Hesitant Fuzzy Preference Relations Research Articles

Two-stage group decision making methodology with hesitant fuzzy preference relations under social network: Multiplicative consistency determination and personalized feedback

Some social network group decision making (SNGDM) researches may overlook two issues: (1) the impact of consistency on decision reliability and decision makers’ (DMs’) status in social network, and (2) DMs’ personalization during consensus reaching process. In response to these two issues, a two-stage SNGDM model is proposed for hesitant fuzzy preference relations (HFPRs). In the first stage, multiplicative consistency determination and improvement of HFPRs are achieved. For complete and incomplete HFPRs, several programming models are constructed to classify consistency types. When it comes to inconsistent HFPRs, an inconsistency fixing method is designed to ensure the original HFPRs as much as possible. With the improvement of DMs’ consistency, their status in social network will be dynamically enhanced. In the second stage, two programming models are devised to elicit the reasonable individual priority weight vector in consistent HFPR. Further, minimum adjustment cost-based personalized feedback mechanism is invented to attain the optimal personalized adjustment coefficient and recommendation, and achieve the harmonious unity of individual personalization and group consensus. Finally, the superiority of our proposal is verified by comparative analysis and illustrative example.

Cooperative Games for Group Decision Making Under Undirected Collaboration Network With Hesitant Fuzzy Preference Relations

Cooperative Games for Group Decision Making Under Undirected Collaboration Network With Hesitant Fuzzy Preference Relations

Consistency and consensus checking and improving methods for group decision-making with hesitant fuzzy preference relations

Decision-makers (DMs) are often hesitant about the evaluations owing to objective or subjective reasons, and determined preference relations always have various limitations on the way that DMs express their evaluations. To address this, this study investigates the group decision-making (GDM) process with hesitant fuzzy preference relations (HFPRs), and develops the methods of consistency and consensus checking and improving processes. To do this, the definitions of best consistency index (BCI) and worst consistency index (WCI) are given. On account of this, the concept of acceptable additive consistent HFPR is proposed. Moreover, the methods of consistency and consensus measurement and improvement processes are introduced for GDM with HFPRs, which can automatically obtain effective and scientific consistency and consensus results. Furthermore, a priority method for HFPRs is employed to rank the alternatives. The procedure of the GDM problem with HFPRs is introduced in detail, and an example of selecting a potential supplier for a solar company is used to demonstrate the proposed method. Comparative analyses shows that the proposed method is more powerful for dealing with the hesitant and uncertain situations and greatly expands the information description scope.

The Ordinal Consistency of a Hesitant Fuzzy Preference Relation

An efficient solution to the misleading solutions of decision-making problems is the study of consistency when the decision makers express their opinions by means of fuzzy preference relations. To elucidate the consistency of HFPRs, the S-ordinal consistency of HFPRs was proposed, and S-OCI was also proposed to evaluate the degree of consistency of a hesitant fuzzy preference relation by calculating the unreasonable 3-cycles in the directed graph. Two novel methods were also proposed for calculation of the S-OCI. Moreover, the inconsistent judgment in hesitation fuzzy preference relation was developed. In order to repair the inconsistency of a hesitant fuzzy preference relation, an algorithm for finding and removing 3-cycles in digraph was developed. Finally, some illustrative examples were given to prove the effectiveness of the method.

An efficiency-based interactive dynamic technique with interval-valued hesitant fuzzy constraint cone for rescue route planning

This paper develops an efficiency-based interactive dynamic technique to design the post-disaster rescue route by combining the data envelopment analysis (DEA), traveling salesman problem (TSP) and interval-valued hesitant fuzzy constraint cone (IVHFCC). The traditional DEA potentially presumes that the weights of the input (output) criteria are unrestricted, resulting in its inapplicability to some complex decision problems. To restrict the weights of input (output) criteria legitimately, this paper constructs an IVHFCC based on expert’s subjective preferences in the form of interval-valued hesitant fuzzy sets. This paper defines the additive consistent normal interval-valued hesitant fuzzy preference relation (NIVHFPR) and analyses its desirable properties. Based on these properties, three linear programming models are proposed to repair the incomplete NIVHFPR, judge the additive consistency of the repaired NIVHFPR and generate the additive consistent NIVHFPR. By incorporating the TSP, DEA and the constructed IVHFCC, an efficiency-based interactive dynamic model is originally proposed to generate the optimal rescue route for the rescue team. Some desirable properties of this efficiency-based interactive dynamic model are analyzed. The validity of this model is demonstrated with a real post-disaster rescue route planning problem of Wenchuan earthquake. Some comparative analyses are provided to show the superiorities of the proposed technique.

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.

