Fuzzy Preference Relations Research Articles

Hierarchical multi-criteria decision making with group voting information: New Tanino’s additive consistency intuitionistic fuzzy translation and utility vector acquisition

The frame of intuitionistic fuzzy preference relations (IFPRs) is an effective tool of representing pairwise preference order based group voting information. However, existing intuitionistic fuzzy translations of Tanino’s additive consistency and previous methods of acquiring utility vectors from IFPRs are often unable to achieve a satisfactory solution for hierarchical multi-criteria decision making (HMCDM) with IFPRs. This study analyzes existing notions of additively consistent IFPRs (ACIFPRs) and shows their shortages. A novel intuitionistic fuzzy translation of Tanino’s additive consistency is developed and an index computational formula is provided to measure additive inconsistency of IFPRs. A new approach is offered to generate ACIFPRs from vectors with intuitionistic fuzzy elements and a frame is put forward to normalize intuitionistic fuzzy vectors. Subsequently, a closed-form solution based method is presented to secure normalized intuitionistic fuzzy utility vectors from ACIFPRs and a linear program is built to acquire an optimal and normalized intuitionistic fuzzy utility vector from any IFPR. An approach is proposed to tackle HMCDM problems with pairwise preference order based group voting information. The reasonability and performance of the models developed are validated by an illustrative example and a case study about outstanding teacher recommendation based on large-scale group votes on teaching satisfaction.

A New Consensus Model Based on Trust Interactive Weights for Intuitionistic Group Decision Making in Social Networks

A promising feature for group decision making (GDM) lies in the study of the interaction between individuals. In conventional GDM research, experts are independent. This is reflected in the setting of preferences and weights. Nevertheless, each expert's role is played through communication, collaboration, and cooperation with other individuals. The interaction from others may affect the power of an expert as well as his/her opinion. Furthermore, it is noted that a link path with the highest degree of trust is the most efficient information transmission channel. Inspired by these findings, an optimal trust-induced consensus process is designed with the usage of intuitionistic fuzzy preference relation. The comprehensive weight of each expert is decomposed into two portions, namely: 1) the individual weights and 2) interactive weights. Three optimization models are constructed to achieve weight parameters under different decision situations, where the weight parameters are represented through a 2-order additive fuzzy measure and the Shapley value. To reflect the interaction, the Choquet integral is employed for aggregating opinions, and a novel distance measure is adopted for accomplishing a consensus index. An illustrative example and comparison are put in practice to show the effectiveness and improvements of the proposed method.

Triangular Bounded Consistency of Interval-Valued Fuzzy Preference Relations

The consistency of interval-valued fuzzy preference relations (IFPRs) is a prerequisite for the application of IFPRs in real problems. To support the application of IFPRs, various types of consistency of IFPRs have been developed. They all satisfy some fixed mathematical conditions under the assumption that decision makers are perfectly rational. In practice, this assumption is usually violated because decision makers generally have bounded rationality. Considering the bounded rationality of decision makers, this article develops a new type of consistency of IFPRs called triangular bounded consistency, which is based on the historical preferences of decision makers. A triangular framework is designed to describe the three IFPRs of any three alternatives. The strict transitivity of IFPRs is defined as the restricted max-max transitivity of IFPRs, which is reconstructed in the triangular framework. In this situation, under the assumption that the preferences of a decision maker are consistent in similar circumstances, the triangular bounded consistency of IFPRs is defined by use of the historical IFPRs of decision makers. Based on the developed consistency, the process of determining the optimal estimations of missing IFPRs in an incomplete IFPR matrix is developed. A problem of selecting suppliers of simulation systems is analyzed using the multicriteria group decision-making (MCGDM) process with the triangular bounded consistency of IFPRs to demonstrate the application of the developed consistency in MCGDM.

