Dual Hesitant Fuzzy Research Articles

Toward Sustainable Transportation: A Pavement Strategy Selection Based on the Extension of Dual-Hesitant Fuzzy Multicriteria Decision-Making Methods

Pavement strategy is critical for achieving sustainable transportation. However, the presence of many evaluation criteria, criteria tradeoffs, criteria conflict, and criteria importance categorize the evaluation and selection of pavement strategies under complex multicriteria decision-making (MCDM) problems. To date, no study has presented an evaluation framework for selecting the most optimal pavement strategy to be utilized as a way to achieve sustainable transportation considering multicriteria evaluation of pavement strategies and sustainable solutions. This article presents a pavement strategy selection based on a new extension of fuzzy MCDM methods. The methodology is developed in two phases. First, the evaluation decision matrix is formulated on the basis of intersecting the “evaluation criteria” and “pavement strategies list.” Second, the proposed MCDM methods are developed: multilayer dual hesitant fuzzy weighted zero inconsistency (DH-FWZIC) to assign weights to the pavement's evaluation criteria followed by dual hesitant fuzzy decision by opinion score method (DH-FDOSM) for selecting the best pavement strategy. Four alternatives, namely, flexible/asphalt, rigid/concrete, reflective, and permeable alternatives pavement strategies, are evaluated on the basis of 30 criteria. Results show the following. 1) The multilayer DH-FWZIC method has weighted the pavement strategies’ evaluation criteria at three layers in a consistent manner, showing that a region's environment criterion has the highest final weight (0.1215) and the lowest importance value (0.0089) assigned for its windy criterion. 2) According to DH-FDOSM, the flexible/asphalt pavement achieved the first rank among the four pavement strategies. Finally, the robustness of the developed framework was assessed by conducting sensitivity analysis and comparison study.

Ranking Objects from Individual Linguistic Dual Hesitant Fuzzy Information in View of Optimal Model-Based Consistency and Consensus Iteration Algorithm

Ranking Objects from Individual Linguistic Dual Hesitant Fuzzy Information in View of Optimal Model-Based Consistency and Consensus Iteration Algorithm

Hesitant Bifuzzy Set (an introduction): A new approach to assess the reliability of the systems

All the available knowledge related to the Fuzzy Sets (FS) is constricted to express the circumstances when the sum of the degrees of membership and non-membership of any element exceeds one. To keep in mind that in real life there are many ill-defined or too inordinately complex situations, in this article, we propose the concept of Hesitant Bifuzzy Set (HBFS), which appraises Fuzzy Set (FS), Intuitionistic Fuzzy Sets (IFS), Hesitant Fuzzy Set (HFS), Conflicting Bifuzzy Set (CBFS) and Dual Hesitant Fuzzy Set (DHFS) as particular cases. Here we discuss the fundamental operations along with the basic properties of HBFSs. A descriptive example is used to illustrate the proposed concept and method. The supremacy of this study is that all the existing methods only provide the reliability of the system in the form of a fuzzy element while the method introduced in this study always provides a crisp value for the reliability of the system.

CODAS Method for Multi-Attribute Decision-Making Based on Some Novel Distance and Entropy Measures Under Probabilistic Dual Hesitant Fuzzy Sets

CODAS Method for Multi-Attribute Decision-Making Based on Some Novel Distance and Entropy Measures Under Probabilistic Dual Hesitant Fuzzy Sets

A novel MADM technique based on extended power generalized Maclaurin symmetric mean operators under probabilistic dual hesitant fuzzy setting and its application to sustainable suppliers selection

