Fuzzy Preference Relations Research Articles

Development direction and focus of new energy industry in Jilin Province

The choice of new energy industry is the key content of the development decision-making of urban new energy industry. Currently, the important problem to be solved in the field of industrial development in China is to adopt scientific methods to select new energy industry conforming to the national industrial adjustment and the characteristics of new energy industry, based on the the analysis of the current situation of new energy development in Jilin Province with a reference to the development rule and trend of new energy industry in developed areas in China and abroad. With the basic principle and method of group decision and fuzzy preference relationship, this paper introduces the consistency into the new energy industry selection, constructs the model of new energy industry selection, and proposes the new method of new energy industry selection. With the above methods, evaluation indexes including the industrial scale economy effect and the resources concentration degree, ability to absorb scientific and technological achievements and technological innovation, the industrial correlation effect, the social benefit, the sustainability were adopted, and the emphases and directions of new energy industry development in Jilin Province were selected.

Consistency Comparison Analysis of Decision Making With Intuitionistic Fuzzy Preference Relations

To ensure the quality and progress of the project, it is very important to select the suitable construction enterprise. Intuitionistic fuzzy preference relations (IFPRs) are useful tools for showing the positive and negative judgments of decision makers. The main purpose of preference relations is to rank compared objects fully. Thus, the analysis of consistency is necessary to guarantee the reasonable ranking. However, the current concepts of consistency are inadequate to define the consistency of IFPRs, particularly for inconsistent and incomplete IFPRs. Therefore, the utilization of IFPRs in practical decision problems is restricted because inconsistent and/or incomplete IFPRs are usually encountered. To solve this issue, a new additive consistency concept for IFPRs is defined in this paper, which is unrelated to object labels and satisfies several reasonable properties. Considering inconsistent case, a mathematical model based method for getting additively consistent IFPRs is provided. A mathematical model for acquiring unknown judgments in IFPRs is established. A procedure for decision making with IFPRs is then given. Meanwhile, numerical examples about evaluating the construction company are offered to indicate the concrete application of the new results, and a comparative analysis is performed.

Nonlinear preferences in group decision‐making. Extreme values amplifications and extreme values reductions

Consensus Reaching Processes (CRPs) deal with those group decision-making situations in which conflicts among experts' opinions make difficult the reaching of an agreed solution. This situation, worsens in large-scale group decision situations, in which opinions tend to be more polarized, because in problems with extreme opinions it is harder to reach an agreement. Several studies have shown that experts' preferences may not always follow a linear scale, as it has commonly been assumed in previous CRP. Therefore, the main aim of this paper is to study the effect of modeling this nonlinear behavior of experts' preferences (expressed by fuzzy preference relations) in CRPs. To do that, the experts' preferences will be remapped by using nonlinear deformations which amplify or reduce the distance between the extreme values. We introduce such automorphisms to remap the preferences as Extreme Values Amplifications (EVAs) and Extreme Values Reductions (EVRs), study their main properties and propose several families of these EVA and EVR functions. An analysis about the behavior of EVAs and EVRs when are implemented in a generic consensus model is then developed. Finally, an illustrative experiment to study the performance of different families of EVAs in CRPs is provided.

A new method for deriving priority from dual hesitant fuzzy preference relations

Dual hesitant fuzzy elements (DHFEs) are suitable to express hesitant possible preferred and nonpreferred judgments of decision makers. Preference relation is an important tool in decision making that only needs the decision makers to compare a pair of objects at one time. This study focuses on decision making with dual hesitant fuzzy preference relations (DHFPRs). Considering the consistency, an additive consistency concept is defined. Meanwhile, the property of the new concept is studied. Using this consistency concept, a method for assessing the additive consistency of DHFPRs is offered. To extend the application of DHFPRs, a programming model to determine the missing DHFEs in incomplete DHFPRs is built, which have the highest additive consistency level for the known ones. Two equivalent methods to calculate the priority vector are offered. One method obtains the probabilistic dual hesitant fuzzy priority vector, and the other derives the intuitionistic fuzzy priority vector. Furthermore, a consensus index is defined to measure the consensus of individual opinions in group decision making (GDM), and an interactive method for increasing the consensus level is offered. On the basis of the additive consistency and consensus, an algorithm to GDM with DHFPRs is offered that can address inconsistent and incomplete cases. Finally, a practical example about evaluating color TV is provided to demonstrate the usefulness of the new procedure.