A CVaR optimization method for priority of hesitant fuzzy preference relation with chance constraint

In this paper, we establish a chance constrained model for the priority of hesitant fuzzy preference relation based on the idea of statistical distribution for preference information as stochastic variables with unknown distribution. Inspired by the idea of conditional value-at-risk (CVaR) robust optimization, a deterministic convex reformulation is proposed for tackling the chance constrained problem. The existing state-of-the-art methods usually assume that the probability density function of preference information is known a priori, such as Gaussian distribution. However, it is generally over-conservatism. On the contrary, our proposed method provides a tractable second-order cone (SOC) reformulation for the chance constrained problem with the first and second moments, which is easy to handle and calculate. We also analyze the weight acquisition problem of hesitant fuzzy preference relation with unknown distribution preference using the SOC programming method, and obtain the priority weight with its approximately equivalent computationally tractable conic optimization model. A case study is conducted which shows that the proposed method achieves a good general conclusion by comparing it with the optimization method under Gaussian distribution. In addition, this method can also get better decision support for incomplete preference information.

FMEA Assessment Under Heterogeneous Hesitant Fuzzy Preference Relations: Based on Extended Multiplicative Consistency and Group Decision Making

Failure mode and effects analysis (FMEA) is a reliability analysis method that analysis all possible failure modes for each product in a system and all possible effects of failure modes on the system, to classify each failure mode and to propose solutions and preventative measures. It is undeniable that the traditional FMEA method has been widely criticized for its simple scoring and single algorithm. To improve the usability of FMEA, hesitation fuzzy preference relation sets (HFPRs) based on hesitant fuzzy sets have been introduced into FMEA research because of their good fuzziness and uncertainty properties. Most existing consistency-based algorithms for HFPR processing, however, do not consider the possible coherence deviation of the reluctant fuzzy set itself, which includes multiplicative consistency (MC) theory, which will result in the reduced accuracy of results from such algorithms, in addition to not supporting group decision-making well in heterogeneous environments. At the same time, when building a group consensus, constantly adjusting HFPRs through group decision feedback can easily lead to conservative or radical scoring by experts. Therefore, an excellent hybrid FMEA assessment method is studied in this paper. In this approach, an extended multiplicative consistency equation is constructed by extending the applicability of MC in the treatment of HFPR, and on this basis, a mathematical model with the ability to deal with sets of heterogeneous fuzzy preference relations (H-HFPRs) is constructed. Lastly, based on the predictability principle of the occurrence level (O), a scoring correction algorithm is constructed based on group consensus theory to reduce the conservative or aggressive bias of the expert group in the results. The new method was used in the risk assessment of Change oilfield subsea pipeline engineering, and the results were compared with several existing methods to verify the effectiveness and advancement of the proposed method.

A Consensus Model for Group Decision Making with Hesitant Fuzzy Information

This article presents a more improved consensus-based method for dealing with multi-person decision making (MPDM) that uses hesitant fuzzy preference relations (HFPRís) that arenít in the usual format. We proposed a Lukasiewicz transitivity (TL-transitivity)-based technique for establishing normalised hesitant fuzzy preference relations (NHFPRís) at the most essential level, after that, a model based on consensus is constructed. After that, a transitive closure formula is created in order to build TL -consistent hesitant fuzzy preference relations (HFPRís) and symmetrical matrices. Afterwards, a consistency analysis is performed to determine the degree of consistency of the data given by the decision makers (DMs), as a result, the consistency weights must be assigned to them. After combining consistency weights and preset(predeÖned) priority weights, the Önal priority weights vector of DMs is obtained (if there are any). The consensus process determines either data analysis and selection of a suitable alternative should be done directly or externally. The enhancement process aims to improve the DMís consensus measure, despite the implementation of an indicator for locating sluggish points, in the circumstance that an unfavorable agreement is achieved. Finally, a comparison case demonstrates the relevance and e§ectiveness of the proposed system. The conclusions indicate that the suggested strategy can provide insight into the MPDM system.

A consensus algorithm based on the worst consistency index of hesitant fuzzy preference relations in group decision-making

This paper mainly solves the individual consistency and group consensus in the decision-making with hesitant fuzzy preference relations (HFPRs). The worst consistency index (WCI) is used to measure the individual consistency level. The envelop of an HFPR called envelop of HFPR (EHFRP) is proposed in the consensus reaching process (CRP). Two algorithms are proposed: one is to improve the WCI, in which only one pair of elements are revised in the consistency improving process each time, which aims to preserve the decision makers’ (DMs’) original information as much as possible. Another algorithm is proposed to improve the consensus in the CRP. To aggregate individual EHFPRs into one group HFPR, a new induced ordered weighted averaging (IOWA) operator is presented, called envelope HFPR-IOWA (EHFPR-IOWA), which allows the experts' preference to be aggregated in such a way that the most consistent ones are given more weight. Finally, an illustrative example and comparisons with the existing methods are provided to show the effectiveness of the proposed method.

