained, it can be stated that, in environments with a large number of different items and orders with high variability in volume, the proposed approach can significantly reduce operating costs while allowing the decision-maker to anticipate the positioning of orders in the dispatch area. [ABSTRACT FROM AUTHOR]

Many papers have been devoted to applying fuzzy sets to algebraic structures. In this paper, based on ideals, we investigate residuated lattices from fuzzy set theory, lattice theory, and coding theory points of view, and some applications of fuzzy sets in residuated lattices are presented. Since ideals are important concepts in the theory of algebraic structures used for formal fuzzy logic, first, we investigate the lattice of fuzzy ideals in residuated lattices and study some connections between fuzzy sets associated to ideals and Hadamard codes. Finally, we present applications of fuzzy sets in coding theory. [ABSTRACT FROM AUTHOR]

Spatial and temporal uncertainties are found in data for many critical applications. This paper describes the use of interval-based representations of some spatial and temporal information. Uncertainties in the information can arise from multiple sources in which degrees of support and non-support occur in evaluations. This motivates the use of intuitionistic fuzzy sets to permit the use of the positive and negative memberships to capture these uncertainties. The interval representations will include both simple and complex or nested intervals. The relationships between intervals such as overlapping, containing, etc. are then developed for both the simple and complex intervals. Such relationships are required to support the aggregation approaches of the interval information. Both averaging and merging approaches to interval aggregation are then developed. Furthermore, potential techniques for the associated aggregation of the interval intuitionistic fuzzy memberships are provided. A motivating example of maritime depth data required for safe navigation is used to illustrate the approach. Finally, some potential future developments are discussed. [ABSTRACT FROM AUTHOR]

This document is a special issue of the journal Nonlinear Studies, featuring interdisciplinary perspectives in applied mathematics. It includes articles on consumer behavior, diffusion of innovation, numerical methods, game theory, and optimization, covering domains such as engineering, management, and physics. The papers have undergone peer review and offer original and high-quality research. The document compiles research contributions on reliability analysis, mathematical modeling, differential equations, and optimization problems, with references for further exploration. The authors express gratitude to the contributors and reviewers for their valuable contributions. [Extracted from the article]

This paper reflects the results of research analyzing models of multi-attribute decision-making based on fuzzy preference relations. Questions of constructing the corresponding multi-attribute models to deal with quantitative information concomitantly with qualitative information based on experts' knowledge are considered. Human preferences may be represented within the fuzzy preference relations and by applying diverse other preference formats. Considering this, so-called transformation functions reduce any preference format to fuzzy preference relations. This paper's results can be applied independently or as part of a general approach to solving a wide class of problems with fuzzy coefficients, as well as within the framework of a general scheme of multi-criteria decision-making under conditions of uncertainty. The considered techniques for fuzzy preference modeling are directed at assessing, comparing, choosing, prioritizing, and/or ordering alternatives. These techniques have served to develop a computing system for multi-attribute decision-making. It has been implemented in the C# programming language, utilizing the ".NET" framework. The computing system allows one to represent decision-makers' preferences in one of five preference formats. These formats and quantitative estimates are reduced to nonreciprocal fuzzy preference relations, providing homogeneous preference information for decision procedures. This paper's results have a general character and were applied to analyze power engineering problems. [ABSTRACT FROM AUTHOR]

Motivated by the fact that the fuzzy quasi-normed space provides a suitable framework for complexity analysis and has important roles in discussing some questions in theoretical computer science, this paper aims to study the nearest point problems in fuzzy quasi-normed spaces. First, by using the theory of dual space and the separation theorem of convex sets, the properties of the fuzzy distance from a point to a set in a fuzzy quasi-normed space are studied comprehensively. Second, more properties of the nearest point are given, and the existence, uniqueness, characterizations, and qualitative properties of the nearest points are obtained. The results obtained in this paper are of great significance for expanding the application fields of optimization theory. [ABSTRACT FROM AUTHOR]

This paper mainly studies and proves the roughness bound of disturbation fuzzy sets. Firstly, based on the theory of determining self-increment and uncertain self-decrement operators, the problem that the execution subsets are not equal sets is effectively solved, which hinders the quantitative study of disturbed fuzzy sets and lays a foundation for the quantitative study of the related properties of disturbed fuzzy sets in the future. The boundary of roughness measure of disturbing fuzzy set is further studied and proved. The new territories proposed in this paper can effectively avoid the unnecessary calculation space outside the boundary in the calculation process, so as to improve the work efficiency. [ABSTRACT FROM AUTHOR]

