Hesitant Fuzzy Linguistic Preference Relations Research Articles

Fuzzy C-means clustering with hesitant fuzzy linguistic preference relation

With the advancement of technology and growing social demand, large scale group decision making has gained significant importance in the field of decision making. Clustering analysis plays a crucial role in enhancing the efficiency of large scale group decision making processes. Linguistic evaluation is more in line with people’s cognitive and expressive habits. The hesitant fuzzy linguistic term set (HFLTS) offers more flexibility in expressing evaluation information. This paper is dedicated to designing a fuzzy C-means clustering model that is specifically applicable for the hesitant fuzzy linguistic preference relation (HFLPR). The objective function of the model is built based on the dissimilarity between HFLPRs and the initial cluster centers to obtain the fuzzy membership matrix and cluster centers. Since initializing cluster centers is a crucial step to produce a reasonable cluster result, three methods are proposed for generating initial centers for HFLPRs. The first and second methods are improvements over existing approaches that dealt with the clustering problem with numerical values. The third approach considers both the preference relation of preferring an alternative and the distribution of the actual preference relations. Based on this, a fuzzy C-means clustering algorithm with HFLPR is designed to obtain the cluster centers and membership matrix for there types of initializing clustering centers. Finally, based on the quality and speed of clustering, a numerical example and comparative analyses illustrate that the proposed clustering algorithm is efficient and effective.

A statistical approach to large-scale group decision making with incomplete hesitant fuzzy linguistic information by incorporating risk attitude

In response to the lack of information and the arguments among the decision-makers (DMs) in large-scale group decision making (LSGDM), this study proposes a method that integrates decision risk and risk attitude into LSGDM with hesitant fuzzy linguistic preference relations (HFLPRs) based on statistical estimation. Firstly, the DMs are arranged into several subgroups via their risk attitudes. Next, the whole or part of the five-number summary for subgroups from incomplete information provided by DMs are collected. After that, the optimization model and Monte Carlo simulation are utilized to obtain mean and standard deviation estimators of the decision information, and the mean estimator is regarded as the evaluation information of subgroup. Then, the hesitant fuzzy linguistic term sets (HFLTSs) with different number of linguistic variables are normalized according to their risk attitudes and confidence interval. Meanwhile, the number of members in subgroups and the decision risk level of subgroups are combined to determine the weights of subgroups. Moreover, a minimum deviation model is derived to rank alternatives. Finally, a case study, sensitivity analysis and comparison are used to guarantee the rationality and availability of the proposed method.

Consistency improvement under incomplete hesitant fuzzy linguistic preference relations in large-scale group decision-making

This paper studies a large-scale group decision-making method (LSGMD) based on incomplete hesitant fuzzy linguistic preference relations (IHFLPRs) and proposes an improved model for additive consistency of hesitant fuzzy linguistic preference relations (HFLPRs). Additionally, consistency control and fuzzy C-means (FCM) clustering are utilized to enhance efficiency and reliability. Firstly, a model is proposed to address the issues of missing elements in IHFLPRs and insufficient additive consistency in HFLPRs, aiming to more accurately reflect decision makers’ preference relationships towards candidate alternatives. Subsequently, the FCM method is employed to cluster decision experts’ preference information and obtain the overall preference information. Finally, the rationality and accuracy of our proposed method are demonstrated through a case study and comparative analysis.

Consensus improvement model in group decision making with hesitant fuzzy linguistic term sets or hesitant fuzzy linguistic preference relations

Hesitant fuzzy linguistic term sets (HFLTSs) and hesitant fuzzy linguistic preference relations (HFLPRs) are widely used where decision makers are permitted to provide qualitative preferences with several linguistic terms over two alternatives. There are several issues deserving further investigation in the existing consensus models of HFLTSs and HFLPRs: the extension process of HFLTSs which is always performed in distance measure and aggregation of HFLTSs distorts the original information, the modified HFLTSs does not belong to standardized HFLTSs, and most of the existing models don’t discussed the number of optimal solutions. In order to solve the above problems, this paper introduces new distance and entropy measures for HFLTSs, by which information aggregation method and two consensus improvement models in group decision making (GDM) with HFLTSs and HFLPRs are proposed. The first model is a four-stage optimization model with four objectives, based on which an equivalent linear weighted optimization model is derived by assigning appropriate weights to four objectives with different priorities. According to either of these two models, the revised individual and collective opinions can be obtained. In addition, the prominent properties of the collective opinion obtained from optimization models are further investigated. As last, some examples are provided to demonstrate the applicability of the optimization models proposed, and the results demonstrate the models proposed can better deal with the abovementioned issues.

