Hesitant Fuzzy Environment Research Articles

Dijkstra’s algorithm for shortest path problem under hesitant fuzzy environment using different operator

Dijkstra’s algorithm for shortest path problem under hesitant fuzzy environment using different operator

A generalized TODIM evaluation approach based on the novel score function and trust network under interval-valued hesitant fuzzy environment

In multi-attribute group decision-making (MAGDM), the social relationships among group members, professional backgrounds and psychological behaviors of decision makers are important factors for achieving high-quality group decisions. However, realizing the consideration of these factors in fuzzy and complex group decision-making scenarios is an important and urgent issue. In MAGDM problems, interval-valued hesitant fuzzy sets (IVHFSs) can better show the hesitant and fuzzy uncertainty information because they are an extension of fuzzy sets. This paper focuses on the score function of IVHFSs and develops a generalized TODIM evaluation method utilizing the novel score functions of IVHFEs and trust networks. The developed method effectively realizes the application of these factors in fuzzy and complex group decision making scenarios. In this contribution, a new deviation function for IVHFSs is created in this paper. It takes into account two types of deviation that are common in IVHFSs: the ambiguity of interval width and the hesitation and uncertainty of multiple intervals. In the sequel, a novel score function for IVHFSs is developed with help of the novel deviation function and the traditional score function. Concerning the perspective of group consistency, a model for determining expert weights is constructed using quality parameters, which combine the novel score function with the trust network. A subjective and objective comprehensive weighting model is made to get attribute weights based on how certain decision information is and the experts’ subjective experience. This is done because the more uncertain something is, the higher the risk. Eventually, we develop a generalized TODIM technique for MAGDM based on the novel score function and trust network in IVHFS environment. The developed approach is demonstrated with a preventive engineering decision-making problem. Sensitivity and comparative analyses are implemented to demonstrate the superiority, stability, and validity of the proposed method in this paper. According to the findings of this study, we conclude that the proposed methodology offers a comprehensive and systematic approach to evaluate MAGDM in the context of IVHFS with trust networks.

Cloud model-based multi-stage multi-attribute decision-making method under probabilistic interval-valued hesitant fuzzy environment

Due to the complexity of multi-stage multi-attribute decision-making (MADM) problems, decision-makers (DMs) frequently provide incomplete and hesitant evaluation information. A crucial difficulty in multi-stage MADM problems is how to make a valid decision under uncertain environment. Firstly, we employ probabilistic interval-valued hesitant fuzzy set (PIVHFS) to characterize the hesitancy of DMs, and then build an optimization model to obtain the probability information based on the score function, deviation function of probabilistic interval-valued hesitant fuzzy element (PIVHFE) and information entropy. Secondly, cloud model is introduced to optimize the calculation process and an optimization model is developed to realize the transformation from PIVHFS to cloud model. Thirdly, a method to solve the stage weights is proposed by synthesizing the within-stage and between-stage decision information. Similarly, the attribute weights are obtained by constructing a mathematical model based on the within-attribute and between-attribute decision information. The noted method can utilize decision information to its fullest. Then, the regret theory is applied to a multi-stage MADM problem. Finally, the applicability and effectiveness of the method are illustrated through case analysis and methods comparison.

A PSO-algorithm-based dual consensus method for large-scale group decision making and its application in medical imaging equipment purchasing

The increasing complexity of social activities requires an expanding number of people to be involved in decision-making, so that the large-scale multi-attribute group decision-making problems have gained widespread attention. After overviewing the researches of large-scale multi-attribute group decision-making methods, we have found that: The existing methods only consider consensus based on evaluation information of alternatives, while ignoring the consensus on importance of attributes. Thus, in order to tackle the issues and describe the hesitancy of decision makers in the decision-making process, this paper proposes a novel dual consensus method in large-scale multi-attribute group decision making under hesitant fuzzy linguistic environment. In the consensus reaching process, the method considers not only the consensus on the evaluation information of alternatives, but also the consensus on the importance of attributes, where both consensus reaching processes are implemented by the particle swarm optimization algorithm. The subjective weights of attributes are derived from the consensus reaching process of preference matrices, and the objective weights of attributes are obtained from the consensus reaching process of decision matrices, so as to acquire the comprehensive weights. After that, the overall ranking of alternatives can be obtained by TODIM. Finally, the proposed method is applied to a case study of medical imaging equipment purchasing decision-making, and the comprehensive analysis is provided to clarify advantages of the proposed method.