In the present paper, we introduce and discuss a new set of separation properties in fuzzy soft topological spaces called F S δ -separation and F S δ -regularity axioms by using fuzzy soft δ -open sets and the quasi-coincident relation. We provide a comprehensive study of their properties with some supporting examples. Our analysis includes more characterizations, results, and theorems related to these notions, which contributes to a deeper understanding of fuzzy soft separability properties. We show that the F S δ -separation and F S δ -regularity axioms are harmonic and heredity property. Additionally, we examine the connections between F S δ ∗ -compactness and F S δ -separation axioms and explore the relationships between them. Overall, this work offers a new perspective on the theory of separation properties in fuzzy soft topological spaces, as well as provides a robust foundation for further research in the transmission of properties from fuzzy soft topologies to fuzzy and soft topologies and vice-versa by swapping between the membership function and characteristic function in the case of fuzzy topology and the set of parameters and a singleton set in the case of soft topology. In the present paper, we introduce and discuss a new set of separation properties in fuzzy soft topological spaces called -separation and -regularity axioms by using fuzzy soft -open sets and the quasi-coincident relation. We provide a comprehensive study of their properties with some supporting examples. Our analysis includes more characterizations, results, and theorems related to these notions, which contributes to a deeper understanding of fuzzy soft separability properties. We show that the -separation and -regularity axioms are harmonic and heredity property. Additionally, we examine the connections between -compactness and -separation axioms and explore the relationships between them. Overall, this work offers a new perspective on the theory of separation properties in fuzzy soft topological spaces, as well as provides a robust foundation for further research in the transmission of properties from fuzzy soft topologies to fuzzy and soft topologies and vice-versa by swapping between the membership function and characteristic function in the case of fuzzy topology and the set of parameters and a singleton set in the case of soft topology. [ABSTRACT FROM AUTHOR]

Corporate e-reputation is becoming more and more relevant for firms, partly because of its importance for firm value. In this context, this paper provides comprehensive theoretical and empirical evidence concerning the relationship between electronic word-of-mouth (eWOM), e-reputation, and bank financial performance. First, the study is also intended to determine the effect of eWOM, in terms of components (strength, sentiment, passion, and reach), on e-reputation, allowing for a holistic understanding of these relationships in the sense of the causal chain of factors, which is of high relevance when managing e-reputation. Second, it investigates the effect of e-reputation on bank performance in the US. This paper applies a fuzzy set qualitative comparative analysis technique to the raw data. The results reveal a significant positive relationship between e-reputation on Facebook and bank performance. Moreover, the findings suggest that eWOM components (strength, sentiment, passion, and reach) significantly positively impact e-reputation among US banks, that is, a higher ranking on Facebook because of an increased number of fans). [ABSTRACT FROM AUTHOR]

Renovating old neighborhoods for the benefit of people has become increasingly important in urban renewal. Nevertheless, old neighborhood renovations are currently considered a group decision-making issue under public participation, involving diverse decision-making subjects. Conflicts within a group are a common problem during group decision-making. In this paper, conflict is examined in the decision-making process for renovating old neighborhoods and novel ideas are provided for quantifying conflict. Public participation in old neighborhood renovations is assessed using conflict degree calculations in group decision-making. Based on the preferences of decision-making experts, a MIP DEA–DA (Mixed Integer Programming Data Envelopment Analysis–Discriminant Analysis) based partial binary tree cyclic clustering model is constructed for clustering experts, and an aggregated group conflict indicator and an aggregated conflict vector are computed, allowing for the quantification of conflict during the renovation process of the old neighborhood based on actual situations. Results indicate that there is primarily a conflict between the benefits of decision-making subject interests and the professionalism of decision-making renovations. This paper contributes to improving public participation, promoting the application of group decision-making theory in old neighborhood renovation, reducing conflict between decision-makers, and speeding up urban renewal. [ABSTRACT FROM AUTHOR]