Public transportation development decision-making under public participation: A large-scale group decision-making method based on fuzzy preference relations

As an intensive travel mode, public transportation is an essential part of a circular economy construction. Scientific decision-making in a PT development plan is a fundamental prerequisite for ensuring its prioritization. In this study, based on the large-scale group decision-making of fuzzy preference relations, we examine PT development decision-making under public participation, to promote the effective use of PT resources. First, we cluster participants in the decision-making process based on the similarity method. Second, based on the clustering, an induced orderly weighting method is used to analyze the decision-making preferences of each sub-group. Finally, the decision-making preferences of each group are prioritized according to an analysis of group heterogeneity. We found that based on the similarity clustering method, when the threshold was set to 0.68, 85 participants were divided into 4 groups, and the demographic characteristics of the sub-groups presented some agglomeration. The four groups paid little attention to improving the quality of PT services. Moreover, the work unit had a significant impact on the decision-making preferences of participants, and public officials paid more attention to society and the government. Group heterogeneity significantly affects decision-making preferences and alternative priorities.

A framework for group decision making with multiplicative trapezoidal fuzzy preference relations

Trapezoidal fuzzy numbers are efficient to represent the quantitative vagueness and ambiguity of decision makers (DMs). Preference relations are powerful to express pairwise judgments of DMs with respect to alternatives. Combining their advantages, this paper focuses on group decision making (GDM) with multiplicative trapezoidal fuzzy preference relations (MTrFPRs) and proposes a new consistency-consensus based GDM method. To achieve this goal, a new consistency concept for MTrFPRs is proposed by analyzing the drawbacks of the previous ones. By utilizing this concept, optimal models for judging the consistency of MTrFPRs are built. Meanwhile, a consistency index is proposed to measure the consistency level of any given MTrFPR. After that, an algorithm for ranking alternatives from acceptable consistent MTrFPRs is proposed. For GDM, a central-derivation model for determining the fuzzy measure on a set of DMs is proposed. Furthermore, an optimal model for reaching the consensus threshold is constructed. Finally, a GDM method with MTrFPRs is proposed and an application example is utilized to show the efficiency of the proposed GDM method and to compare with the existing GDM methods. The proposed GDM method outperforms the existing GDM methods. It provides us with a very useful way for GDM based on MTrFPRs.

Group decision making based on multiplicative consistency-and-consensus preference analysis for incomplete q-rung orthopair fuzzy preference relations

The q-rung orthopair fuzzy preference relations are useful tools to represent hesitant and uncertain judgments of decision makers. In this paper, we propose a new group decision making method based on multiplicative consistency-and-consensus preference analysis for incomplete q-rung orthopair fuzzy preference relations. First, we provide a novel concept of multiplicative consistency for q-rung orthopair fuzzy preference relations. Then, a multiplicative consistency index is offered, by which we derive the concept of acceptable multiplicative consistency for q-rung orthopair fuzzy preference relations. Following this concept, optimization models for ascertaining unknown values in an incomplete q-rung orthopair fuzzy preference relation are built. Furthermore, optimization models for obtaining acceptable multiplicative q-rung orthopair fuzzy preference relation are proposed. Then, an optimization model for group decision making is proposed to attain an enough consensus. Afterward, a group decision making method with incomplete and unacceptable multiplicative consistent q-rung orthopair fuzzy preference relations is proposed. Finally, we use an application example to show the practicality of the proposed group decision making method. The proposed group decision making method outperforms the existing group decision making methods for group decision making in incomplete q-rung orthopair fuzzy environments.

Approaches for multicriteria decision-making based on the hesitant fuzzy best\u2013worst method

Hesitant fuzzy preference relations (HFPRs) have been widely applied in multicriteria decision-making (MCDM) for their ability to efficiently express hesitant information. To address the situation where HFPRs are necessary, this paper develops several decision-making models integrating HFPRs with the best worst method (BWM). First, consistency measures from the perspectives of additive/multiplicative consistent hesitant fuzzy best worst preference relations (HFBWPRs) are introduced. Second, several decision-making models are developed in view of the proposed additive/multiplicatively consistent HFBWPRs. The main characteristic of the constructed models is that they consider all the values included in the HFBWPRs and consider the same and different compromise limit constraints. Third, an absolute programming model is developed to obtain the decision-makers’ objective weights utilizing the information of optimal priority weight vectors and provides the calculation of decision-makers’ comprehensive weights. Finally, a framework of the MCDM procedure based on hesitant fuzzy BWM is introduced, and an illustrative example in conjunction with comparative analysis is provided to demonstrate the feasibility and efficiency of the proposed models.

