Hesitant Fuzzy Numbers Research Articles

A novel MADM model integrating hybrid information for evaluating the development prospects of urban new energy vehicles.

As an effective approach to mitigating urban environmental issues, New Energy Vehicles (NEVs) have become a focal point of research regarding their current development status and future prospects in China. Addressing the significant disparities in the development of the NEVs industry across different cities, this study focuses on ten typical Chinese cities and develops a novel multi-attribute decision-making (MADM) framework to evaluate the prospects of NEVs promotion in these cities. The study first establishes a comprehensive indicator system that covers key dimensions such as economy, policy support, infrastructure, technological innovation, and environment, encompassing five different types of evaluation information. This system incorporates five different types of evaluation information: exact numbers, interval numbers, triangular fuzzy numbers, hesitant fuzzy numbers, and probabilistic linguistic term sets (PLTS), enhancing the framework's ability to handle diverse data types. Subsequently, the improved entropy (IEntropy) weight method is employed to determine the objective weights of the evaluation indicators. These objective weights are then integrated with the Vlsekriterijumska Optimizacija I Kompromisno Resenje (VIKOR) method, facilitating a structured group decision-making approach that synthesizes hybrid evaluation information. Based on modular thinking, hybrid evaluation information is synthesized to evaluate and rank the NEVs development prospects of each city. Sensitivity analysis and comparative analysis further demonstrate the robustness and reliability of the proposed MADM framework. The ranking results indicate that Shanghai and Guangzhou lead in NEVs promotion, while cities like Harbin and Zhengzhou lag behind. Based on these findings, the study proposes targeted policy recommendations to promote the sustainable development of the NEVs industry in major Chinese cities.

A Hesitation-Associated Multi-Attribute Decision-Making Method Based on Generalized Interval-Valued Hesitation Fuzzy Weighted Heronian Averaging Operator

In multi-attribute decision making (MADM), complex situations often arise where decision attributes are interval-valued hesitant fuzzy numbers (IVHFNs) and the attributes are interrelated. Traditional decision-making methods may be ineffective in handling such cases, highlighting the practical importance of seeking more effective approaches. Therefore, finding a more effective decision-making approach has important practical significance. By combining the theories of Archimedean S-norms and T-norms, we innovatively propose a multi-attribute decision-making method based on the generalized interval-valued hesitant fuzzy weighted Heronian mean (GIVHFWHM) operator to address the aforementioned issues. Initially, based on the operational laws of IVHFNs and the Heronian mean (HM) operator, we introduce the generalized interval-valued hesitant fuzzy Heronian mean (GIVHFHM) operator and the GIVHFWHM operator. We then examine properties of the GIVHFHM operator, including permutation invariance, idempotency, monotonicity, boundedness, and parameter symmetry. A multi-attribute decision-making model is constructed based on the GIVHFWHM operator. Finally, we validate the proposed model through numerical experiments in MADM. The results demonstrate that the new decision-making method, based on the GIVHFWHM operator, is feasible and effective in handling multi-attribute decision problems involving IVHFNs with interdependent attributes. This approach provides a novel perspective and method for solving MADM problems under interval-valued hesitant fuzzy conditions with interdependent attributes. It enriches the theoretical framework of multi-attribute hesitant decision models and expands the application of the Heronian mean operator within interval-valued hesitant fuzzy environments. This methodology assists decision makers in making more accurate decisions within complex decision-making contexts, enhancing both the scientific rigor and reliability of decision-making processes.

Hesitant Fuzzy Monotonic Dependent OWA Operator and Its Application in Symmetric Group Decision-Making

Some new techniques of aggregating hesitant fuzzy numbers (HFNs) by using monotonic dependent OWA (MDOWA) operators are investigated. By utilizing the score value of HFN, the concepts of hesitant fuzzy configuration vector and hesitant fuzzy hybrid configuration vector are proposed. Then, some methods of calculating variable weights related to the MDOWA operators under hesitant fuzzy environments are presented. Further, some operators, including hesitant fuzzy monotonic dependent OWA (HFMDOWA) operators and hesitant fuzzy hybrid monotonic dependent OWA (HFHMDOWA) operators, are developed, such as balanced HFMDOWA operators, rewarded HFMDOWA operators, balanced HFHMDOWA operators, rewarded HFHMDOWA operators, and so on. These developed operators are applied to multiple criteria group decision making (MCGDM), and a novel MCGDM algorithm is presented. By using the presented operators and algorithm, we can obtain symmetric decision-making results. Finally, an application example is provided to demonstrate the effectiveness of the developed MCGDM techniques.

