Types Of Preference Relations Research Articles

Conflict analysis of multiple decision-makers ecological environment governance of water resources based on graph model with heterogeneous preference in China's South-to-North water transfer project

Ecological environment governance of water resources is the foundation and key measures to ensure good water quality in China's South-to-North Water Transfer Project. However, as a limited rational economic person, considering their economic benefit, different involvers in China's South-to-North Water Transfer Project show different types of preference relations and make different action decisions as well as play conflicts with each other, which have a negative effect on ecological environmental governance. To overcome above-described shortcomings, heterogeneous preferences are integrated into graph model for conflict resolution (GMCR) to resolve ecological environment governance conflict of water resources. Specifically, first, four different structures of preference expression, including preference orderings, utility functions, multiplicative preferences, and additive preferences, are used to represent decision-maker's (DM's) preference information over states. Then, a novel preference ranking method is designed to calculate the ordinal preferences over all states by using matrix representation. Based on this, a set of heterogeneous stability definitions is proposed in GMCR to describe human diversified choice and behavior in detail, and it is applied to the ecological environment governance conflict of water resources in China's South-to-North Water Transfer Project. The heterogeneous stability analysis result showed that incentive policies used by water resources agencies can effectively encourage local governments and enterprises to actively participate in the ecological environment governance, and promote the ecological environment governance conflict to evolve into a state of equilibrium.

A Group Decision Making Approach Considering Self-confidence Behaviors and Its Application in Environmental Pollution Emergency Management.

Self-confidence as one of the human psychological behaviors has important influence on emergency management decision making, which has been ignored in existing methods. To fill this gap, we dedicate to design a group decision making approach considering self-confidence behaviors and apply it to the environmental pollution emergency management. In the proposed method, the self-confident fuzzy preference relations are utilized to express experts’ evaluations. This new type of preference relations allow experts to express multiple self-confidence levels when providing their evaluations, which can deal with the self-confidence of them well. To apply the proposed group decision making method to environmental pollution emergency management, a novel determination of the decision weights of experts is given combining the subjective and objective weights. The subjective weight can be directly assigned by organizer, while the objective weight is determined by the self-confidence degree of experts on their evaluations. Afterwards, by utilizing the weighted averaging operator, the individuals’ evaluations can be aggregated into a collective one. To do that, some operational laws for self-confident fuzzy preference relations are introduced. And then, a self-confidence score function is designed to get the best solution for environmental pollution emergency management. Finally, some analyses and discussions show that the proposed method is feasible and effective.

A new procedure for hesitant multiplicative preference relations

Hesitant information is powerful and flexible to denote decision maker's judgments. Hesitant multiplicative preference relations (HMPRs) own the advantages of preference relations and hesitant fuzzy sets that permit the decision makers (DMs) to compare objects by using several values. Just as other types of preference relations, how to derive the priority weight vector is a crucial step. According to the principle of the consistency concept for multiplicative preference relations, this paper first introduces a new consistency concept for HMPRs, which avoids the disadvantages of the previous ones. Using the new concept, models to judge the consistency of HMPRs are built. Then, a consistency probability-based method to derive the hesitant fuzzy priority weight vector from HMPRs is offered. Considering the incomplete case, consistency-based programming models to determine the missing values are constructed. To address group decision making with HMPRs, a distance measure is defined to determine the weights of the DMs, and a consensus index is proposed. Then, a consistency and consensus-based group decision-making algorithm is performed. Finally, two practical examples, an investment problem and a water conservancy problem are offered to illustrate the feasibility and efficiency of the new algorithm. Comparison analysis from the numerical and theoretical aspects verifies the potential application of the new procedure.