Zero-carbon measure prioritization for sustainable freight transport using interval 2 tuple linguistic decision approaches

Freight transport is the main source of carbon emissions. Implementing freight transport zero-carbon measures in an orderly manner has a very important practical value for sustainable development. Thus, the interval 2-tuple linguistic multi-attribute decision-making (I2TL-MADM) approach of zero-carbon measure prioritization for sustainable freight transport is presented. Considering the advantages of interval 2-tuple variables (I2TLVs) expressing the uncertainty evaluation information of zero-carbon measures, the decision model is developed based on I2TLVs. Firstly, the shortcomings of the inconsistent fuzzy preference relations (FPRs) constructed by comparing attribute values expressed by I2TLVs are revealed. Then, additive and multiplicative dominance degrees of I2TLVs are proposed, and their properties are discussed to ensure the consistency of decision information. Two I2TL-MADM methods based on the novel dominance degrees are developed to rank the zero-carbon measures of sustainable freight transport. Finally, the rationality of the developed I2TL-MADM decision framework is illustrated by numerical examples of Guangzhou. The results show that the developed decision methods can effectively construct the consistent FPRs and rank the zero-carbon measures.

Consistency threshold- and score function-based multi-attribute decision-making with Q-rung orthopair fuzzy preference relations

As a general form of intuitionistic fuzzy preference relations (IFPRs) and Pythagorean fuzzy preference relations (PFPRs), q-rung orthopair fuzzy preference relations (q-ROFPRs) provide a more flexible information representation for decision makers (DMs) to express their vagueness and uncertainty. However, there have been only a few studies conducted on q-ROFPRs. Therefore, in the context of multi-attribute decision-making (MADM), a decision framework for MADM with q-ROFPRs is proposed. First, a novel score function is proposed to compare two different q‐rung orthopair fuzzy numbers (q‐ROFNs). Subsequently, an algorithm is developed to check and improve the multiplicative consistency of q-ROFPRs. Moreover, to consider the rationality of the threshold determination, an objective method for determining the threshold of q-ROFPRs is developed considering the number of alternatives and rung q. Finally, a new method for determining the weights of attributes is discussed. In addition, an illustrative example involving the brand evaluation of new energy vehicles is used to verify the applicability of the above methods. The rationality and superiority of the proposed methods are highlighted by a comparative analysis with existing studies.

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.

Note on “The breaking of additively reciprocal property of fuzzy preference relations and its implication to decision making under uncertainty”

A recent article by Liu et al. [8] devised measurement models to calculate additive consistency indices and weak transitivity indices for fuzzy preference relations (FPRs) with additive reciprocity breaking (ARB), and developed some decision models, such as the equivalency between FPRs with ARB and inconsistent FPRs with additive reciprocity, the optimization based weak transitivity improving model and priority vector derivation models. This paper utilizes six numerical illustrations to show that the measurement models are technically incorrect and sometimes the decision models are invalid or create contradictory results. New frameworks are proposed to define and measure additive consistency and weak transitivity for FPRs with ARB. Computational formulas are brought forward to acquire interval-valued or intuitionistic fuzzy priority vectors from additively consistent FPRs with ARB, and a linear programming model is built to ascertain interval-valued or intuitionistic fuzzy priority vectors from inconsistent FPRs with ARB.

Multiplicative Consistency and DEA Cross-Efficiency-Driven Decision-Making Method with Fuzzy Preference Relations

Owing to the uncertainty and vagueness of practical decision-making problems, it is more convenient for decision-makers (DMs) to express evaluation information with fuzzy preference relations (FPRs) than precise numerical values. As two important issues in the decision-making process with FPRs, improving consistency and acquiring the priority weights are worth further studying. In this paper, we first provide an approach for constructing the FPR with multiplicative consistency, and then an algorithm of improving consistency is presented to generate an acceptable FPR, in which the initial evaluation information is retained to the largest extent through the local adjustment strategy. Then, an input-oriented CCR DEA model is developed to derive the priority weight vector of alternatives, which is followed that a DEA cross-efficiency model is constructed to discriminate multiple DEA efficient DMUs. Subsequently, the complete rankings of alternatives can be generated by a novel DEA-driven decision-making method. Finally, a numerical example is proposed to verify the feasibility and effectiveness of the developed method. The advantages of the developed method are performed by comparative analysis and sensitivity analysis.