Decision-making techniques based on aggregation operators and similarity measures under q-rung orthopair hesitant fuzzy connection numbers and their application

The concept of q-rung orthopair hesitant fuzzy set represents an advancement and extension of hesitant fuzzy sets, encompassing both fuzzy sets and q-rung orthopair fuzzy sets. q-rung orthopair hesitant fuzzy set characterizes a set of membership and non-membership grades within the interval [0, 1], which enhances its adaptability compared to existing methods. This flexibility proves invaluable in providing more insightful data about various objects. The primary objective of this research is to introduce a decision-making technique in the context of q-RHF using the theory of set pair analysis (SPA). q-RHFS effectively handles ambiguous data by incorporating membership and non-membership grades, while the connection number (CN) based on SPA theory manages the intricacies of uncertainty and certainty structures by relying on "identity", "discrepancy" and "contrary" grades. Building on the relationship between q-RHFS and the connection number of set pair analysis, a comprehensive framework known as q-rung hesitant fuzzy connection number set (qHCNs) is developed. This model not only addresses uncertainty, but also offers valuable insights. Furthermore, this research introduces similarity measures derived from qHCN and examines their advantages through illustrative examples. Additionally, a novel approach to decision modeling utilizing these measures applied to medical diagnosis is also introduced. The application of this established model contributes to an effective approach and demonstrated its soundness and efficiency. In addition, a detailed comparative study is conducted with the existing models and advantages of proposed model. The research concludes with a summary of the authors' findings, highlighting the consistency and effectiveness of their work.

An intelligent decision method of quality risk in electromagnet assembly process based on digital twin and q-rung dual hesitant fuzzy number

In order to solve the problem of online risk analysis of assembly process, an intelligent decision-making method of electromagnet assembly risk based on Digital Twin (DT) was proposed. Firstly, a DT model of electromagnet assembly process is constructed, and the potential failure modes are collected in real time at the physical layer. Secondly, in the virtual layer, real-time potential failure modes are obtained through information synchronization and transmitted to the application layer. Then, in the application layer, the optimized Failure Mode and Effects Analysis (FMEA) method is used to analyze the risk of failure mode, and the risk value of failure mode is fed back to the virtual layer. In the improved FMEA method, the q-Rung Dual Hesitant Fuzzy Number (q-RDHFN) is used as the evaluation language. The weight of experts is calculated by Bidirectional Projection Method (BPM), and the comprehensive weight of risk factors is calculated by Best and Worst Method (BWM) method, entropy weight method and Criteria Importance Through Intercriteria Correlation (CRITIC) method. Finally, the physical layer is adjusted to reduce the probability and risk of failure mode occurrence. An example of risk intelligent decision making is given to verify the objectivity and practicability of the new method.

A Hybrid Multi-Attribute Decision-Making Approach Considering Correlations Among Indicators

Considering the fuzzy and uncertainty of the evaluation information of the evaluation object, the type of indicators are expanded into five types of mixed evaluation information, namely, exact number, interval number, triangular fuzzy number, hesitant fuzzy number, and probabilistic linguistic term sets, and different types of evaluation information are adopted according to the different characteristics and types of indicators, respectively. When the evaluation information is hybrid information, the generalized Shapley function based on fuzzy measurement is used to analyze the interaction between indicators and determine the weights of indicators, considering that the interaction between indicators is more complicated. In view of the fact that the conversion of mixed information into the same kind of information will lead to the problem of complicated calculation and missing information, the VIKOR method is used to comprehensively evaluate the evaluation objects and select the best ones. Finally, the validity and feasibility of the proposed method is verified by taking the assessment of data literacy level and competence of teachers in a university in a western province of China as an example.

GHF-COPRAS Multiple Attribute Decision-Making Method Based on Cumulative Prospect Theory and Its Application to Enterprise Digital Asset Valuation

With the rapid development of the economy, data have become a new production factor and strategic asset, enhancing efficiency and energy for technological innovation and industrial upgrading in enterprises. The evaluation of enterprise digital asset value (EDAV) is a typical multi-attribute decision-making (MADM) problem. Generalized hesitant fuzzy numbers (GHFNs) can better express the uncertainty and fuzziness of evaluation indexes, thus finding wide applications in MADM problems. In this paper, we first propose the Kullback–Leibler (K-L) divergence distance of GHFNs and prove its mathematical properties. Second, recognizing that decision-makers often have finite rationality in practical problems, we combine the cumulative prospect theory (CPT) with the Complex Proportional Assessment (COPRAS) method to propose the GHF-CPT-COPRAS model for solving MADM problems. Simultaneously, we extend the distance correlation-based Criteria Importance Through Intercriteria Correlation (D-CRITIC) method to the GHF environment to rationally calculate the weights of attributes in the EDAV evaluation problem. Finally, we apply the proposed GHF-CPT-COPRAS model to the EDAV evaluation problem and compare it with existing GHF decision-making methods to verify its effectiveness and feasibility. This study provides an important reference for addressing the EDAV assessment problem within an uncertain fuzzy environment and extends its application methods in the decision-making field.