A new multi-attribute group decision-making method based on Einstein Bonferroni operators under interval-valued Fermatean hesitant fuzzy environment

Faced with the increasing complexity and uncertainty of decision-making information, interval-valued Fermatean hesitant fuzzy sets (IVFHFSs) were presented as a novel mathematical model that handled uncertain data more effectively. However, existing multi-attribute group decision-making (MAGDM) methods based on IVFHFSs do not thoroughly investigate the operational laws. Also, these existing MAGDM methods do not take into account the connections between attributes and are less flexible. To address these issues, this paper proposes a new MAGDM method based on Einstein Bonferroni operators under IVFHFSs. First, we thoroughly examine the operational laws of Einstein t-norms under the IVFHFSs to further extend the study of the operational laws. Then, we introduce the interval-valued Fermatean hesitant fuzzy Einstein Bonferroni mean operator and the interval-valued Fermatean hesitant fuzzy Einstein weighted Bonferroni mean operator under Einstein t-norms. Our suggested aggregation operators consider the relationship between attributes and are far more flexible in comparison to the current approaches. Later, a novel MAGDM method based on Einstein Bonferroni operators under the IVFHFSs is given. Finally, the practicality and validity of the proposed method are demonstrated by a cardiovascular disease diagnosis application.

Ensemble feature selection using q-rung orthopair hesitant fuzzy Hamacher, Einstein and Dombi Aggregation operators

The article aims in addressing the issue of ensemble feature selection problem by modeling it as a multi-criteria decision making technique. To build such a model, initially, aggregation operators such as weighted arithmetic, weighted geometric, ordered weighted arithmetic, ordered weighted geometric aggregation of Hamacher, Einstein and Dombi operators in the q-rung orthopair hesitant fuzzy environment are proposed. The properties of these operators are also discussed to provide a more elaborate understanding of them. Such an approach to ensemble feature selection has not yet been carried out in the literature which adds to the novelty of our work. Validation is provided through comparison of the performance metrics with existing and base feature selection methods and also by carrying out statistical tests. Through this article, a model for ensemble feature selection incorporating the advantages of Einstein, Hamacher, Dombi and q-rung orthopair hesitant fuzzy set was constructed which was reflected in the results.

A multi-criteria decision-making approach for pressurized water reactor based on hesitant fuzzy-improved cumulative prospect theory and 2-additive fuzzy measure

As one of the world's largest energy consumers, China has paid much attention to the development of non-fossil energy sources. The nuclear power is regarded as the top priority for development due to its remarkable ecological and economic advantages. Given the large investment, long lifecycle, and rigorous quality control, the conceptual design plays a critical role in the pressurized water reactor development. Multitudinous design alternatives are presented at this stage and it is essential to develop an advanced evaluation approach. Hence, this work proposes a multi-criteria decision-making approach for pressurized water reactor based on hesitant fuzzy-improved cumulative prospect theory and 2-additive fuzzy measure. Firstly, considering the inherent uncertainty and cognitive biases of nuclear power experts, cumulative prospect values are calculated for design alternatives by adopting dual prospect reference points and two-tuple entropy measure under a hesitant fuzzy environment. Secondly, a linear programming model based on bidirectional projection measures is constructed to eliminate the discordance between the independent criteria assumption and interdependent evaluation information. This model helps to identify optimal 2-additive fuzzy measures, which serve as the basis for determining the Shapley importance and interaction indices of evaluation criteria. Then, taking Shapley interaction indices modification into account, a quadratic programming model based on the global criterion method is built. Finally, 2-additive Choquet integral-based TOPSIS method is proposed to select the optimal design alternative. A case study on the essential service water system is implemented to demonstrate the reliability and superiority of the proposed approach.

