Fuzzy Linguistic Preference Relations Research Articles

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.

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.

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.

Integrated fuzzy linguistic preference relations approach and fuzzy Quality Function Deployment to the sustainable design of hybrid electric vehicles

Through the prevalence of sustainable ideas, automobiles are increasingly pursuing environmental protection strategies for green design, the non-traditional hybrid electric vehicles (HEV) are promoted continuously. If the company can add emotional value to the modeling of HEV, it will be helpful to its sustainable design and sales promotion of it. Therefore, an innovative model combining fuzzy linguistic preference relations (FLPR) and fuzzy quality function deployment (QFD) is proposed here to explore the connection between customer sentiment and the front view of the HEV. Compared with the previous methods, FLPR has the advantages of fewer comparison times and high consistency. First, find out the customer’s emotional expectations and attribute weight ranking for HEV through FLPR, and import customer requirements (CRs) on the left side of fuzzy QFD. Second, the grey prediction model was used to screen out the key engineering features (ECs) and the initial weight of HEV. Finally, based on human subjective imprecise natural semantics, fuzzy QFD established a matrix association between CRs and key ECs, then finally obtained the optimal combination of ECs' final weight and morphological design. The results can assist designers to shorten product development cycles and improve customers' emotional satisfaction, which provides a theoretical reference for the sustainable design and marketing of environmentally friendly cars in the future.

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.

Multiple stage optimization driven group decision making method with interval linguistic fuzzy preference relations based on ordinal consistency and DEA cross-efficiency

Interval linguistic term (ILT) is highly useful to express decision-makers’ (DMs’) uncertain preferences in the decision-making process. This paper proposes a new group decision-making (GDM) method with interval linguistic fuzzy preference relations (ILFPRs) by integrating ordinal consistency improvement algorithm, cooperative game, Data Envelopment Analysis (DEA) cross-efficiency model, and stochastic simulation. Firstly, the ordinal consistency of ILFPR is developed. For improving the ordinal consistency of an ILFPR, a two-stage integer optimization model is presented to derive an ILFPR with ordinal consistency. Then, a weight-determination method for obtaining DMs’ weights is presented based on cooperative games. Moreover, a DEA cross-efficiency model is presented to obtain the priorities of linguistic preference relation derived from ILFPR. Meanwhile, the expected ranking vector of ILFPR is obtained based on the DEA cross-efficiency model by integrating stochastic preference analysis and Monte Carlo stochastic simulation. Finally, a numerical example of emergency logistics selection illustrates the applicability and credibility of the proposed method.

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.

Developing Universally Applicable Service Quality Assessment Model Based on the Theory of Consumption Values, and Using Fuzzy Linguistic Preference Relations to Empirically Test Three Industries

Service quality is an important factor for a successful company. The SERVQUAL model is widely used. However, it has been controversial over the past 30 years. This research aims to develop a service quality measurement model that can be supported in conceptualization and universal applicability, and uses this model to identify the most important key factors of service quality for three industries. First, based on the theory of consumption values, this study used conceptualization and the modified Delphi method to develop a service quality assessment model—the consumption values-based service quality model (CV-SQ). The CV-SQ model was then used in conjunction with the fuzzy linguistic preference relations (Fuzzy LinPreRa) method to address MCDM problems. The findings suggested that the most important key factors of service quality comprised safety in the aviation companies, innovativeness in the travel agencies, and comfort in the hotels. The CV-SQ model can be supported by theoretical and empirical tests in conceptualization and universal applicability, and has made theoretical contributions to service quality management. The research results have provided practical contributions to the improvement of service quality in the three industries. What is more noteworthy is the weight of epistemic value ranked first and second among the three industries, but it had not been included in any service quality aspect classification schemes during the past three or four decades.

Distribution Linguistic Fuzzy Group Decision Making Based on Consistency and Consensus Analysis

The development of distribution linguistic provides a new research idea for linguistic information group decision-making (GDM) problems, which is more flexible and convenient for experts to express their opinions. However, in the process of using distribution linguistic fuzzy preference relations (DLFPRs) to solve linguistic information GDM problems, there are few studies that pay attention to both internal consistency adjustment and external consensus of experts. Therefore, this study proposes a fresh decision support model based on consistency adjustment algorithm and consensus adjustment algorithm to solve GDM problems with distribution linguistic data. Firstly, we review the concept of DLFPRs to describe the fuzzy linguistic evaluation information, and then we present the multiplicative consistency of DLFPRs and a new consistency measurement method based on the distance, and investigate the consistency adjustment algorithm to ameliorate the consistency level of DLFPRs. Subsequently, the consensus degree measurement is carried out, and a new consensus degree calculation method is put forward. At the same time, the consensus degree adjustment is taken the expert cost into account to make it reach the predetermined level. Finally, a distribution linguistic fuzzy group decision making (DLFGDM) method is designed to integrate the evaluation linguistic elements and obtain the final evaluation information. A case of the evaluation of China’s state-owned enterprise equity incentive model is provided, and the validity and superiority of the proposed method are performed by comparative analysis.

A Fuzzy MCDM Analytic Model for Building Customers’ Brand Attachment Preference in Car Firms

The more attached a customer becomes toward a specific brand, the stronger the extent of customer loyalty he or she will present. However, studies on brand attachment (BA) have been limited to the perspectives of enterprises about the manner in which to consolidate customer loyalty while opinions and views of customers are absent. This study integrates the views of enterprises and those of customers to build a BA-based multi-criteria decision-making (MCDM) model and adopts consistent fuzzy linguistic preference relations (CFLPR) to conduct empirical research on three car brands, namely Lexus, Mercedes-Benz, and BMW, by analyzing differences in customers’ BA preference to the three brands and assessing management performance. Findings reveal that the customers of the two German brands, Mercedes-Benz and BMW, emphasize hedonic needs while customers of Lexus, the Japanese brand, stress on bonds of personal emotional factors. Apart from being able to measure the precise strength of customers’ BAs, this analytic model can also help enterprises to examine changes of factors concerning customers’ BA on a regular basis as well as serving as the foundation for evoking consumers’ identification about brand personality, consolidating brand loyalty, and developing marketing communications strategies.