A Decision Analysis Model for the Brand Experience of Branded Apps Using Consistency Fuzzy Linguistic Preference Relations

Branded apps are not only an important platform for enterprises and customers to have real-time interactions and communicate marketing messages, but also a new business model that encourages value co-creation between the two. In order to explore the impact of branded apps on customers, this study constructs a fuzzy multi-criteria decision making (FMCDM) analysis model, and it uses consistent fuzzy linguistic preference relations (CFLPR) to set up a symmetric pairwise comparison matrix, which greatly reduces the complexity and error rate of calculations. Empirical research findings show that brand experience attributes and the influence of brand experience on customer loyalty and satisfaction can be more accurately measured. As a consequence of this study, we show that, among the brand experience facets of two retail chain branded apps, behavioral experience is the most favored, while affective experience is the least favored. Furthermore, brand attachment and active participation should be strengthened to enhance customer loyalty. Through the analytical model employed in this study, enterprises can regularly monitor changes in the brand experience preferences of branded app users and evaluate app performance to flexibly adjust mobile device-based marketing campaigns and strategies. It can also aid enterprises in using mobile devices effectively to improve customer loyalty and address the issue of diminishing brand loyalty.

A comprehensive study of upward fuzzy preference relation based fuzzy rough set models: Properties and applications in treatment of coronavirus disease.

In this paper, we first introduce a new type of rough sets called α‐upward fuzzified preference rodownward fuzzy preferenceugh sets using upward fuzy preference relation. Thereafter on the basis of α‐upward fuzzified preference rough sets, we propose approximate precision, rough degree, approximate quality and their mutual relationships. Furthermore, we presented the idea of new types of fuzzy upward β‐coverings, fuzzy upward β‐neighborhoods and fuzzy upward complement β‐neighborhoods and some relavent properties are discussed. Hereby, we formulate a new type of upward lower and upward upper approximations by applying an upward β‐neighborhoods. After employing the upward β‐neighborhoods based upward rough set approach to it any times, we can only get the six different sets at most. That is to say, every rough set in a universe can be approximated by only six sets, where the lower and upper approximations of each set in the six sets are still lying among these six sets. The relationships among these six sets are established. Subsequently, we presented the idea to combine the fuzzy implicator and t‐norm to introduce multigranulation (ℐ,T)‐fuzzy upward rough set applying fuzzy upward β‐covering and some relative properties are discussed. Finally we presented a new technique for the selection of medicine for treatment of coronavirus disease (COVID‐19) using multigranulation (ℐ,T)‐fuzzy upward rough sets.

A new decision making model based on Rank Centrality for GDM with fuzzy preference relations

Preference aggregation in Group Decision Making (GDM) is a substantial problem that has received a lot of research attention. Decision problems involving fuzzy preference relations constitute an important class within GDM. Legacy approaches dealing with the latter type of problems can be classified into indirect approaches, which involve deriving a group preference matrix as an intermediate step, and direct approaches, which deduce a group preference ranking based on individual preference rankings. Although the work on indirect approaches has been extensive in the literature, there is still a scarcity of research dealing with the direct approaches. In this paper we present a direct approach towards aggregating several fuzzy preference relations on a set of alternatives into a single weighted ranking of the alternatives. By mapping the pairwise preferences into transitions probabilities, we are able to derive a preference ranking from the stationary distribution of a stochastic matrix. Interestingly, the ranking of the alternatives obtained with our method corresponds to the optimizer of the Maximum Likelihood Estimation of a particular Bradley-Terry-Luce model. Furthermore, we perform a theoretical sensitivity analysis of the proposed method supported by experimental results and illustrate our approach towards GDM with a concrete numerical example. This work opens avenues for solving GDM problems using elements of probability theory, and thus, provides a sound theoretical fundament as well as plausible statistical interpretation for the aggregation of expert opinions in GDM.

Decision support model with Pythagorean fuzzy preference relations and its application in financial early warnings

Pythagorean fuzzy sets (PFSs) retain the advantages of intuitionistic fuzzy sets (IFSs), while PFSs portray 1.57 times more information than IFSs. In addition, Pythagorean fuzzy preference relations (PFPRs), as a generalization of intuitionistic fuzzy preference relations (IFPRs), are more flexible and applicable. The objective of this paper is to propose a novel decision support model for solving group decision-making problems in a Pythagorean fuzzy environment. First, we define the concepts of ordered consistency and multiplicative consistency for PFPRs. Then, aiming at the group decision-making problem of multiple PFPRs, a consistency improving model is constructed to improve the consistency of group preference relations. Later, a consensus reaching model is developed to reach the degree of group consensus. Furthermore, a decision support model with PFPRs is established to derive the normalized weights and output the final result. Holding these features, this paper builds a decision support model with PFPRs based on multiplicative consistency and consensus. Finally, the described method is validated by an example of financial risk management, and it is concluded that the solvency of a company is an important indicator that affects the financial early warning system.