Group decision making with hesitant fuzzy linguistic preference relations based on multiplicative DEA cross-efficiency and stochastic acceptability analysis

The aim of this paper is to investigate a novel approach to group decision making (GDM) based on multiplicative DEA cross-efficiency and stochastic acceptability analysis with hesitant fuzzy linguistic preference relations (HFLPRs), which can avoid information distortion and obtain more credible decision-making results. First, a transform function is defined, which can extract effective information of the hesitant fuzzy linguistic term set (HFLTS) sufficiently. Then, an optimization model is proposed to derive the occurring probabilities of the elements in the HFLTS. It can avoid the normalization process of HFLPRs and simulate the element-selection process of decision makers (DMs). Moreover, a Maximum Log DEA Cross Efficiency model is proposed to evaluate the relative efficiency of each alternative from HFLPR. We further develop the stochastic weight space acceptability analysis method to solve the GDM problem and a step-by-step procedure is presented. Finally, numerical examples are given to illustrate the validity and applicability of the proposed method. This is the first attempt of employing the multiplicative DEA cross-efficiency to the GDM with HFLPRs.

An Additive Consistency and Consensus Approach for Group Decision Making With Probabilistic Hesitant Fuzzy Linguistic Preference Relations and Its Application in Failure Criticality Analysis.

In this article, probabilistic hesitant fuzzy linguistic preference relations (PHFLPRs) are proposed to present the qualitative pairwise preference information of decision makers (DMs) with hesitation and probability uncertainty assessments. The measurements and improvements of additive consistency and consensus of PHFLPRs are investigated in group decision making (GDM). First, a new concept of probabilistic hesitant fuzzy linguistic term sets is defined. Second, the consistency and consensus measurements are established to survey the additive consistency and consensus levels of PHFLPRs. Subsequently, an optimization model is developed to improve the unacceptably additive consistent PHFLPR. By optimizing the unacceptable consensual PHFLPRs with repeating additive consistency improvement, the acceptably additive consistent and consensual PHFLPRs are obtained, based on which DMs' weights are determined objectively and then, the collective PHFLPR is aggregated from individual PHFLPRs. Alternatives' priority weights are derived from the collective PHFLPR as GDM. Finally, an example about failure criticality analysis is given, and a comparison analysis is presented.

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.

Hesitant fuzzy linguistic iterative method for consistency and consensus-driven group decision making

Hesitant fuzzy linguistic information has been used as a powerful expression to present the judgments under uncertainty. To improve its decision-making theory and enhance its application ability, we propose a decision-making method that considers the individual acceptable consistency and the group consensus of hesitant fuzzy linguistic preference relations (HFLPRs). Firstly, we define a multiplicative consistency of a HFLPR and make hypothesis testing analyses for the consistency threshold. Then, we establish a group consensus procedure to achieve comprehensive decision-making results that possibly reserve the original judgments of decision makers. Some experiments are conducted to show the values of the consistency threshold in different scenarios, and make support for using the proposed method. An illustrative example is finally given to perform the method.

Revisiting Additive Consistency of Hesitant Fuzzy Linguistic Preference Relations

Consistency has always been a hot topic in the study of decision-making based on preference relations. This paper focuses on the consistency of hesitant fuzzy linguistic preference relations (HFLPRs). Firstly, a new definition of the additive consistency of HFLPRs is given. Secondly, to examine whether an HFLPR is additively consistent, two equivalent programming models are constructed. Thirdly, for inconsistent HFLPRs, the corresponding consistency improvement model is further proposed, where only upper triangular elements in the HFLPRs are considered in view of the symmetry of HFLPRs. Using the consistency improvement model, an inconsistent HFLPR can be adjusted to the consistent one, which retains the original information as much as possible. Fourthly, a hesitant fuzzy linguistic weight vector is introduced and a programming model is constructed to derive the weight vector. Finally, the feasibility and effectiveness of the proposed method are illustrated by numerical examples and comparative analysis. This result demonstrates that the consistency model proposed considers each element of HFLPRs such that the consistent HFLPRs derived fully retain the original information. Moreover, only some preference values in the HFLPR are adjusted, and no preference value is out of range of the predefined HFLTSs.