Sustainable suppliers selection is a typical multi-attribute decision-making (MADM) problem. MADM is a common problem in the field of decision-making, which is full of uncertainty and fuzziness. As a novel extension of fuzzy set (FS), probabilistic dual hesitant fuzzy set (PDHFS) can more fully and comprehensively express the uncertain and fuzzy information in MADM problems. In order to more effectively integrate the information of PDHFS, in this study, depend on extended power average (EPA) and generalized Maclaurin symmetric mean (GMSM) operators, probabilistic dual hesitant fuzzy extended power average generalized Maclaurin symmetric mean (PDHFEPMSM) operator and its weighted form (PDHFWEPMSM) which can consider the extremely data and the interrelationship among all decision attributes are defined and studied. Evidently, the novel proposed operators can obtain more accurate results than other existing methods. In addition, some precious properties and some special cases of these operators are discussed and studied. Afterwards, a novel PDHF MADM technique is developed based on the PDHFWEPGMSM and applied to MADM problem with probabilistic dual hesitant fuzzy elements (PDHFEs). Finally, a numerical example of sustainable suppliers selection is built to illustrate the practicality of the proposed MADM technique. Sensitivity analysis of parameters and further comparative analysis attest the flexibility and validity of the proposed MADM technique. The method presented in this paper can effectually solve the MADM problems which the decision-making information is expressed by PDHFEs and the attributes are interactive.

A genetic algorithm based on dual hesitant fuzzy preference relations for consensus group decision making

Consensus is an important issue in group decision making as it aims to avoid future contestation by the decision makers. The elicitation of criteria and decision makers’ weights is an essential part of decision-making problems. This study proposes a new consensus model for group decision making based on dual hesitant fuzzy and evolutionary algorithm for the definition of unknown criteria and decision makers’ weights. The Dual Hesitant Fuzzy Preference Relations combines the advantages of intuitionistic and hesitant fuzzy representations, and it is used to deal with the imprecision in decision makers’ judgments. In order to find decision makers weights to reach a better level of consensus without the need to modify initial assessments, the proposed Genetic Algorithm (GA) is applied. An illustrative application case is presented in a large steel company considering sustainable criteria. An instance generator was proposed to create different scenarios of decision making varying the number of criteria, decision makers, and level of hesitation. Several instances were used in the computational tests for the evaluation of the GA performance. The effectiveness of the proposed GA was verified by comparing its results with the results of the implemented Particle Swarm Optimization (PSO) algorithm. The GA yielded solutions with improved consensus levels in a reasonable runtime, especially for a small or medium number of decision makers.

A Novel Decision-Making Method for Selecting Superintendent Based on a Q-Rung Dual Hesitant Fuzzy Power Partitioned Bonferroni Mean Operator

The Q-rung dual hesitant fuzzy (q-RDHF) set is famous for expressing information composed of asymmetry evaluations, because it allows for several possible evaluations in both the membership degree and non-membership degree. Compared with some existing extended fuzzy theories, the q-RDHF set is more superior and flexible because it can handle asymmetric assessments. In order to assemble the evaluation information expressed by q-RDHF elements, this paper aims to propose new operators to integrate q-RDHF elements. The partitioned Bonferroni mean (PBM) operator is well-known for its advantages in coping with the inhomogeneous relationship between asymmetry input arguments. In this paper, we combine the PBM operator with the power average operator, and propose a family of q-RDHF power PBM operators. Some theorems and special cases for the new proposed operators are discussed. Furthermore, we provide a general framework for dealing with multiple attribute decision-making (MADM) problems using the novel proposed method. To better show the calculation details, a numerical case study of the application of the proposed method in a superintendent selection problem is introduced. In addition, we utilize the proposed method to compare it with some existing methods in order to show its flexibility and superiority. The results show that our method is much more advantageous when considering flexible actual situations. Finally, the conclusion is given. The main contributions of this study are to propose an appropriate method to solve unbalanced and asymmetry information in a q-RDHF environment, and to apply it into a realistic superintendent selection problem.

A Novel q-Rung Dual Hesitant Fuzzy Multi-Attribute Decision-Making Method Based on Entropy Weights.

In this paper, a new multiple attribute decision-making (MADM) method under q-rung dual hesitant fuzzy environment from the perspective of aggregation operators is proposed. First, some aggregation operators are proposed for fusing q-rung dual hesitant fuzzy sets (q-RDHFSs). Afterwards, we present properties and some desirable special cases of the new operators. Second, a new entropy measure for q-RDHFSs is developed, which defines a method to calculate the weight information of aggregated q-rung dual hesitant fuzzy elements. Third, a novel MADM method is introduced to deal with decision-making problems under q-RDHFSs environment, wherein weight information is completely unknown. Finally, we present numerical example to show the effectiveness and performance of the new method. Additionally, comparative analysis is conducted to prove the superiorities of our new MADM method. This study mainly contributes to a novel method, which can help decision makes select optimal alternatives when dealing with practical MADM problems.