Prospect-regret theory based decision-making approach for incomplete probabilistic hesitant fuzzy environment: An application to medical field

In the era of uncertainty and indeterminacy, probabilistic hesitant fuzzy sets (PHFS) an extension of hesitant fuzzy sets (HPS) have received much attention due to their ability to increase the reliability of information by considering the occurrence probabilities of each opinion. Considering the studies of PHFS following points can be identified, (i) preferences are aggregated without considering the inter-relationship among arguments, (ii) occurrence probabilities are not always prior known, (iii) approaches for attribute weights do not consider interactions among attributes (iv) decision-makers are not completely rational. Thus, we present a decision-making approach in which incomplete probabilities are estimated using the Shannon entropy optimization model. A projection entropy-based Shapley value method is used to attain attribute weights. Heronian operator (HM) is extended under the PHFS environment to capture the inter-relationship among arguments. Considering the psychological behavior of decision-makers, final ranking is provided combining the merits of prospect and regret theory. Finally, the proposed framework is applied to a real case study from the medical field. Comparative analysis verifies the effectiveness, and the sensitivity analysis determines the stability of the proposed approach.

A new energy vehicle battery supplier selection using SWARA-MEREC-MARCOS approach under probabilistic triangular intuitionistic hesitant fuzzy environment

In this manuscript, we construct a Multi-Criteria Decision-Making (MCDM) model to study the new energy vehicle (NEV) battery supplier selection problem. Firstly, we select criteria to build an evaluation index system. Secondly, SAWARA and MEREC methods are used to calculate subjective and objective weights in the ranking process, respectively, and PTIHFS (Probabilistic Triangular Intuitionistic Hesitant Fuzzy Set) is employed to describe the decision maker’s accurate preferences in performing the calculation of subjective weights. Then, the game theory is used to find the satisfactory weights. We use TFNs to describe the original information in the MARCOS method to obtain the optimal alternative. Finally, a correlation calculation using Spearman coefficients is carried out to compare with existing methods and prove the model’s validity.

Research on Case Reasoning Multi-attribute Group Decision-making Method Based on Hesitant Fuzzy Set

In this study, a hesitant fuzzy set-based case-based reasoning integration method is proposed for the multi-attribute group decision-making problem with unknown attribute weights and mixed forms of attribute values. First, from two perspectives, traditional distance measure and information theory, a multi-objective optimization model is constructed using the distance similarity measure and information entropy of each type of attributes to determine the attribute weights. Secondly, considering the hybrid and nonlinear characteristics of case data, based on the principle of symmetric interaction entropy and TOPSIS method, a global similarity measure based on symmetric interaction entropy is proposed and a case inference algorithm suitable for hesitant fuzzy environment is designed. Finally, by analyzing the arithmetic cases of the target case in the case base, the most similar historical cases to the target case are retrieved to determine the decision-making scheme, and the practicality and feasibility of the decision-making method are verified. The results show that considering hesitant fuzzy theory for case-based reasoning research will help improve the accuracy and reliability of decision-making and provide more effective support for multi-attribute group decision management.

Evolution learning method to derive missing elements and optimal classification under the connection hesitant fuzzy environment

Generally, in the qualitative decision-making process, the attributes are independent of each other, thus the given attributes' evaluation data could ignore their connection relationships and make a decision based on incomplete information. To do this, this paper first introduces the hesitant fuzzy set (HFS), an emerging evaluation tool, to develop the connection HFS (CHFS). Furthermore, considering the missing-element situation, which is a normal phenomenon in the experts' subjective evaluation process, we extend the CHFS to the missing CHFS (M−CHFS). Thus, the M−CHFS can quantitatively express the connection relationship and missing-element characteristic simultaneously. Then, to derive the missing elements in the M−CHFS evaluation information, this paper proposes the hesitant fuzzy generative adversarial network to convert the M−CHFS to the CHFS according to a deep learning process. After that, we propose a hesitant fuzzy long short-term memory network to complete the evolution learning on the obtained CHFS and then get the classification results, occurrence probabilities, and optimal classification. Then, this paper develops an evolution learning algorithm introducing the decision makers' subjective guidance and applies it to an example of intelligent manufacturing analysis. The calculation process and derived results present the feasibility and effectiveness of the given methods in this paper.