Consensus reaching with consistency control in group decision making with incomplete hesitant fuzzy linguistic preference relations

Due to complicated decision environment and limited knowledge of decision makers, decision makers may provide incomplete hesitant fuzzy linguistic preference relations (IHFLPRs) in group decision making (GDM) problems. Furthermore, to guarantee that decision makers are non-random and logical and obtain decision results that are accepted by most decision makers, it is necessary to consider individual consistency control in consensus reaching processes (CRPs) for GDM problems. In this paper, some models are developed to manage incomplete information and consensus for GDM with IHFLPRs. First, we develop an optimization model to impute missing elements for an IHFLPR, in which the best additive consistency index (BCI) and the average additive consistency index (ACI) are utilized to measure the additive consistency level of an IHFLPR. Afterwards, for CRPs in GDM with IHFLPRs, some local adjustment strategy-based feedback adjustment rules are proposed to assist decision makers in modifying HFLPRs by considering the BCI and the ACI. Moreover, an iterative consensus reaching algorithm for GDM with IHFLPRs is further proposed. Eventually, a numerical example of 3D visualization management system selection for an automobile manufacturing enterprise is presented to elaborate the feasibility of the consensus reaching algorithm, and detailed numerical results are also provided to justify the algorithm.

Selection of a solar water heater for large-scale group decision making with hesitant fuzzy linguistic preference relations based on the best-worst method

Selection of a solar water heater for large-scale group decision making with hesitant fuzzy linguistic preference relations based on the best-worst method

Consistency and consensus driven for hesitant fuzzy linguistic decision making with pairwise comparisons

Hesitant fuzzy linguistic preference relation (HFLPR) is of interest because it provides an efficient way for opinion expression under uncertainty. For enhancing the theory of group decision making (GDM) with HFLPR, the paper introduces a method for addressing the GDM based on consistency and consensus measurements, which involves (1) defining a hesitant fuzzy linguistic geometric consistency index (HFLGCI) and proposing an algorithm for consistency checking and inconsistency improving for HFLPR; (2) proposing a worst consensus index based on the minimum similarity measure between each individual HFLPR and the overall perfect HFLPR in order to build a consensus reaching algorithm based on the acceptable HLFPRs. The convergence and monotonicity of the proposed two procedures is proved. Experiments are performed to investigate the critical values of the defined HFLGCI, and comparative analyses are conducted to show the effectiveness of the proposed method. A case concerning the performance evaluation of venture capital guiding funds is given to illustrate the applicability of the proposed method. As an application of our work, an online decision-making portal is finally provided for decision makers to utilize the proposed method to solve GDM with HFLPRs.

Clustering and compatibility-based approach for large-scale group decision making with hesitant fuzzy linguistic preference relations: An application in e-waste recycling

Considering that large-scale group decision making (LSGDM) has been widely concentrated on clustering and lower compatibility problems, this paper focuses on clustering and consensus reaching of hesitant fuzzy linguistic preference relations (HFLPRs) in LSGDM. Firstly, we define the hesitant degree and the fuzzy degree functions for hesitant fuzzy linguistic term sets (HFLTSs) according to their scale and deviation of elements. To normalize HFLTSs with different length, a minimum deviation model based on the hesitant and the fuzzy degrees is developed. After that, we propose a new similarity measure and compatibility measure via integrating the hesitant and fuzzy degrees. Then a clustering process combining similarity and compatibility is used to assign large-scale experts into several clusters. The clustering method not only strengths the cohesion of subgroups, but also guarantees that HFLPRs in subgroups are acceptable compatibility. Moreover, a compatibility adjusting process with self-selected feedback mechanism is presented to improve the compatibility level of clusters until they reach a predefined threshold in selection process. And we combine the number of members in subgroups and the compatibility level of subgroups to determine weights of subgroups. Finally, a case of e-waste recycling and comparison are analyzed to show the availability of the proposed method.