A Novel Multi-attribute Group Decision-Making Method Based on q-Rung Dual Hesitant Fuzzy Information and Extended Power Average Operators

A Novel Multi-attribute Group Decision-Making Method Based on q-Rung Dual Hesitant Fuzzy Information and Extended Power Average Operators

Z-Score Functions of Dual Hesitant Fuzzy Set and Its Applications in Multi-Criteria Decision Making

Dual hesitant fuzzy set (DHFS) consists of two parts: membership hesitant function and non-membership hesitant function. This set supports more exemplary and flexible access to set degrees for each element in the domain and can address two types of hesitant in this situation. It can be considered a powerful tool for expressing uncertain information in the decision-making process. The function of z-score, namely z-arithmetic mean, z-geometric mean, and z-harmonic mean, has been proposed with five important bases, these bases are hesitant degree for dual hesitant fuzzy element (DHFE), DHFE deviation degree, parameter α (the importance of the hesitant degree), parameter β (the importance of the deviation degree) and parameter ϑ (the importance of membership (positive view) or non-membership (negative view). A comparison of the z-score with the existing score function was made to show some of their drawbacks. Next, the z-score function is then applied to solve multi-criteria decision making (MCDM) problems. To illustrate the proposed method's effectiveness, an example of MCDM specifically in pattern recognition has been shown.

A Novel Approach of Complex Dual Hesitant Fuzzy Sets and Their Applications in Pattern Recognition and Medical Diagnosis

Complex dual hesitant fuzzy set (CDHFS) is an assortment of complex fuzzy set (CFS) and dual hesitant fuzzy set (DHFS). In this manuscript, the notion of the CDHFS is explored and its operational laws are discussed. The new methodology of the complex interval-valued dual hesitant fuzzy set (CIvDHFS) and its necessary laws are introduced and are also defensible with the help of examples. Further, the antilogarithmic and with-out exponential-based similarity measures, generalized similarity measures, and their important characteristics are also developed. These similarity measures are applied in the environment of pattern recognition and medical diagnosis to evaluate the proficiency and feasibility of the established measures. We also solved some numerical examples using the established measures to examine the reliability and validity of the proposed measures by comparing these with existing measures. To strengthen the proposed study, the comparative analysis is made and it is conferred that the proposed study is much more superior to the existing studies.

Ancient Chinese Character Image Retrieval Based on Dual Hesitant Fuzzy Sets

The complex and changeable structures of ancient Chinese characters result in the decreasing accuracy of their image retrieval. To resolve this problem, a new retrieval method based on dual hesitant fuzzy sets is proposed. Dual hesitation fuzzy sets that can express uncertain information more comprehensively are employed in the feature extraction process of directional line elements. The multiattribute evaluation index of adjacent grids for the current grid and its corresponding membership and nonmembership functions are established, and the weight of each attribute is calculated by the dual hesitation fuzzy entropy, such that the proposed features can fully reflect the topological structure of ancient Chinese characters. Using the dual hesitation fuzzy correlation coefficient to measure the similarity between the ancient Chinese character images to be retrieved and the candidate images, the retrieval of ancient Chinese character images is realized. Experiments show that when the t0hreshold value of the correlation coefficient is 0.9, the average retrieval accuracy is 90.4%.