Some Methods Considering Multiplicative Consistency and Consensus in Group Decision Making with Interval-Valued Intuitionistic Fuzzy Preference Relations

In decision making with interval-valued intuitionistic fuzzy preference relations (IVIFPRs), the consistency and its improvement are key issues. The aim of this paper is to investigate a new multiplicative consistency of IVIFPRs based on interval arithmetic, and propose goal programming approach to improve consistency and consensus. Based on analysis of the drawbacks of the existing consistency definitions of IVIFPR, new definition for multiplicative consistent IVIFPR is introduced. Based on the proposed multiplicative consistency and analysis of the relationship between interval-valued intuitionistic fuzzy weights and multiplicative consistent IVIFPR, goal programming-based model is developed for deriving interval-valued intuitionistic fuzzy weights from IVIFPR. To measure the multiplicative consistency degree of IVIFPRs, a consistency index is introduced and then an acceptable consistency is defined. For an IVIFPR with unacceptable consistency, a mathematical programming approach is proposed to improve its consistency. By considering the experts’ subjective and consensus weights, the experts’ comprehensive weights are determined. Some numerical examples illustrate the proposed models.

Roles selection: a computational approach using ELECTRE and CFFR based on Multi Criteria Tacit Knowledge Acquisition

During the Talent Development Intervention programme, there is a need to provide an effective model to assess awareness, skills and experience among potential academics. To qualify as an Academic Leader or Academic Manager, there are certain characteristics and t raits necessary. However, there is a lack of research on the training of talented academicians to improve and avoid the loss of these characteristics and traits. Lack of this training would also contribute to vacancy positions of Academic Administrator without being hired. This paper aims to formulate and compare the Multi-criteria Decision-Making methods using ELECTRE (Elimination and Choice Expressing Reality) and CFPR (Consistent Fuzzy Preference Relations) based on proposed model of Multi Criteria Tacit Knowledge Acquisition (MC-TKAF). One set of empirical study based on proposed model contain seventeen (17) main criteria’s and one hundred eights (108) sub criteria are used to select the best candidate to fill in academic administrator roles. In this study, our focus is to integrate MCDM using CFFR and ELECTRE into implementation of Talent Development Intervention based on MC-TKAF development criteria. This paper also highlighted previous literatures which has shown how MC TKAF is formed and the justification of MCDM technique that will be used. The finding shows that both techniques produce the same results.

H-Rank Consensus Models for Fuzzy Preference Relations Considering Eliminating Rank Violations

Fuzzy preference relations (FPRs) have been widely used when ranking alternatives using pairwise comparison. However, when the FPRs have rank violations, the ranking results tend to contradict the decision makers’ (DMs) preferences. To date, no studies have examined the elimination of these FPR rank violations. Further, traditional consensus models utilizing distance measures between individual preferences are not suitable to manage classification-based consensus problems. To overcome these problems, this article develops several optimization models to address rank violations and h-rank consensus issues. First, the conditions that satisfy the FPRs’ preservation of order preferences (POPs) are analyzed and a system of constraints derived to ensure that the POPs are explicitly controlled by the optimization model, after which a mixed integer linear optimization model is developed to assist DMs to satisfy both the POP conditions and acceptable consistency. Finally, a linear model for the h-rank ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$h \geq 2$</tex-math></inline-formula> ) consensus reaching process is designed to ensure that each individual FPR also satisfies the POP conditions and acceptable consistency. The feasibility of the proposed models is illustrated using numerical examples, with extensive comparisons further validating the usefulness of the proposed models for group decision-making problems.