Granular computing and optimization model-based method for large-scale group decision-making and its application

In large-scale group decision-making process, some decision makers hesitate among several linguistic terms and cannot compare some alternatives, so they often express evaluation information with incomplete hesitant fuzzy linguistic preference relations. How to obtain suitable large-scale group decision-making results from incomplete preference information is an important and interesting issue to concern about. After analyzing the existing researches, we find that: i) the premise that complete preference relation is perfectly consistent is too strict, ii) deleting all incomplete linguistic preference relations that cannot be fully completed will lose valid assessment information, iii) semantics given by decision makers are greatly possible to be changed during the consistency improving process. In order to solve these issues, this work proposes a novel method based on Granular computing and optimization model for large-scale group decision-making, considering the original consistency of incomplete hesitant fuzzy linguistic preference relation and improving its consistency without changing semantics during the completion process. An illustrative example and simulation experiments demonstrate the rationality and advantages of the proposed method: i) semantics are not changed during the consistency improving process, ii) completion process does not significantly alter the inherent quality of information, iii) complete preference relations are globally consistent, iv) final large-scale group decision-making result is acquired by fusing complete preference relations with different weights.

A cloud‐based and web‐based group decision support system in multilingual environment with hesitant fuzzy linguistic preference relations

Due to the growing needs in decision-making under uncertainty, existing studies introduced consistency and consensus-driven algorithms for group decision-making (GDM) problems with hesitant fuzzy linguistic preference relations (HFLPRs). A decision support system (DSS) that can host these GDM algorithms to provide decision-support services or tools for practical use is urgently needed. However, the state-of-the-art architectures cannot organize these algorithms and related data to run within one framework. This is mainly due to the running environments for these GDM algorithms are different since these algorithms were not originally designed to be compatible. Given the multilingual consistency and consensus-based decision support algorithms, how to design and implement a cloud-based DSS in a multilingual environment is still an open question. To fill this gap, this paper provides a web-based and cloud-based DSS with a novel architecture that utilizes the advantages of microservices. The proposed system implements a multilingual support framework to dynamically upload, manage and run multilingual consistency and consensus-based decision support algorithms. An algorithm recommendation module is developed to help users choose suitable decision support algorithms. Tokenization is applied to deal with regulatory issues of knowledge protection, data privacy, and security while storing, analyzing, and transforming data into different algorithms for effective decision-making. An expert feedback study verified that our web and cloud-based DSS is a right artifact to fulfill the objective claimed in this paper.

Expected loss utility for natural hazards and its application in pricing property insurance products

Due to climatic hazards and extreme weather events, the pricing of property insurance products is increasingly attracting the attention of policyholders, insurance companies, and governments. Pricing based on market-oriented methods has to consider the affecting factors from policyholders’ perceived value. Pricing strategy design generates the need for natural hazards risk assessments. A natural hazard risk assessment is closely related to the human factors of a disaster-bearing body. In response to this need, we design an extension of the expected utility that is inconsistent with the additive expected utility, considering the human factors of policyholders, which is referred to as the expected loss utility (ELU). The ELU presents two improvements of the currently used utility. First, subjective probability, which is derived from individual predictions over acts, is applied to the ELU function to overcome the disadvantage that objective probability attaches to uncertainty does not reflect the uncertainty of human factors. Policyholders’ risk attitudes are reflected by the interpretation of interactions among uncertain events. Second, the hesitant fuzzy linguistic preference relation (HFLPR) is employed as the assessment of individual loss evaluation to reflect a policyholder’s hesitation. We apply the techniques of fuzzy linguistic term aggregation and perform a comparison to simplify our loss utility function. A detailed process of expected loss assessment is proposed due to variations in natural environment factors, local social characteristics, and disaster-bearing body factors. An illustrative example is given to perform a comparison with cumulative prospect theory to show the merits of the ELU. This study quantifies policyholder’s cognition of uncertain event and the cognition’s influence on risk assessment which can guide pricing strategy of property insurance products.