Supplier selection for carbon emission reduction collaboration in green supply chain using an improved multi-criteria decision-making method

PurposePlatform-based enterprises, as micro-entities in the platform economy, have the potential to effectively promote the low-carbon development of both supply and demand sides in the supply chain. Therefore, this paper aims to provide a multi-criteria decision-making method in a probabilistic hesitant fuzzy environment to assist platform-type companies in selecting cooperative suppliers for carbon reduction in green supply chains.Design/methodology/approachThis paper combines the advantages of probabilistic hesitant fuzzy sets (PHFS) to address uncertainty issues and proposes an improved multi-criteria decision-making method called PHFS-DNMEREC-MABAC for aiding platform-based enterprises in selecting carbon emission reduction collaboration suppliers in green supply chains. Within this decision-making method, we enhance the standardization process of both the DNMEREC and MABAC methods by directly standardizing probabilistic hesitant fuzzy elements. Additionally, a probability splitting algorithm is introduced to handle probabilistic hesitant fuzzy elements of varying lengths, mitigating information bias that traditional approaches tend to introduce when adding values based on risk preferences.FindingsIn this paper, we apply the proposed method to a case study involving the selection of carbon emission reduction collaboration suppliers for Tmall Mart and compare it with the latest existing decision-making methods. The results demonstrate the applicability of the proposed method and the effectiveness of the introduced probability splitting algorithm in avoiding information bias.Originality/valueFirstly, this paper proposes a new multi-criteria decision making method for aiding platform-based enterprises in selecting carbon emission reduction collaboration suppliers in green supply chains. Secondly, in this method, we provided a new standard method to process probability hesitant fuzzy decision making information. Finally, the probability splitting algorithm was introduced to avoid information bias in the process of dealing with inconsistent lengths of probabilistic hesitant fuzzy elements.

A multi-attribute group decision making method based on novel distance measures and regret theory under probabilistic dual hesitant fuzzy sets

As a decision information preference which includes membership degree (MD), non-membership degree (NMD), and probability, the probabilistic dual hesitant fuzzy set (PDHFS) is a crucial tool for effectively expressing uncertain information. In the domains of multi-attribute decision making (MADM) and multi-attribute group decision making (MAGDM), distance measures are extremely helpful tools. In this study, a novel PDHFS distance measure is put out, on which a MAGDM method that takes decision-makers’ (DMs’) psychological behavior into account is proposed. First, a novel distance measure is put forward to effectively assess the difference between different PDHFSs by adding consideration of the distances between MDs and between NMDs. Second, a similarity-trust analysis method based on the new distance measure is employed to calculate expert weights for integrating group decisions, and the group satisfaction index and regret theory are extended to a probabilistic dual hesitant fuzzy information environment. A MAGDM method based on the novel distance measure and regret theory is proposed. Finally, the proposed method is applied to the selection of radiation protection strategies in nuclear power plants, and it is also determined through parametric analysis that DMs’ tendency to avoid regret has an impact on the outcomes of decisions. When the method proposed in this study is compared to existing approaches, the findings demonstrate that the method’s performance in resolving MAGDM issues in a PDHFS environment is superior.

A novel MCGDM technique based on correlation coefficients under probabilistic hesitant fuzzy environment and its application in clinical comprehensive evaluation of orphan drugs.