Dynamic person-position matching decision method based on hesitant fuzzy number information

In view of the fact that people pay more and more attention to the principle of "getting the position according to the person" and "adapting the person to the position" in person-position matching, a dynamic person-position matching decision method based on hesitant fuzzy numbers is proposed. First, the dynamic person-position matching problem with hesitant fuzzy numbers is described. Then, according to hesitant fuzzy evaluation matrices of positions and candidates, expected score matrices of bilateral subjects are calculated. Furthermore, based on the idea of the generalized optimal order method and the dominant correlation and the missing correlation coefficients, satisfaction means of people and positions are calculated. According to satisfaction means, growth satisfactions at each period are obtained, and then the exponential decay formula is used to determine weights of growth satisfactions. Dynamic satisfactions of bilateral subjects are calculated by aggregating initial satisfaction means and growth satisfactions. On this basis, a stable person-position matching model considering dynamic satisfactions is established and then is solved to obtain the optimal stable person-position matching scheme. Finally, the feasibility and effectiveness of the proposed method are verified by an example analysis of person-position matching. Main contributions of this paper are as follows: an effective calculation method for the missing correlation coefficient is presented; a novel effective calculation method for dynamic satisfactions is proposed by introducing the correlation parameter to combine the missing correlation coefficient with the dominant correlation coefficient; an effective stable person-position matching model considering dynamic satisfactions is established.

Optimized distance measures on hesitant fuzzy numbers: An application

As the rapidly progressing applications of uncertainty theories, the need for modifications to some of their existing mathematical tools or creating new tools to deal correctly with them in various environments is also exposed. Hesitant fuzzy numbers (HFNs), as a particular case of fuzzy numbers, are not an exception to this rule. Considering the necessity of determining the distance between given HFNs in many of their practical applications, this article shows that the existing methods either do not provide correct results or are not able to meet the needs of users. This paper aims to present new methods for distance measures of hesitant fuzzy numbers. To do them, three prevalent distance measures, i.e., the generalized distance measure, the Hamming distance measure, and the Euclidean distance measure, will be optimized into three distinct trinal categories. With the approach of reducing error propagation via reducing some unnecessary mathematical computations, new distance measures on HFNs will be introduced, first. The middle is the modification of the first category, which is more suitable when the given HFNs are equal-distance by the previous formula. Also, as the third category, the weighted form of these distance measures has been proposed, to be used where the real and membership parts of HFNs are not of equal importance. As an application of these, a TOPSIS-based technique for solving multi-attribute group decision-making problems with HFNs has been proposed. A numerical example will be implemented to describe the presented method. Finally, along with the validation of the proposed method, its numerical comparison with some other existing methods will be discussed in detail.

On SIR-based MCDM approach: Selecting a charcoal firm using hybrid fuzzy number on a Triple Vague structure

Multi-Criteria Decision Making (MCDM) is a widely used method across various sectors to help decision-makers assess and choose the most suitable solutions from a range of available options. This research introduces an innovative framework called the Triple Vague (TV) structure for Superiority and Inferiority Ranking (SIR) within the context of MCDM. This framework incorporates interval fuzzy numbers and hesitant fuzzy numbers, including negative interval fuzzy numbers for different vague ideas. The main goal of this research is to present an effective solution to the challenge of selecting a firm, specifically focusing on the manufacturing of charcoal from waste coconut shells. The SIR approach is employed to establish two complete rankings, and a TV value is used to articulate the assessment information. In this article, our contribution lies in the proposed Triple Vague approach, which utilizes the superiority and inferiority ranking methodology to identify the best firm for charcoal manufacturing. Further, it demonstrates through an application example involving the selection of the most suitable firm among four different options based on specified criteria for charcoal production from coconut shell waste. Also, comparative analysis has been done with other MCDM methods like TOPSIS, Grey method and PROMETHEE method. This analysis examines that the proposed structure is better than other MCDM technique. Moreover, the results highlight the framework's capability to handle the hesitation, vagueness, and like other undesirable characteristics. Hence it provides valuable insights for decision-makers to thoroughly evaluate and consider the best alternatives.