An Interactive Consensus Model in Group Decision Making with Heterogeneous Hesitant Preference Relations

This paper proposes an interactive consensus reaching model in the group decision making for heterogeneous hesitant preference relations (i.e., hesitant fuzzy preference relations, hesitant multiplicative preference relations, hesitant fuzzy linguistic preference relations). First, the consistencies of three hesitant preference relations are defined, respectively. Then, based on their definitions, three optimization models are constructed to obtain the weight vector of alternatives, based on which an interactive consensus adjustment algorithm is established based on the direct consensus framework. This framework adopts feedback mechanism to facilitate the information correction of decision makers. After several rounds of adjustment, the decision results with satisfactory consensus level are achieved. Finally, the practicability and effectiveness of the model are illustrated through a case study of mine accident emergency decision making.

A Similarity-Based Hesitant Fuzzy Group Decision Making Approach and Its Application in Hydraulic Engineering Project Management

Hesitancy and uncertainty features of experts are common in the decision-making process, especially for the project management events. To solve this problem, a novel similarity-based decision-making approach is put forward, as well as an application to the hydraulic engineering project management. Several experts, who are invited in the decision-making process, are suggested to adopt hesitant fuzzy preference relations (HFPRs) to show their evaluations. To measure the similarity degree of experts, a novel integrated similarity index (SI) is given combining the alternative ranking-based similarity index (SIAR) and distance-based similarity index (SID) between HFPRs. The SIAR can be derived from the comparison of the alternative rankings, while the SID depends on evaluations’ distance degree. After that, on the basic of opinion transition probabilities, experts’ weights are allocated, which is necessary for the aggregation process. Then, the collective preferences can be aggregated from the individuals’ evaluations. Afterwards, the above methods along with a score function are adopted to obtain the optimal solution for an actual hydraulic engineering project management event. Finally, for verifying the feasible and effective features of the presented methods, some significative discussions and comparative analyses are provided.

Verifying and managing additive consistency and deriving weights for hesitant fuzzy preference relations

Hesitant fuzzy preference relation (HFPR) is a valid tool to describe the hesitation, ambiguity and uncertainty of decision makers. As a crucial criterion to ensure the rationality of preferences and final decision results, the consistency of preference relations is a valuable research topic. In this study, the additive consistency of HFPRs is investigated. Two kinds of consistency, completely additive and weakly additive, for HFPRs are introduced. Some 0–1 mixed programming models and simple algebraic operations are developed to detect the additive consistency type for HFPRs. Further, the priority weights of a consistent HFPR can be derived by constructing and solving two linear programming models. If an HFPR is identified to be inconsistent, we present a straightforward method to rectify inconsistency. Then, an integrated algorithm is proposed to ascertain the additive consistency type, improve consistency and rank alternatives. Finally, the applicability and validity of this proposal are verified through a case study, discussion and comparative analysis with the existing methods.

Consensus checking and improving methods for AHP with q-rung dual hesitant fuzzy preference relations

Decision makers (DMs) are often hesitant about the evaluations for subjective or objective reasons, and established preference relations always have various limitations on the way that DMs express themselves. Aiming at investigating the consensus reaching process where DMs needs more decision freedom, this study proposes a novel decision support model for AHP with q-rung dual hesitant fuzzy preference relations (q-RDHFPRs). To do this, we give the definition of q-RDHFPRs and explore the corresponding operational rules. On account of this, we propose a family of algorithms to check and improve consistency and consensus of q-RDHFPRs, which can automatically obtain scientific and effective consensus results. Moreover, a priority method for q-RDHFPRs is proposed to rank the alternatives. The procedure of the q-RDHF-AHP is given in detail, and the example of risk evaluation of Hospital-acquired infections is employed to demonstrate our results. Comparative analyses show that the proposed q-RDHF-AHP method is more powerful for coping with the hesitant and uncertain situations and greatly expands the information description scope of the method.

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.

Decision-making models based on satisfaction degree with incomplete hesitant fuzzy preference relation

To address the situation where incomplete hesitant fuzzy preference relation (IHFPR) is necessary, this paper develops decision-making models taking into account decision makers’ satisfaction degree. First, the consistency measures, respectively, from the perspectives of additive and multiplicative consistent IHFPR are defined, which is based on the relationships of the IHPFRs and their corresponding priority weight vector. Second, two decision-making models are developed, respectively, in view of the proposed additive and multiplicative consistency measures. The main characteristic of the constructed models is they taking into account the decision makers’ satisfaction degree. The objective functions of the models are developed by maximizing the parameter of the satisfaction degree. Third, a square programming model is developed to obtain the decision makers’ weights by utilizing the optimal priority weight vectors information, the solution of the model is obtained by solving the partial derivatives of Lagrange function. Finally, a procedure for multi-criteria decision-making (MCDM) problems with IHFPRs is given, and an illustrative example in conjunction with comparative analysis is used to demonstrate the proposed models are feasible and efficiency for practical MCDM problems.