Probabilistic hesitant fuzzy sets (PHFSs) are superior to hesitant fuzzy sets (HFSs) in avoiding the problem of preference information loss among decision makers (DMs). Owing to this benefit, PHFSs have been extensively investigated. In probabilistic hesitant fuzzy environments, the correlation coefficients have become a focal point of research. As research progresses, we discovered that there are still a few unresolved issues concerning the correlation coefficients of PHFSs. To overcome the limitations of existing correlation coefficients for PHFSs, we propose new correlation coefficients in this study. In addition, we present a multi-criteria group decision-making (MCGDM) method under unknown weights based on the newly proposed correlation coefficients. In addition, considering the limitations of DMs' propensity to use language variables for expression in the evaluation process, we propose a method for transforming the evaluation information of the DMs' linguistic variables into probabilistic hesitant fuzzy information in the newly proposed MCGDM method. To demonstrate the applicability of the proposed correlation coefficients and MCGDM method, we applied them to a comprehensive clinical evaluation of orphan drugs. Finally, the reliability, feasibility and efficacy of the newly proposed correlation coefficients and MCGDM method were validated.

Three-way group decisions using evidence theory under hesitant fuzzy linguistic environment

In the actual decision-making process, there will be situations where decision-makers with hesitant attitudes have difficulties in evaluating alternatives numerically, and hesitant fuzzy linguistic term sets can provide decision-makers with an effective way to describe hesitancy in linguistic terms. In multi-attribute group decision-making, each decision maker typically holds different preferences. If the variation in decision makers’ assessment weights across evaluations of each attribute for every alternative is not adequately accounted for, it can result in a problem of coarse-grained calculations, leading to information loss. Additionally, the three-way decision model faces significant challenges in information fusion within the context of the hesitant fuzzy linguistic environment. Therefore, we propose a new three-way decision-making model under the hesitant fuzzy linguistic environment. The model obtains the confidence of different decision makers in attribute evaluations through the fusion of D-S evidence theory, and can perform more fine-grained fusion calculations on the evaluation information of different decision makers. In addition, the model considers the cost function of each alternative in different decision-making actions under hesitant fuzzy linguistic environment, calculates the two thresholds of each alternative in the three-way decision model, and derives the decision rules. The effectiveness of the model is verified through a numerical example and two comparative experiments, therefore, the model can be applied in intelligent classification or recommendation systems of hesitant fuzzy linguistic information systems.

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.

Site evaluation of subsea tunnels with sightseeing function based on dynamic complex MARCOS method

Subsea tunnels with sightseeing function (STSF) are valuable for integrating transportation across different locations, particularly in cross-sea regions. Given their technical complexity, significant capital commitment, and substantial social impact, site evaluation of STSF has become a critical priority. In this study, a dynamic complex measurement alternative and ranking according to the compromise solution (MARCOS) framework is proposed for STSF site evaluation in a Pythagorean hesitant fuzzy environment. A novel score function for a Pythagorean hesitant fuzzy set is defined to handle an incomparable problem. Moreover, a growth coefficient matrix is constructed to reflect the internal development potential of decision objects, considering changes in expert and criteria weights during the dynamic decision-making process. An STSF evaluation system is designed to satisfy stability, sociality, and economic developments. An empirical study is conducted in Zhejiang Province, China, to verify the robustness and effectiveness of the proposed evaluation framework by comparing its results with other methods.

Assessing the triage and efficacy of strategies of SAARC to improve regional integrity of South Asia using multicriteria group decision making under q-rung orthopair hesitant fuzzy environment