Arithmetic Operations on Generalized Trapezoidal Hesitant Fuzzy Numbers and Their Application to Solving Generalized Trapezoidal Hesitant Fully Fuzzy Equation

Algebraic operations on generalized hesitant fuzzy numbers are key tools to address the problems with decision uncertainty. In this paper, by studying the arithmetic operations on generalized trapezoidal hesitant fuzzy numbers, modified arithmetic operations are introduced for this class of numbers so that, using these arithmetic operations, the multiplication and division of two generalized trapezoidal hesitant fuzzy numbers are always generalized trapezoidal hesitant fuzzy numbers. Furthermore, a generalized trapezoidal hesitant fuzzy number raised to the power of a real number is a generalized trapezoidal hesitant fuzzy number, and in the defined division, the case where the denominator becomes zero is not considered. Numerical examples are used to show the shortcomings of the previous arithmetic operations as well as the efficiencies of the arithmetic operations proposed in this research for generalized trapezoidal hesitant fuzzy numbers. Finally, the application of the proposed new arithmetic operations to generalized trapezoidal hesitant fuzzy numbers in solving the generalized trapezoidal hesitant fully fuzzy equation is discussed.

Prioritized Aggregation Operators of GTHFNs MADM Approach for the Evaluation of Renewable Energy Sources

In this paper, firstly, we propose two new GTHFNs-prioritized aggregation operators called generalized trapezoidal hesitant fuzzy number prioritized weighted average operator and generalized trapezoidal hesitant fuzzy number prioritized weighted geometric operator. Secondly, we investigate the fundamental properties of the operators in detail such as idempotency, boundedness and monotonicity. Thirdly, we propose a method based on the developed GTHF-numbers prioritized aggregation operators for solving an MADM problem with GTHF-numbers. Fourthly, we give a numerical example of the developed method. Finally, a comparative analysis is given with some existing methods in solving an MADM problem with GTHF-numbers.

Group decision making in the analytic hierarchy process by hesitant fuzzy numbers

Due to the increasing complexity of decision problems, many managers employ multiple experts to reach a good decision in a group decision making. Now, if there is ambiguity in the evaluation of experts, the use of fuzzy numbers can be useful for each expert. In these situations, the use of hesitant fuzzy numbers (HFNs) which consists of several fuzzy numbers with special conditions can be suggested. HFNs are as an extension of the fuzzy numbers to take a better determining the membership functions of the parameters by several experts. Because of simple and fast calculations, in this paper, we use triangular HFNs in the pairwise comparison matrix of analytic hierarchy process by opinions of a group of decision makers in a hesitant fuzzy environment. We define consistency of the hesitant fuzzy pairwise comparison matrix and use the arithmetic operations on the HFNs and a new method of comparing HFNs to get the hesitant fuzzy performance score. By using score function to hesitant fuzzy score we can get a final score for alternatives. Finally, a practical example is provided to show the the effectiveness of this study. The obtained results from this paper show that new method can get a better answer by keeping the experts’ opinions in the process of solving the problem.

Picture hesitant fuzzy grey compromise relational bidirectional projection method with application in multi-attribute recommendation

In view of the technical defects of the existing grey relational projection method, a new grey compromise relational bidirectional projection method is proposed. By incorporating the information expression advantage of picture hesitant fuzzy number, the distance formula of picture hesitant fuzzy statistics is constructed based on the centralized trend measurement and discrete trend measurement in descriptive statistics. On this basis, a multi-attribute recommendation method of picture hesitant fuzzy grey compromise relational bidirectional projection is proposed by combining compromise idea and bidirectional projection technology. The validity and advantage of this method are verified by numerical analysis, which also suggested the rationality of the picture hesitant fuzzy statistical distance and the grey compromise relational bidirectional projection method.

Research on decision method based on probability hesitation fuzzy comprehensive distance measure

Aiming at the defects of the existing probabilistic hesitation fuzzy distance measures, which require the number of membership degree to be consistent and the order to be rearranged, a probabilistic hesitation fuzzy multi-attribute decision making method based on the comprehensive characteristic distance measure is proposed. First, a new law of probability hesitant fuzzy number comparison is defined. Then four characteristics of aggregation, discreteness, fuzziness and consistency are defined, and a new comprehensive distance measure is defined based on definitions above. Finally, on the basis of traditional TODIM method and prospect theory, the validity and rationality of the distance measure and new probability hesitant fuzzy recognition method in this paper are verified by examples and comparative analysis.