This paper considers the interactive effects between the ego vehicle and other vehicles in a dynamic driving environment and proposes an autonomous vehicle lane-changing behavior decision-making and trajectory planning method based on graph convolutional networks (GCNs) and multi-segment polynomial curve optimization. Firstly, hierarchical modeling is applied to the dynamic driving environment, aggregating the dynamic interaction information of driving scenes in the form of graph-structured data. Graph convolutional neural networks are employed to process interaction information and generate ego vehicle's driving behavior decision commands. Subsequently, collision-free drivable areas are constructed based on the dynamic driving scene information. An optimization-based multi-segment polynomial curve trajectory planning method is employed to solve the optimization model, obtaining collision-free motion trajectories satisfying dynamic constraints and efficiently completing the lane-changing behavior of the vehicle. Finally, simulation and on-road vehicle experiments are conducted for the proposed method. The experimental results demonstrate that the proposed method outperforms traditional decision-making and planning methods, exhibiting good robustness, real-time performance, and strong scenario generalization capabilities. [ABSTRACT FROM AUTHOR]

This paper's aim is to extend and generalize the classic results regarding spectral radii and the corresponding resolvent sets for some different classes of bounded operators acting on fuzzy normed spaces. In this context, the fuzzy norm definition introduced giving shape to a new topology for a fuzzy space, namely a fuzzy topology, also gives the opportunity to study the behavior of various types of operators defined between fuzzy normed spaces, along with their spectral properties. There are several definitions for resolvent sets and consequently, several corresponding definitions of spectral radii that will be considered in this work, since these are non-equivalent ways of defining such notions. Spectral radii are calculated for a fuzzy Volterra type operator acting between fuzzy normed spaces. [ABSTRACT FROM AUTHOR]

This paper aims to support decision-makers improve their ability to accurately capture and represent their judgment in a wide range of situations. To do this, we propose a new type of fuzzy set called a p , q -cubic quasi-rung orthopair fuzzy set ( p , q -CQOFS). The p , q -CQOFS allows for a more flexible and detailed expression of incomplete information through the use of an additional parameter. The paper describes the concept of p , q -CQOFS and its relationship to other types of fuzzy sets, introduces score and accuracy functions for p , q -CQOFS and analyzes some of its mathematical properties, defines the Hamming distance measure between two p , q -CQOFSs and examines some of its important properties, investigates the basic operations of p , q -CQOFSs and extends these laws to aggregation operators, and introduces weighted averaging and geometric aggregation operators for combining p , q -cubic quasi-rung orthopair fuzzy data. [ABSTRACT FROM AUTHOR]

On the basis of K. Kuratowski's definitions of a topological structure with a closure or interior operator, the concept of a modal topological structure (MTS) with one of these operators was introduced by the author. This new structure was illustrated with examples with intuitionistic fuzzy topological operators from both examples, and for this reason, these structures were named intuitionistic fuzzy MTSs (IFMTSs). In a series of papers, the author introduced some modifications and extensions to the IFMTSs, e.g., intuitionistic fuzzy temporal topological structures, intuitionistic fuzzy level topological structures and others, and intuitionistic fuzzy multi modal topological structures and others. In the present paper, four new examples of intuitionistic fuzzy multi modal topological structures are given. On their base, the concepts of a modal multi-topological structure and of a multi-modal multi-topological structure are introduced and illustrated with examples from the area of the intuitionistic fuzzy sets—intuitionistic fuzzy modal multi-topological structure with a closure or an interior operator; and intuitionistic fuzzy multi-modal multi-topological structure with one of these operators. Two intuitionistic fuzzy topological operators are defined. Their basic properties are studied and they are used in the new structures. [ABSTRACT FROM AUTHOR]

In this paper, we state the problem of the network flow interdiction in a set of initial and destination nodes so that each initial is capable of only delivering products to certain pre-determined destinations. The network user's purpose is to deliver the highest value of flow from the sources to the sinks and the network interdictor's purpose is to reduce the highest value of flow being used. In this paper, the networks flow interdiction in multi-source and multi-sink conditions is addressed in a way that the parameters of arc capacity are trapezoidal fuzzy sets. [ABSTRACT FROM AUTHOR]