Group decision making with hesitant fuzzy linguistic preference relations based on modified extent measurement

The paper presents a consensus model for group decision making (GDM) with hesitant fuzzy linguistic preference relations (HFLPRs), which is composed of two parts: (1) clustering HFLPRs by mapping them into a higher dimension space based on a kernel function; (2) building a consensus model based on measuring the modified extents of decision makers’ HFLPRs for reducing the biased judgements existing in their less-familiar ways. The paper further makes comprehensive analyses for the proposed model on: (1) the influence of decision makers’ different sensitive attitudes towards the distances between the individual HFLPRs and the overall HFLPRs on decision-making results; (2) the differences and complexities of another model with a different consensus perspective and the proposed model. The experimental analyses provide the support for the maximum modified extent determination in different decision scenarios, and show that the proposed consensus model makes sense. Finally, the proposed model is illustrated by the application in choosing an optimal flood discharge technique for a hydropower station.

A hesitant fuzzy linguistic bi-objective clustering method for large-scale group decision-making

Large-scale group decision-making process has received an increasing attention in recent years. After making the general survey of the existing large-scale group decision-making methods, we have found that: 1) consistency threshold value of hesitant fuzzy linguistic preference relation is fixed in traditional consistency measures; 2) the clustering process of LSGDM does not consider the similar relationship between different evaluation information and the information quality simultaneously. Thus, in order to tackle the above issues and describe the hesitancy of experts in the decision-making process, the paper proposes a hesitant fuzzy linguistic bi-objective clustering method considering consensus and information entropy for tackling large-scale group decision-making problems. Firstly, a selection procedure for preference information is developed to quickly select suitable experts who meet the consistency requirements. Then, a bi-objective clustering method based on the group consensus degree indicator and group information entropy indicator is proposed to divide the experts into different clusters, considering the similar relationship and the quality of evaluation information simultaneously. After that, comprehensive preference information and the overall ranking of alternatives can be obtained. In the end, an illustrative example of choosing the optimal way to protect the personal information while defending against COVID-19 and some comparative study show that the proposed method is valid for large-scale group decision-making problems and has good performance and strong robustness.

A consensus measure for group decision making with hesitant linguistic preference information based on double alpha-cut

The hesitant fuzzy linguistic term set, which is characterized by a set of possible linguistic terms, becomes a useful tool to describe the complex cognitions of experts. In many cases, it is much more flexible for experts to provide evaluation information via pairwise comparisons rather than give their evaluation information on options directly. In this regard, the hesitant fuzzy linguistic preference relation (HFLPR) whose elements are hesitant fuzzy linguistic elements was introduced. Besides, to make a reasonable decision, a group of experts are usually involved in practice and thus how to reach an agreement among experts whose perceptions are represented by HFLPRs turns to be significantly important. To meet this challenge, in this study, we propose a novel consensus measure for group decision making with HFLPRs. Firstly, we define an alpha-cut-based method to calculate the similarities among different hesitant fuzzy linguistic evaluations and then develop an alpha-cut-based consensus measure for group decision making with HFLPRs. By converting the linguistic terms of hesitant fuzzy linguistic elements into numerical values of 0 or 1, the consensus measure can be simplified. Finally, to illustrate the effectiveness of the method, we apply it to a practical case study. A comparative analysis is provided to demonstrate the advantages and significance in practical applications of the proposed method.

Interval Consistency Repairing Method for Double Hierarchy Hesitant Fuzzy Linguistic Preference Relation and Application in the Diagnosis of Lung Cancer

Natural language is more in line with the real thoughts of people than crisp numbers considering that qualitative language information is more consistent with the expression habits of experts. Double hierarchy hesitant fuzzy linguistic preference relation (DHHFLPR) can be used to express complex linguistic preference information accurately because the pairwise comparison methods are more accurate than non-pairwise methods. Consistency reflects the rationalization of a preference relation and can be used to judge whether a preference relation is self-contradictory or not. In this paper, an interval consistency index of DHHFLPR is developed, which is consisted by the consistency indices of all double hierarchy linguistic preference relations associated with the DHHFLPR. Additionally, an average consistency index of DHHFLPR is given by calculating the average value of the consistency indices of all double hierarchy linguistic preference relations. Moreover, we develop a consistency checking and repairing method for DHHFLPR. Finally, we apply the proposed method into a practical group decision-making problem that is to identify the most critical factors in developing lung cancer, and some comparative analyses involving the connections and differences among the proposed consistency indices are analysed.