A fuzzy preference-based Dempster-Shafer evidence theory for decision fusion

Dempster-Shafer evidence theory (D-S) is an effective instrument for merging the collected pieces of basic probability assignment (BPA), and it exhibits superiority in achieving robustness of soft computing and decision making in an uncertain and imprecise environment. However, the determination of BPA is still uncertain, and merely applying evidence theory can sometimes lead to counterintuitive results when lines of evidence conflict. In this paper, a novel BPA generation method for binary problems called as the base algorithm is designed based on the kernel density estimation to construct the probability density function models, using the pairwise learning method to establish binary classification pairs. By means of the new BPA generation method, a new decision-making algorithm based on D-S evidence theory, fuzzy preference relation and nondominance criterion is effectively designed. The strength of the proposed method is presented in applying pairwise learning, which transforms the original complex problem into simple subproblems. With this process, the complexity of the problem to be solved is greatly reduced, which increases the feasibility for industrial applications. Furthermore, the fuzzy computing technique is used to aggregate the output for each single subproblem, and the nondominance degree of each class is determined from the fuzzy preference relation matrix, which can be directly used for the determination of the input instance. Based on several industrial-based classification experiments, the proposed BPA generation method and decision-making algorithm present the effectiveness and improvement in terms of precision and Cohen’s kappa.

On the Analytic Hierarchy Process Structure in Group Decision-Making Using Incomplete Fuzzy Information with Applications

The multi-criteria decision-making (MCDM) problem has a solution whose quality can be affected by the experts’ inclinations. Under essential conditions, the fuzzy MCDM method can provide more acceptable and efficient outcomes to select the best alternatives. This work consists of a consensus-based technique for selecting and evaluating suppliers in an incomplete fuzzy preference relations (IFPRs) environment utilizing TL-transitivity (Lukasiewicz transitivity). The suggested method is developed based on the criteria of the Analytical Hierarchy Process (AHP) Fframework, and the decision matrix is construtced using consistent fuzzy preference relations (FPRs). We use the symmetrical decisional matrix approach. A variety of numerical explanations and an analysis of quantitative results illustrate the suggested methodology’s logic and effectiveness.

Assessing the label’s mandatory information for fishery and aquaculture products in the EU28. A consumer approach based on a consistent fuzzy preference relation with geometric Bonferroni mean

Fishery and aquaculture products (FAPs) are a very important source of the protein intake of the European Union (EU) citizens. Despite the importance, the knowledge on labelling is still scarce. Two important issues regarding the labelling preferences of 27732 EU residents (the criteria interrelationship as well as the relationship that exists at the country level) will be assessed through a method based on a modified Consistent Fuzzy Preference Relation (CFPR) that uses the Geometric Bonferroni Mean (GBM) operator. The results show that not all the EU countries are homogeneous, so the subsidiarity principle might have been applicable. Our results also contribute to the strand of the fishery and aquaculture market. Policy implications, as well as future research studies, are discussed.

Group decision making based on the modified probability calculation method and DEA cross-efficiency with probabilistic hesitant fuzzy preference relations

In this paper, we propose a novel group decision making (GDM) method with probabilistic hesitant fuzzy preference relations (PHFPRs) based on the modified probability calculation method and data envelopment analysis (DEA) cross-efficiency. The primary advantage of the method is that it can reduce information loss and ensure the reliability of the decision-making result. A modified probability calculation method for hesitant fuzzy preference relations (HFPRs) is first proposed to obtain complete and normalized PHFPRs. Then, for the consistent additive preference relation (APR), we construct an output-oriented DEA model to derive the priority vector, in which each alternative is regarded as a decision-making unit (DMU). A DEA cross-efficiency model is further proposed to yield the priority vector, irrespective of whether the desired consistency level is achieved. Furthermore, a stochastic analysis method is developed to obtain the expected priority vector for any PHFPR, and a mathematical programming model is established to obtain the weight vector of decision makers based on group consensus. Finally, the procedure of the GDM method based on the modified probability calculation and the DEA cross-efficiency is designed. We also show the applicability and effectiveness of the proposed GDM method using illustrative examples.

Priority weights acquisition of linear uncertain preference relations and its application in the ranking of online shopping platforms

The linear uncertain preference relations (LUPRs) uses an uncertain variable to represent the decision-maker’s pairwise comparison judgment of the scheme. The variable is subject to the linear uncertain distribution, which is the extension of the traditional fuzzy preference relations (FPRs) and interval fuzzy preference relations (IFPRs). This paper proposes a group decision modeling problem, constructs the priority weights acquisition models of the additively and multiplicatively consistent LUPRs, and especially solves the problem that the weight solution is negative value or no solution by using traditional methods to acquire weights in consistent FPRs and IFPRs. Based on these two types of consistent structure of LUPRs, this study constructs the crisp number, interval number weight solving models of LUPRs and the group decision ranking models with LUPRs. The results show that these new models are suitable for solving the weight vector of traditional FPRs and IFPRs. The case of online shopping platform selection compares the results obtained by various methods of calculating weights, further illustrating the effectiveness and rationality of the new methods.