In the port domain, quayside container cranes are an indispensable component of maritime freight transport. These cranes are not only costly but also associated with safety accidents that often result in casualties and property loss, severely impacting port operations and the surrounding environment. Given their complex operational environment, rapid technological updates, high dependency on human factors, and the challenges of maintenance and inspection, the safety of quayside container cranes is a significant concern for port enterprises and managers. This paper, based on the operational modes and structural characteristics of the cranes, divides them into five main systems and identifies twenty-eight safety evaluation indicators, covering a comprehensive range of risk factors from equipment integrity to operator behavior, as well as environmental factors. However, numerous pain points exist in the safety risk evaluation process of quayside container cranes, such as fuzziness, uncertainty, and complex multi-criteria decision-making (MCDM) environments. These issues make traditional safety evaluation methods inadequate in accurately reflecting the actual safety conditions. Therefore, this paper proposes a safety evaluation method for quayside container cranes based on the Best–Worst Method (BWM) and Pythagorean hesitant fuzzy VIKOR. This method effectively overcomes the uncertainties and fuzziness of traditional safety evaluation methods by integrating the decision maker's preference information from the BWM and the fuzzy handling capability of Pythagorean hesitant fuzzy sets, enhancing the accuracy and reliability of the evaluation results. A case study was conducted on a quayside container crane at a specific port. Through empirical analysis, the feasibility of the proposed method was validated. Overall, the safety evaluation method for quayside container cranes based on the BWM and Pythagorean hesitant fuzzy VIKOR proposed in this paper enriches the theoretical research on the safety risk assessment of quayside container cranes and offers a new approach and tool for port enterprises and managers in practice. [ABSTRACT FROM AUTHOR]

Online and offline integration is an increasingly popular method of performing modern medical services. To provide suggestions for physician selection by patients with full use of previous online and offline patient evaluations, this paper investigates online and offline social network group decision making (OAOSNGDM) in depth. With the aim of inferring the indirect trust relationships of online and offline patients, we first construct a q-rung orthopair fuzzy dual trust propagation operator based on the q-rung orthopair fuzzy trust function, which can effectively deal with inconsistency in trust functions among patients. Considering patient inconsistency in online and offline scenarios, which can increase the uncertainty of the trust relationship in cross-network propagation, we propose a q-rung orthopair fuzzy dual trust cross-network propagation operator by introducing cross-network propagation efficiency. Considering the signal-to-noise ratio, we calculate the trust propagation efficiency and introduce it into the trust propagation operators. To aggregate the trust information of multiple trust paths among patients, we introduce the Dempster rule from evidence theory which can handle the uncertainty of trust functions. In addition, to accurately determine the patient weights according to online and offline social networks, we integrate the ranking results of patients in terms of degree centrality, neighbor importance and betweenness centrality by developing an improved linear assignment method. We then propose a novel decision-making method for OAOSNGDM and design a complete decision-making process for the evaluation of physicians. Finally, we verify the effectiveness of our proposed method for the evaluation of physicians in an online and offline scenario. [ABSTRACT FROM AUTHOR]

Breeding in large-scale marine aquafarms faces many challenges in terms of precise feeding, including real-time decisions as to the precise feeding amount, along with disturbances caused by the feeding speed and the moving speed of feeding equipment. Involving many spatiotemporal distributed parameters and variables, an effective predictive model for environment and growth stage perception is yet to obtained, further preventing the development of precise feeding strategies and feeding equipment. Therefore, in this paper, a hierarchical type-2 fuzzy system based on a quasi-Gaussian membership function for fast, precise, on-site feeding decisions is proposed and validated. The designed system consists of two layers of decision subsystems, taking in different sources of data and expert experience in feeding but avoiding the rule explosion issue. Meanwhile, the water quality evaluation is considered as the secondary membership function for type-2 fuzzy sets and used to adjust the parameters of the quasi-Gaussian membership function, decreasing the calculation load in type reduction. The proposed system is validated, and the results indicate that the shape of the primary fuzzy sets is altered with the secondary membership, which influences the defuzzification results accordingly. Meanwhile, the hardware of feeding bins for UAVs with variable-speed coupling control systems with disturbance compensation is improved and validated. The results indicate that the feeding speed can follow the disturbance in the level flying speed. [ABSTRACT FROM AUTHOR]

The transportation problem is one of the most significant mathematical programming applications that appears in various real-world decision-making problems. In an actual scenario, the supply, demand, and cost parameters of a transportation problem cannot be exactly quantified due to market instability. To deal with such types of impreciseness, the researchers have widely used fuzzy numbers and their extensions. Pythagorean fuzzy set theory is a prominent tool for handling uncertain and vague information in complex decision-making situations. This paper aims to develop a solution approach to solve the transportation problem with uncertainty in input parameters by incorporating Pythagorean fuzzy numbers. To do so, first, a new score function is proposed to rank Pythagorean fuzzy numbers more efficiently. A comparative study highlights some flaws in existing score functions, which depicts the advantages of the proposed score function over existing ones. Afterward, we solve the Pythagorean fuzzy transportation problem using the proposed score function. The solution technique is demonstrated with the help of some numerical examples. In addition, a comparative study is also included to show the efficacy of the proposed approach over existing ones. [ABSTRACT FROM AUTHOR]