Group decision making method with hesitant fuzzy preference relations based on additive consistency and consensus

To address the situation where the multi-criteria decision making (MCDM) has problems with hesitant fuzzy preference relations (HFPRs), this paper develops a group decision making method considering the additive consistency and consensus simultaneously. First, a new normalized method for HFPRs is developed to address the situation where the evaluation information has different number of elements. Second, for improving the unacceptable consistent HFPRs, an algorithm is designed to derive acceptable consistent HFPRs. The main characteristic of the design algorithm is that the values that need to be revised are identified first, and then design the local adjustment process. Third, an algorithm is developed to obtain a group of normalized HFPRs (NHFPRs), considering the additive consistency of HFPRs. Fourth, for improving the individual consistency and group consensus simultaneously, an algorithm is designed to obtain a group of HFPRs with acceptable consistency and consensus. Finally, the method of determining the decision makers’ weights and a procedure for MCDM problems with HFPRs are given. An illustrative example in conjunction with comparative analysis is used to demonstrate the proposed method which is feasible and efficient for practical MCDM problems.

Social network clustering and consensus-based distrust behaviors management for large-scale group decision-making with incomplete hesitant fuzzy preference relations

With the development of social network platforms, large-scale group decision-making in social network (LSGDM-SN) has been formed. As decision makers (DMs) come from different fields and have complex individual backgrounds, which leads to their distrust in the moderator. Moreover, in LSGDM-SN, since DMs can hardly grasp all the information about the decision problem, the hesitant fuzzy preference relations (HFPRs) they have expressed may be incomplete. However, in current LSGDM-SN issues, the distrust behaviors and incomplete HFPRs have never been discussed simultaneously. In this context, this paper aims to propose a method to estimate incomplete values in HFPRs, and develop a consensus management process which considers distrust behaviors. This paper focuses on LSGDM-SN on the basis of social network clustering and consensus-based distrust behaviors management with incomplete HFPRs. In this paper, a social network clustering method based on grey clustering algorithm is proposed to classify the DMs with similar social clustering degree into a subset. Afterwards, a method including two situations is developed to estimate incomplete values in HFPRs. Furthermore, an identification mechanism is presented to detect the DMs’ distrust behaviors, and three modification strategies are provided for managing different types of distrust behaviors. In addition, a case study is given to illustrate the feasibility of the proposed method. Finally, comparative analysis and discussion are explored to verify the advantages of the proposed LSGDM-SN with incomplete HFPRs.

Some models to manage additive consistency and derive priority weights from hesitant fuzzy preference relations

Consistency has a crucial influence on the rationality of preference information and even the final decision result. This paper presents two new definitions of additive consistency for hesitant fuzzy preference relations (HFPRs): completely additive consistency (CAC) and weakly additive consistency (WAC). To verify the CAC or WAC of HFPRs, some linear programming models and 0–1 mixed programming models are developed. The methods consider all the information given by the decision maker without changing the length of hesitant fuzzy elements (HFEs). Accordingly, a method of modifying an inconsistent HFPR into an additively consistent HFPR is proposed. The deviation between the original complementary matrix and the modified one is minimal. Then, several linear programming models are developed to obtain priority weights from an HFPR. From these, an integrated algorithm is designed to illustrate the process of consistency test, inconsistency modification and weights derivation for HFPRs. The proposed methods are also extended to deal with WAC and CAC of incomplete HFPRs. Finally, three numerical examples and comparative analysis are presented to illustrate the feasibility and effectiveness of the proposed method.

Improved multi‐criteria group decision‐making method considering hesitant fuzzy preference relations with self‐confidence behaviours for environmental pollution emergency response process evaluation

AbstractEnvironmental pollution is one of the major challenges in China, which seriously affects people's life, economy and society. This paper proposes a multi‐criteria group decision‐making method based on hesitant fuzzy preference relations with self‐confidence (HFPRs‐SC) behaviours and applies it to the evaluation of the environmental pollution emergency response process. Firstly, a comprehensive evaluation system is proposed that covers the environmental pollution emergency response process. Moreover, is utilized to obtain the normalized hesitant fuzzy preference relationship, and an algorithm that considers both the hesitant fuzzy preference value and the self‐confidence level is proposed to improve the consistency of HFPRs‐SC. In addition, combined with subjective and objective weights of experts, a weighted average operator based on the confidence level is applied to aggregate individual HFPR‐SC. Furthermore, the score function of HFPRs‐SC is designed to get the best ranking. Finally, a case study on an explosion accident in Fujian Province of China is conducted to verify the practicability and effectiveness of the proposed method with comparative analysis and sensitivity analysis. Based on the analysis, some suggestions are put forward for improving environmental pollution emergency response.