Risk prioritization based on the combination of FMEA and dual hesitant fuzzy sets method

Paper aims This paper proposes the combination of the quality tool FMEA (Failure Modes Effects and Analysis) with the DHFS (Dual Hesitant Fuzzy sets) technique to process judgements with hesitation and hence conduct the prioritization of failure modes considering a group decision making problem. Originality There are no studies that combine the FMEA tool with the DHFS technique. Research method Firstly, this paper presents a review of the current FMEA literature. Then, the group decision model is presented combining the FMEA and the DHFS. Finally, an illustrative example in the context of supplier failure modes is brought to guide future applications of the proposal. Main findings The paper presents a model that combines the FMEA tool with the DHFS. It allows considering different risk factors weights in a group decision process with experts from several areas. The model is also able to deal with the different types of hesitations present in the judgements. Implications for theory and practice The traditional FMEA does not deal with individual judgments of different decision makers. The new proposal can be easily applied in different contexts of potential failure modes analysis considering different types of hesitation in group decision making, such as medical and humanitarian.

MAGDM-oriented dual hesitant fuzzy multigranulation probabilistic models based on MULTIMOORA

In real world, multi-attribute group decision making (MAGDM) is a complicated cognitive process that involves expression, fusion and analysis of multi-source uncertain information. Among diverse soft computing tools for addressing MAGDM, the ones from granular computing (GrC) frameworks perform excellently via efficient strategies for multi-source uncertain information. However, they usually lack convincing semantic interpretations for MAGDM due to extreme information fusion rules and instabilities of information analysis mechanisms. This work adopts a typical GrC framework named multigranulation probabilistic models to enrich semantic interpretations for GrC-based MAGDM approaches, and constructs MAGDM-oriented multigranulation probabilistic models with dual hesitant fuzzy (DHF) information in light of the MULTIMOORA (Multi-Objective Optimization by Ratio Analysis plus the full MULTIplicative form) method. After reviewing several basic knowledge, we first put forward four types of DHF multigranulation probabilistic models. Then, according to the MULTIMOORA method, a DHF MAGDM algorithm is designed via the proposed theoretical models in the context of person-job (P-J) fit. Finally, an illustrative case study for P-J fit is investigated, and corresponding validity tests and comparative analysis are conducted as well to demonstrate the rationality of the presented models.

Jaccard and Dice Similarity Measures Based on Novel Complex Dual Hesitant Fuzzy Sets and Their Applications

Complex dual hesitant fuzzy set (CDHFS) is a combination of two modifications, called complex fuzzy set (CFS) and dual hesitant fuzzy set (DHFS). CDHFS makes two degrees, called membership valued and nonmembership valued in the form of a finite subset of a unit disc in the complex plane, and is a capable method to solve uncertain and unpredictable information in real-life problems. The goal of this study is to describe the notion of CDHFS and its operational laws. The novel approach of the complex interval-valued dual hesitant fuzzy set (CIvDHFS) and its fundamental laws are also described and defended with the help of an example. Further, the vector similarity measures (VSMs), weighted vector similarity measures (WVSMs), hybrid vector similarity measure, and weighted hybrid vector similarity measure are additionally explored. These similarity measures (SM) are applied to the environment of pattern recognition and medical diagnosis to assess the capability and feasibility of the interpreted measures. We additionally solved some numerical examples utilizing the established measures. We examine the dependability and validity of the proposed measures by comparing them with some existing measures. The advantages, comparative analysis, and graphical portrayal of the investigated interpreted measures and existing measures are additionally described in detail.

Fuzzy Reliability Based on Hesitant and Dual Hesitant Fuzzy Set Evaluation

In this study, we calculate hesitant and dual hesitant fuzzy reliability of linear and circular consecutive 2-out-of-4:G system from reliability function and Weibull distribution. After that, we introduced some basic methods for investigating the fuzzy reliability in the form of upper and lower membership and non- membership function having an aggregation operator with equal weights. At last, two numerical examples are also illustrated with the considered technique.