This paper describes a generalized Diophantine fuzzy sets, which can be seen as a generalization of both Diophantine fuzzy sets and Pythagorean fuzzy sets. We define the basic properties of generalized Diophantine fuzzy set, as well as their relationships and distances. We compare Diophantine fuzzy sets with other Diophantine Pythagorean fuzzy sets to demonstrate their importance in the literature. We introduce new operators including necessity, possibility, accuracy function and score function. Furthermore, we discuss the new distance between normalized Euclidean distance and normalized Hamming distance. For a generalized Diophantine fuzzy relation, image and inverse image functions are defined. Numerous real-world applications can be found for the prevalent ideas of intuitionistic fuzzy sets, Pythagorean fuzzy sets, Diophantine fuzzy sets and q-rung orthopair fuzzy sets. Regretfully, these theories about the membership and non-membership grades have their own limits. We provide a new idea the generalized Diophantine fuzzy set that eliminates these limitations by including reference parameters. Compared to other kinds of fuzzy sets, there are more applications for generalized Diophantine fuzzy sets. We offer practical examples that show how different enhanced distances might be used in everyday situations. Additionally, to demonstrate the effectiveness of the suggested approach, flowchart based multi-criteria decision-making is provided and used to a numerical example. The outcomes are assessed for various parameter values. Furthermore, a comparative analysis developed to demonstrate the superiority of the suggested technique over current methodologies. [ABSTRACT FROM AUTHOR]

From the perspective of configuration, this paper takes the region of manufacturing efficiency as the explanatory variable, selects eight antecedent conditions, and applies fuzzy set qualitative comparative analysis (fsQCA) to study the paths and methods of improving manufacturing emission efficiency. The results of the study show that there are two configuration paths of carbon emission efficiency in manufacturing industry, namely, research frontier and technological innovation level and labour force structure, R&D investment, science and technology innovation level, manufacturing output value, and environmental regulation synergistic path. [ABSTRACT FROM AUTHOR]

Big data pertains to extensive and intricate compilations of information that necessitate the implementation of proficient and cost-effective evaluation and analysis tools to derive insights and support decision making. The Fermatean fuzzy set theory possesses remarkable capability in capturing imprecision due to its capacity to accommodate complex and ambiguous problem descriptions. This paper presents the study of the concepts of dynamic ordered weighted aggregation operators in the context of Fermatean fuzzy environment. In numerous practical decision making scenarios, the term "dynamic" frequently denotes the capability of obtaining decision-relevant data at various time intervals. In this study, we introduce two novel aggregation operators: Fermatean fuzzy dynamic ordered weighted averaging and geometric operators. We investigate the attributes of these operators in detail, offering a comprehensive description of their salient features. We present a step-by-step mathematical algorithm for decision making scenarios in the context of proposed methodologies. In addition, we highlight the significance of these approaches by presenting the solution to the decision making problem and determining the most effective big data analytics platform for YouTube data analysis. Finally, we perform a thorough comparative analysis to assess the effectiveness of the suggested approaches in comparison to a variety of existing techniques. [ABSTRACT FROM AUTHOR]

Twin support vector machine (TSVM) is an effective machine learning tool for classification problems. However, TSVM classifier works on empirical risk principle only and also while training, each sample contributes equally, even if it is a noise or an outlier. It does not incorporate the uncertainties associated with data into modeling and hence its generalization ability declines. To address these issues, intuitionistic fuzzy regularized least square twin support vector machine having intuitionistic fuzzy network has been proposed in this paper. The non-parallel classifiers are obtained by solving two systems of linear equations only rather than the solution of two quadratic programming problems as in TSVM, which leads to speed up the training process. Moreover, the method follows both structural risk and empirical risk minimization principles. In order to de-escalate the effect of pollutant patterns, their contribution of the patterns into learning the decision function has been made according to their importance in the classification. The significance of the training patterns is measured in terms of intuitionistic fuzzy numbers based on their geometrical locations and surroundings. The method is further extended to find non-parallel decision planes in the feature space using nonlinear kernel function, which also gives rise to the solution of two systems of linear equations. To show the efficacy of the proposed method, computer simulations on fourteen standard and six big UCI datasets using linear and Gaussian kernels are performed and their results have been compared with well-established methods in the literature. The experimental results are represented in terms of accuracy, computational time, F-measure, sensitivity and specificity rates. The outcomes demonstrate that the proposed method outperforms the existing methods and is also feasible for big datasets. The comparison and statistical inferences using two non-parametric: Friedman and Nemenyi tests, conclude that the proposed approach is fast and yields better generalization. [ABSTRACT FROM AUTHOR]