Multi-criteria decision analysis: Hesitant fuzzy methodology towards expert systems for analyzing financial markets dynamics

AbstractDecision support systems are a mixture of different methods and tools combined by machine learning approach. This study uses the most important machine learning techniques (logistic regression, artificial neural networks, and support vector machines) and the expert-based method (fuzzy analytic hierarchy process and hesitant fuzzy numbers) to study some financial markets dynamics. The objective of the study is to examine the main approaches developed by theory and operational practice for the purposes of conceptual representation, management and quality assessment. Different tools are applied to support decisions makers, such as AHPSort II to model the hierarchical structure, FAHP to determine weights in the construction of the matrix of the pairwise comparison and hesitant fuzzy sets (HFS) to better represent the preferences of the decisions makers.

Optimisation of Master’s Degree Programmes in Translation Based on Multi-Attribute Decision-Making Approach

Abstract In this paper, first of all, in the quality assessment of the teaching quality of the translation course, it is proposed to use a multi-attribute decision model to assess the quality of the set of alternatives for all the courses and to use the existing decision ideal points to rank and select the best of a set of optimized solutions for the translation course through the hesitant fuzzy number and objective optimization model. Finally, to explore the optimization problem of the curriculum, a research analysis was conducted on MTI master’s students who recently graduated from the institution. The results show that by optimizing the MTI course specifically, the students’ positive interest (p 1 = 0.03) and independent inquiry interest (p 2 = 0.01) are less than 0.05, showing significant differences (p<0.05). The special optimization scheme of the MTI course proposed in this paper can reflect some problems worth pondering in the curriculum and provide a guiding reference for optimizing the MTI course in schools.

Vikor method based on the entropy measure for generalized trapezoidal hesitant fuzzy numbers and its application

Vikor method based on the entropy measure for generalized trapezoidal hesitant fuzzy numbers and its application

Q-rung orthopair hesitant fuzzy preference relations and its group decision-making application

To express the opinions of decision-makers, q-rung orthopair hesitant fuzzy sets (q-ROHFSs) have been employed extensively. Therefore, it is necessary to construct q-rung orthopair hesitant fuzzy preference relations (q-ROHFPRs) as a crucial decision-making tool for decision-makers. The goal of this paper aims to define a new consistency and consensus approach for solving q-ROHFPR group decision-making (GDM) problems. To do this, we first state the definitions of q-ROHFPRs and additive consistent q-ROHFPRs based on q-ROHFSs, an additive consistency index and acceptable additive consistent q-ROHFPRs. Second, based on minimizing the deviation, we establish an acceptable goal programming model for unacceptable additive consistent q-ROHFPRs. Third, an iterative algorithm is created for achieving acceptable consistency and reaching a rational consensus. The degree of rational consensus among individual q-ROHFPRs is quantified by a distance-based consensus index. Afterward, a non-linear programming model is formulated to derive the priority vector of alternatives, which are q-rung orthopair hesitant fuzzy numbers (q-ROHFNs). Based on this model, a GDM model for q-ROHFPRs is then developed. To demonstrate the validity and utility of the proposed GDM model, a case study on the risk assessment of hypertension is provided. The finding of sensitivity and comparison analyses supports the feasibility and efficacy of the suggested approach.

EDAS method for multi-attribute decision-making with generalized hesitant fuzzy numbers and its application to energy projects selection

Generalized hesitant fuzzy numbers (GHFNs) can reflect the real situation of the event, in which we may encounter limited known values and known values of the set of the degree of doubt, as a quantitative approximation of uncertainty or quantification of linguistic expressions. The score function and weighting method of GHFNs are of great significance in multi-attribute decision-making (MADM) problems. In different ambiguous environments, many scholars have proposed score functions and entropy measures for different fuzzy sets. Firstly, the existed score function of GHFNs was analyzed in detail and a new score function of GHFNs was established by combining previous references. Secondly, a combined weighting method is built based on the minimum identification information principle by fusing GHF entropy and Method based on the Removal Effects of Criteria (MEREC). Thirdly, a novel GHF MADM method (GHF-EDAS) is built by extending evaluation based on distance from average solution (EDAS) method to the GHF environment to solve the issue that the decision attribute information is GHFNs. Finally, the validity and usefulness of the technique are verified by applying the GHF-EDAS technique to energy projects selection and comparing with the existing GHF-MADM method, the practicability and effectiveness of the model are verified, which offer a new way to solve the MADM problem of GHFNs.