Multiple Criteria Decision-Making Based on Vector Similarity Measures under the Framework of Dual Hesitant Fuzzy Sets

Similarity measures have a great importance in the decision-making process. In order to identify the similarity between the options, many experts have established several types of similarity measures on the basis of vectors and distances. The Cosine, Dice, and Jaccard are the vector similarity measures. The present work enclosed the modified Jaccard and Dice similarity measures. Founded on the Dice and Jaccard similarity measures, we offered a multiple criteria decision-making (MCDM) model under the dual hesitant fuzzy sets (DHFSs) situation, in which the appraised values of the alternatives with respect to criteria are articulated by dual hesitant fuzzy elements (DHFEs). Since the weights of the criteria have a much influence in making the decisions, therefore decision makers (DMs) allocate the weights to each criteria according to their knowledge. In the present work, we get rid of the doubt to allocate the weights to the criteria by taking an objective function under some constraints and then extended the linear programming (LP) technique to evaluate the weights of the criteria. The Dice and Jaccard weighted similarity measures are practiced amongst the ideal and each alternative to grade all the alternatives to get the best one. Eventually, two practical examples, about investment companies and selection of smart phone accessories are assumed to elaborate the efficiency of the proposed methodology.

New Similarity Measures for Dual Hesitant Fuzzy Sets and Their Application

Dual hesitant fuzzy sets (DHFSs) are powerful and efficient to express hesitant preferred and non-preferred information simultaneously. This paper focuses on similarity measures for DHFSs. To do this, it first analyzes the limitations of previous similarity measures for DHFSs. Then, several new dual hesitant fuzzy similarity measures are defined that can avoid the issues of previous ones. To discriminate the importance of decision-making criteria, several weighted similarity measures are further defined in views of additive and 2-additive measures. When the weighting information is not exactly known, optimization methods for determining additive and 2-additive measures are built, respectively. Furthermore, a method for multi-criteria decision-making based on new weighted similarity measures is developed. Finally, two numerical examples are provided to show the utilization of the new method and compare with previous methods.

Multiple Attribute Group Decision-Making Based on Power Heronian Aggregation Operators under Interval-Valued Dual Hesitant Fuzzy Environment

In this paper, we focus on new methods to deal with multiple attribute group decision-making (MAGDM) problems and a new comparison law of interval-valued dual hesitant fuzzy elements (IVDHFEs). More explicitly, the interval-valued dual hesitant fuzzy 2nd-order central polymerization degree (IVDHFCP2) function is introduced, for the case that score values of different IVDHFEs are identical. This function can further compare different IVDHFEs. Then, we develop a series of interval-valued dual hesitant fuzzy power Heronian aggregation operators, i.e., the interval-valued dual hesitant fuzzy power Heronian mean (IVDHFPHM) operator, the interval-valued dual hesitant fuzzy power geometric Heronian mean (IVDHFPGHM) operator, and their weighted forms. Some desirable properties and their special cases are discussed. These proposed operators can simultaneously reflect the interrelationship of aggregated arguments and reduce the influence of unreasonable evaluation values. Finally, two approaches for interval-valued dual hesitant fuzzy MAGDM with known or unknown weight information are presented. An illustrative example and comparative studies are given to verify the advantages of our methods. A sensitivity analysis of the decision results is analyzed with different parameters.

Dual hesitant fuzzy graphs with applications to multi-attribute decision making

In real world, there exist a kind of Multi-Attribute Decision Making (MADM) problems in which correlations and prioritization relationships of attributes can be found. The notion of Fuzzy Graphs (FGs) performs well when expressing correlations between attributes via edges between vertices in fuzzy information systems, which makes it possible for addressing correlational MADM problems. In addition, as a significant information depiction tool, Dual Hesitant Fuzzy Sets (DHFSs) generalize traditional Intuitionistic Fuzzy Sets (IFSs) to the context of hesitations, thus DHFSs excel in recording numerous imprecise and hesitant information. In this paper, we aim to investigate FGs in the Dual Hesitant Fuzzy (DHF) background and further explore efficient approaches to complicated MADM situations. Following the above motivation, we first develop the definition of Dual Hesitant Fuzzy Graphs (DHFGs). Then, some common operational laws and mapping relationships are put forward. Afterwards, we construct a two-stage MADM approach by means of DHFGs for addressing complicated MADM situations with correlations and prioritization relationships. At last, a realistic case study along with a comparative analysis is presented to show the applicability of the established methodology. The proposed model and approach are conducive to addressing DHF MADM problems that are characterized by correlations and prioritization relationships between attributes at the same time, and further enrich the family of DHF MADM methods to a large extent.