The South Asian Association for Regional Cooperation (SAARC) plays a crucial role in fostering regional integration and cooperation among the countries of South Asia. However, the organization faces various challenges in achieving its objectives due to the complex and dynamic nature of the region. This study aims to assess the triage and efficacy of strategies employed by SAARC in pursuit of regional integrity in South Asia, using a Multi-Criteria Group Decision Making (MCGDM) technique. The assessment process involves several uncertainties which are resolved using q-rung orthopair hesitant fuzzy (q-ROHF) set. A distance measure is developed for q-ROHF sets and is applied to find the best strategy among six well known strategies, viz., SAARC Agreement on Trade in Services (SATIS), SAARC Development Fund (SDF), Establishment of South Asian University (SAU), SAARC Arbitration Council (SARCO), South Asian Preferential Trade Agreement (SAPTA) and South Asian Free Trade Area (SAFTA) through SWARA-TOPSIS based MCGDM technique. The MCGDM method is updated by developing several aggregation operators, viz., Archimedean q-ROHF weighted average, q-ROHF Einstein weighted average, q-ROHF Hamacher weighted average, q-ROHF Frank weighted average along with their geometric forms to combine decision makers’ individual decision. The result shows that the most effective strategy for the economic integration of SAARC is SDF; SATIS comes next as best strategy for economic integration of SAARC. The study reveals that SAU has least impact on the regional economic integration of SAARC. The achieved results reveals the age old proverb that “play on the stomach and sit on the back” – the members of SAARC who are by nature economically poor can afford to take initiative for a successful effective regionalization if it is planned to bring socio economic development of themselves.

Basic uncertainty information hesitant fuzzy multi-attribute decision-making method with credibility

This study addresses the inadequacy of the current quantitative calculation method for decision-maker credibility in hesitant fuzzy multi-attribute decision-making, where credibility is considered. To overcome this limitation, a novel quantitative calculation method for decision-maker credibility is proposed based on the principles of basic uncertainty information theory under a hesitant fuzzy environment. Furthermore, a credible-based hesitant fuzzy multi-attribute decision model is developed. Initially, the paper introduces the concept of a basic uncertainty hesitant fuzzy set by combining basic uncertainty information theory with hesitant fuzzy set theory, thereby enhancing the understanding of basic uncertainty information theory within the realm of non-interval fuzzy information. Building on this foundation, the method for determining the hesitant degree of each element in the basic uncertainty hesitant fuzzy set is provided, followed by the proposed quantitative calculation method for decision-maker’s credibility under the hesitant fuzzy environment, which addresses the lack of a quantitative approach for assessing expert credibility under such circumstances. Subsequently, an attribute weight assignment method is introduced, considering the decision-maker’s credibility, leading to the formulation of a basic uncertainty hesitant fuzzy multi-attribute decision model based on credibility. This model enhances existing hesitant fuzzy multi-attribute decision-making methods that take credibility into account. To validate the proposed approach, the study applies it to the selection of new energy vehicle battery suppliers. The results of the analysis using actual data and sensitivity analysis demonstrate that decision-maker credibility can be quantitatively determined using the proposed method. Additionally, the basic uncertainty hesitant fuzzy multi-attribute decision-making model based on credibility effectively aids in supplier selection. The feasibility and stability of this method are verified through the examination of risk appetite coefficient and hesitancy coefficient.

Multi-attribute decision-making based on dual probabilistic interval-valued intuitionistic hesitant fuzzy weighted heronian mean aggregation operator

Probabilistic interval-valued intuitionistic hesitant fuzzy sets (PIVIHFSs) can well describe the evaluation information of decision-makers (DMs) in multi-attribute decision-making (MADM) problems. However, PIVIHFSs only depict the situation where both membership and non-membership information occur with equal probability while ignoring the situations of non-equal possibility due to DMs’ subjective preferences. In this paper, we develop dual probabilistic interval-valued intuitionistic hesitant fuzzy sets (DPIVIHFSs) concept based on the truncated normal distribution. The DPIVIHFSs overcome the shortcomings of PIVIHFSs and are more interpretable. Then, the operations and ranking method of DPIVIHFSs are introduced. Furthermore, we study MADM methods in dual probabilistic interval-valued intuitionistic hesitant fuzzy environments by aggregation operators (AOs). We propose a series of AOs including the DPIVIHF heronian mean (DPIVIHFHM) operator and the DPIVIHF weighted heronian mean (DPIVIHFWHM) operator. The basic properties of the presented are discussed and proved. Finally, a novel method for solving the MADM problem is proposed based on the DPIVIHFWHM operator and a numerical example of express company selection strategy is used to illustrate the effectiveness of the method. The proposed method in this article can capture more fuzzy and uncertain information when solving MADM problems and have a wider application range.