Data envelopment analysis (DEA) is one of the widely used methods to measure the efficiency scores of decision making units (DMUs). Conventional DEA is unable to consider both uncertainty in data and decision makers' (DMs) judgments in the evaluations. This study, to address the shortcomings of the conventional DEA, proposes a new best worst method (BWM)- robust credibility DEA (BWM-RCDEA) model to estimate the efficiency scores of DMUs considering DMs' preferences and uncertain data, simultaneously. First, to handle uncertainty in input and output variables, fuzzy credibility model has been applied. Additionally, uncertainty in constructing fuzzy sets is modeled using robust optimization with fuzzy perturbation degree. In this paper, two new types of RCDEA models are proposed: RCDEA model with exact perturbation in fuzzy inputs and outputs and RCDEA model with fuzzy perturbation in fuzzy inputs and outputs. In addition, to deal with flexibility of weights and incorporating DMs' judgement into the RCDEA model, a bi-objective BWM-RCDEA model is introduced. Finally, the proposed bi-objective model is solved using min–max approach. To illustrate the usefulness and capability of the proposed model, efficiency scores of 39 distribution companies in Iran is investigated and results are analyzed and discussed. Finally, based on the results, recommendations have been made for policy makers. [ABSTRACT FROM AUTHOR]

Belief and plausibility functions based on evidence theory (ET) have been widely used in managing uncertainty. Various generalizations of ET to fuzzy sets (FSs) have been reported in the literature, but no generalization of ET to q-rung orthopair fuzzy sets (q-ROFSs) has been made yet. Therefore, this paper proposes a novel, simple, and intuitive approach to distance and similarity measures for q-ROFSs based on belief and plausibility functions within the framework of ET. This research addresses a significant research gap by introducing a comprehensive framework for handling uncertainty in q-ROFSs using ET. Furthermore, it acknowledges the limitations inherent in the current state of research, notably the absence of generalizations of ET to q-ROFSs and the challenges in extending belief and plausibility measures to certain aggregation operators and other generalizations including Hesitant fuzzy sets, Bipolar fuzzy sets, Fuzzy soft sets etc. Our contribution lies in the proposal of a novel approach to distance and similarity measures for q-ROFSs under ET, utilizing Orthopairian belief and plausibility intervals (OBPIs). We establish new similarity measures within the generalized ET framework and demonstrate the reasonability of our method through useful numerical examples. Additionally, we construct Orthopairian belief and plausibility GRA (OBP-GRA) for managing daily life complex issues, particularly in multicriteria decision-making scenarios. Numerical simulations and results confirm the usability and practical applicability of our proposed method in the framework of ET. [ABSTRACT FROM AUTHOR]

Task scheduling is a critical challenge in cloud computing systems, greatly impacting their performance. Task scheduling is a nondeterministic polynomial time hard (NP-Hard) problem that complicates the search for nearly optimal solutions. Five major uncertainty parameters, i.e., security, traffic, workload, availability, and price, influence task scheduling decisions. The primary rationale for selecting these uncertainty parameters lies in the challenge of accurately measuring their values, as empirical estimations often diverge from the actual values. The integral-valued Pythagorean fuzzy set (IVPFS) is a promising mathematical framework to deal with parametric uncertainties. The Dyna Q+ algorithm is the updated form of the Dyna Q agent designed specifically for dynamic computing environments by providing bonus rewards to non-exploited states. In this paper, the Dyna Q+ agent is enriched with the IVPFS mathematical framework to make intelligent task scheduling decisions. The performance of the proposed IVPFS Dyna Q+ task scheduler is tested using the CloudSim 3.3 simulator. The execution time is reduced by 90%, the makespan time is also reduced by 90%, the operation cost is below 50%, and the resource utilization rate is improved by 95%, all of these parameters meeting the desired standards or expectations. The results are also further validated using an expected value analysis methodology that confirms the good performance of the task scheduler. A better balance between exploration and exploitation through rigorous action-based learning is achieved by the Dyna Q+ agent. [ABSTRACT FROM AUTHOR]