METHOD FOR WEIGHTS CALCULATION BASED ON INTERVAL MULTIPLICATIVE PAIRWISE COMPARISON MATRIX IN DECISIONMAKING MODELS

Context. The pairwise comparison method is a component of several decision support methodologies such as the analytic hierarchy and network processes (AHP, ANP), PROMETHEE, TOPSIS and other. This method results in the weight vector of elements of decision-making model and is based on inversely symmetrical pairwise comparison matrices. The evaluation of the elements is carried out mainly by experts under conditions of uncertainty. Therefore, modifications of this method have been explored in recent years, which are based on fuzzy and interval pairwise comparison matrices (IPCMs).
 Objective. The purpose of the work is to develop a modified method for calculation of crisp weights based on consistent and inconsistent multiplicative IPCMs of elements of decision-making model.
 Method. The proposed modified method is based on consistent and inconsistent multiplicative IPCMs, fuzzy preference programming and results in more reliable weights for the elements of decision-making model in comparison with other known methods. The differences between the proposed method and the known ones are as follows: coefficients that characterize extended intervals for ratios of weights are introduced; membership functions of fuzzy preference relations are proposed, which depend on values of IPCM elements. The introduction of these coefficients and membership functions made it possible to prove the statement about the required coincidence of the calculated weights based on the “upper” and “lower” models. The introduced coefficients can be further used to find the most inconsistent IPCM elements.
 Results. Experiments were performed with several IPCMs of different consistency level. The weights on the basis of the considered consistent and weakly consistent IPCMs obtained using the proposed and other known methods have determined the same rankings of the compared objects. Therefore, the results using the proposed method on the basis of such IPCMs do not contradict the results obtained for these types of IPCMs using other known methods. Rankings by the proposed method based on the considered highly inconsistent IPCMs are much closer to rankings based on the corresponding initial undisturbed IPCMs in comparison with rankings obtained using the known FPP method. The most inconsistent elements in the considered IPCMs are found.
 Conclusions. The developed method has shown its efficiency, results in more reliable weights and can be used for a wide range of decision support problems, scenario analysis, priority calculation, resource allocation, evaluation of decision alternatives and criteria in various application areas.

Cooperative game theory based consistency and consensus reaching process for group decision making with fuzzy preference relations

Fuzzy preference relations (FPRs) are potent in denoting the pairwise comparison of objects. Besides the consistency analysis, the consensus is critical to making decision results reasonably in group decision making (GDM). Different from current research that either adopts feedback interactive method or optimal model-based total minimum adjustment method, this paper introduces new consensus adjustment mechanisms in the perspective of cooperative games, which determine decision makers (DMs) consistency and consensus adjustments by considering all consistency and consensus adjustment coalitions (CCACs). Compared with previous methods, the main merit of the new method is the reasonable and fair allocation of consistency and consensus adjustment. To achieve this goal, this paper first regards DMs as players in cooperative games and considers each DM coalition’s consistency and consensus adjustment as its payoff. Then, two crucial single-valued payoff indices are offered to allocate the consistency and consensus adjustments to DMs. The axioms of these payoff indices identify rationality and efficiency. Further, a new method is performed that follows the ordinal consistency, acceptable additive consistency, and consensus. Finally, a case study is offered to show the concrete application of the new method, and a comparison is carried out.

Operation mode selection of public-funded private-run elderly care agencies based on triangular intuitionistic fuzzy preference relations group decision-making

Operation mode selection of public-funded private-run elderly care agencies based on triangular intuitionistic fuzzy preference relations group decision-making

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.

A Fractional Programming Model for Improving Multiplicative Consistency of Intuitionistic Fuzzy Preference Relations

In this paper, we propose a method that improves multiplicative consistency based on a fractional programming model to derive the normalized intuitionistic fuzzy priority weight vector from an intuitionistic fuzzy preference relation. To do so, a new definition is formulated that captures previous definitions for multiplicative consistency of intuitionistic fuzzy preference relations. A transformation formula is proposed to convert the normalized intuitionistic fuzzy priority weight vector into a multiplicative consistent intuitionistic fuzzy preference relation. By using the properties of some function, we construct a deviation matrix and prove that the elements in the intuitionistic fuzzy preference relation corresponding to the largest value in the deviation matrix is the most inconsistent. This method not only preserves a lot of the original preference judgments, but also reduce many operations in comparison with previous methods to improve multiplicative inconsistency. Several numerical examples are given to convince the proposed model and method.