We studied a paper to apply a method of maximizing deviations to multiple attribute decision-makings under intuitionistic fuzzy environment that have found several new methods and theorems for maximum problem under some specific conditions with insufficient information environment. We showed that the Lagrange multiplication method used by the paper can be replaced by our simplify approach with the Cauchy Schwarz inequality. The purpose of this paper is fourfold. First, the iteration method for the problem within the range of weights is well developed and with appropriate explanation if the weight vector of attributes is bounded. Second, if the weight vector of attributes is completely unknown, we could directly and swiftly derive the weight by the Cauchy-Schwarz inequality such that the complicated approach by the Lagrange multiplication method becomes redundant. Third, we prove the results of score function and rank for one-norm will not be preserved in the two-norm. Fourth, the same numerical examples are examined again and have different outcome to demonstrate our findings is superior to the previously published results. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a distance measure on single-valued neutrosophic sets by sine function which is a generalization of intuitionistic fuzzy sine distance measure. The axiom of metric on single-valued neutrosophic sets is verified and shows that the difference of distance measure from unity is a similarity measure. A new methodology for multi-attribute decision-making problems (MADM) is developed for the most common decision by the smallest measure value of the proposed single-valued neutrosophic distance measure. We further apply this distance measure to a multi-attribute decision-making problem (MADM) for student career determination in a neutrosophic environment to find the best career for suitable students. Finally, the comparison is made between the proposed distance measure and the other distance measures for the final decision chosen from the most common decisions of them. [ABSTRACT FROM AUTHOR]

Rough fuzzy clustering algorithms have received extensive attention due to the excellent ability to handle overlapping and uncertainty of data. However, existing rough fuzzy clustering algorithms generally consider single view clustering, which neglects the clustering requirements of multiple views and results in the failure to identify diverse data structures in practical applications. In addition, rough fuzzy clustering algorithms are always sensitive to the initialized cluster centers and easily fall into local optimum. To solve the above problems, the multi-view and transfer learning are introduced into rough fuzzy clustering and a robust multi-view knowledge transfer-based rough fuzzy c-means clustering algorithm (MKT-RFCCA) is proposed in this paper. First, multiple distance metrics are adopted as multiple views to effectively recognize different data structures, and thus positively contribute to clustering. Second, a novel multi-view transfer-based rough fuzzy clustering objective function is constructed by using fuzzy memberships as transfer knowledge. This objective function can fully explore and utilize the potential information between multiple views and characterize the uncertainty information. Then, combining the statistical information of color histograms, an initialized centroids selection strategy is presented for image segmentation to overcome the instability and sensitivity caused by the random distribution of the initialized cluster centers. Finally, to reduce manual intervention, a distance-based adaptive threshold determination mechanism is designed to determine the threshold parameter for dividing the lower approximation and boundary region of rough fuzzy clusters during the iteration process. Experiments on synthetic datasets, real-world datasets, and noise-contaminated Berkeley and Weizmann images show that MKT-RFCCA obtains favorable clustering results. Especially, it provides satisfactory segmentation results on images with different types of noise and preserves more specific detail information of images. [ABSTRACT FROM AUTHOR]

In crisp graph theory, there are numerous topological indices accessible, including the Misbalance Prodeg Index, which is one of the most well-known degree-based topological indexes. In crisp graphs, both vertices and edges have membership values of 1 or 0, whereas in fuzzy graphs, both vertices and edges have different memberships. This is an entire contrast to the crisp graph. In this paper, we introduce the Fuzzy Misbalance Prodeg Index of a fuzzy graph, which is a generalized form of the Misbalance Prodeg Index of a graph. We find bounds of this index and find bounds of certain classes of graphs such as path graph, cycle graph, complete graph, complete bipartite graph, and star graph. We give an algorithm to find the Fuzzy Misbalance Prodeg Index of a graph for the model of multi-criteria decision-making is established. We present applications from daily life in multi-criteria decision-making. We apply our obtained model of the Fuzzy Misbalance Prodeg Index for the multicriteria decision-making to the choice of the best supplier and we also show the graphical analysis of our index with the other indices that show how our index is better than other existing indices. [ABSTRACT FROM AUTHOR]