Supplier Selection Model Based on D Numbers and Transformation Function

Selecting reasonable suppliers can effectively improve the efficiency of enterprise supply chain management. Among them, expert evaluation is an important part of supplier selection problem, but the uncertainty, fuzziness and incompleteness of expert opinions make supplier selection problem difficult to solve. In order to systematically and effectively solve the uncertainty, ambiguity and incompleteness in supplier selection problem, this paper presents a new supplier selection method based on D numbers and transformation function. First, fuzzy preference relation is generated based on the decision matrix of pairwise comparisons given by experts. D numbers which can effectively deal with uncertain information extend fuzzy preference relation (D matrix). Second, the D matrix is converted into a crisp matrix form based on the integration representation of D numbers according to different situations whether or not the information in D matrix is complete. Third, the crisp matrix is converted into judgement matrix by using the transformation functions. Finally, analytic hierarchy process (AHP) method is applied based on the judgment matrix to give a priority weights for decision making. Three numerical examples and application of the supplier selection are used to show the feasibility and 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.

The Hybrid Multiple-Criteria Decision-Making Model for Home Healthcare Nurses' Job Satisfaction Evaluation and Improvement.

Objectives: To investigate and evaluate the key factors related to job satisfaction performance of home healthcare nurses (HHNs). Methods: A total of 31 HHNs from three community hospitals in Zhejiang province were invited to participate in the study. They completed a questionnaire survey based on the home healthcare nurse job satisfaction scale (HHNJS) from February to March 2022. Consistent fuzzy preference relation (CFPR) methods and important-performance analysis (IPA) were used to obtain the attribute weights and performance for HHNs job satisfaction. Results: The results showed that the attributes of C 13, C 14, C 15, C 23, C 24, C 42, C 51, and C 52 were key factors influencing HHNs job satisfaction. Conclusion: The hybrid multiple-criteria decision-making (MCDM) model can help home-healthcare-agency administrators better understand the key factors related to HHNs job satisfaction and establish reasonable improvement strategies.

Additive consistent triangular fuzzy preference relation and likelihood comparison algorithm based group decision making

Additive consistent triangular fuzzy preference relation and likelihood comparison algorithm based group decision making

An Alternative to Coping with COVID-19—Knowledge Management Applied to the Banking Industry in Taiwan

This study seeks to find an alternative strategy to cope with the impact of COVID-19. Though various measures have been adopted to respond to the threat of the pandemic, the problem remains unchanged. Undoubtedly, COVID-19 is also a crisis of knowledge, so this study explores whether the banking industry in Taiwan can apply knowledge management (KM) and fight the catastrophe of the century successfully and effectively. This study adopts an actual case to analyze the relationship between KM implementation and the banking industry; applies consistent fuzzy preference relations (CFPRs) to evaluate influential criteria including computational simplicity and guarantee the consistency of decision matrices; illustrates a decision-making model with seven criteria; and conducts pairwise comparisons, which are utilized to determine the priority weights of influential criteria amongst the outcome rankings and to formulate accurate KM strategies. The results show that predictions of success probabilities are higher than those of failure probabilities among the seven influential criteria and, in particular, the headquarters system and human resources are the most important priority indicators for implementing KM successfully during the pandemic or post-pandemic. The conclusion suggests significant policy implications for policymakers within other industries or countries in coping with COVID-19.

The service quality of travel service centers in international airports in Taiwan

This pioneering study aimed to analyze the quality of service at international airport travel service centers in Taiwan. A total of 250 customers filled the survey questionnaire and 11 panel experts provided views on service quality attributes. The Fuzzy Delphi Method was used to determine the leading service quality attributes and cluster them into reliability, proficiency, and empathy. Confirmatory factor analysis supported the factorial validity of these dimensions. Consistent fuzzy preference relations was applied to evaluate attributes’ weights. Moreover, importance-performance analysis was used to identify excellent service quality attributes and elicit marketing strategies. The results revealed 22 attributes that pleased consumers or required further development. The study builds a multi-criteria decision service quality assessment system, and through the empirical method, points out a direction for improvement to travel service centers in Taiwan. The findings provided solutions to improve marketing strategies through education, training, and managerial policy changes. The findings may serve as a guide for further cross-border or longitudinal research and practice.

Identify Information Variability in Reciprocal Cognitive Fuzzy Preference Relations by an Additive Transitivity Learning Model

Identify Information Variability in Reciprocal Cognitive Fuzzy Preference Relations by an Additive Transitivity Learning Model