Deriving the priority weights from multiplicative consistent single-valued neutrosophic preference relations

Preference relation is one of the most important and relatively simple approaches to address decision-making problems. As a special case of neutrosophic sets, the single-valued neutrosophic set (SVNS) is an efficient and powerful tool to deal with imprecise and inconsistent information. Taking the advantages of preference relations and SVNSs, this paper introduces single-valued neutrosophic preference relations (SVNPRs). Just as other types of preference relations, consistency and consensus analyses are indispensable to guarantee the ranking order logically. A multiplicative consistency concept for SVNPRs is introduced. On the basis of this concept, several multiplicative consistency-based 0–1 mixed programming models are established to derive multiplicatively consistent SVNPRs and estimate missing values in incomplete SVNPRs, respectively. As for group decision-making, a distance measure-based consensus index is presented. Moreover, an algorithm for group decision-making with SVNPRs is developed, which can deal with incomplete and inconsistent SVNPRs. Finally, a practical example is offered to show the practicability of the new procedure, and comparison is made with several previous methods about decision-making with SVNSs.

An approach to decision-making with triangular fuzzy reciprocal preference relations and its application

ABSTRACTTriangular fuzzy reciprocal preference relations (TFRPRs) are powerful tools to denoting decision-makers’ fuzzy judgments, which permit the decision-makers to apply triangular fuzzy ratio rather than real numbers to express their judgements. Consistency analysis is one of the most crucial issues in preference relations that can guarantee the reasonable ranking order. However, all previous consistency concepts cannot well address this type of preference relations. Based on the operational laws on triangular fuzzy numbers, this paper introduces an additive consistency concept for TFRPRs by using quasi TFRPRs, which can be seen as a natural extension of the crisp case. Using this consistency concept, models to judging the additive consistency of TFRPRs and to estimating missing values in complete TFRPRs are constructed. Then, an algorithm to decision-making with TFRPRs is developed. Finally, two numerical examples are offered to illustrate the application of the proposed procedure, and comparison analysis is performed.

A consistency and consensus-based method to group decision making with interval linguistic preference relations

Preference relations are a powerful tool to address decision-making problems. In some situations, because of the complexity of decision-making problems and the inherent uncertainty, the decision makers cannot express their preferences by using numerical values. Interval linguistic preference relations, which are more reliable and informative for the decision-makers’ preferences, are a good choice to cope with this issue. Just as with the other types of preference relations, the consistency and consensus analysis is very importance to ensure the reasonable ranking order by using interval linguistic preference relations. Considering this situation, this paper introduces a consistency concept for interval linguistic preference relations. To measure the consistency of interval linguistic preference relations, a consistency measure is defined. Then, a consistency-based programming model is built, by which the consistent linguistic preference relations with respect to each object can be obtained. To cope with the inconsistency case, two models for deriving the adjusted consistent linguistic preference relations are constructed. Then, a consistency-based programming model to estimate the missing values is built. After that, we present a group consensus index and present some of its desirable properties. Furthermore, a group consensus-based model to determine the weights of the decision makers with respect to each object is established. Finally, an approach to group decision making with interval linguistic preference relations is developed, which is based on the consistency and consensus analysis. Meanwhile, the associated numerical examples are offered to illustrate the application of the procedure.

A technical note on two inconsistency indices for preference relations: A case of functional relation

Different representations of valued preferences have been studied and used over the years; however, one common factor has been the prominence of the concept of consistency. Inconsistency indices have been introduced to estimate the deviation of preferences from a fully consistent form. In this note we shall recall two types of preference relations (reciprocal relations and multiplicative preference relations) and show that two inconsistency indices introduced in these two different frameworks are functionally related. Besides this main result, some reflections on the consequences of being functionally related are presented.

A GOAL PROGRAMMING APPROACH TO GROUP DECISION MAKING WITH INCOMPLETE FUZZY AND INTERVAL PREFERENCE RELATIONS

In order to solve group decision making (GDM) problems where the preference relations are provided by decision makers with incomplete fuzzy and interval numbers, this paper develops a GDM approach on the basis of multiple objective optimization and goal programming methods. The proposed approach first analyzes the two types of preference relations and then builds their respective optimization models. Subsequently, an integrated programming model combining the two preference relations is developed to minimize the inconsistency among the decision makers' opinions. By solving the programming model, the ranking of alternatives or selection of the most desirable alternative can be obtained using the intermediate priority vector. Two numerical examples including incomplete fuzzy and interval preference relations are examined to illustrate and show the applicability of the proposed approach.

On the priority vector associated with a reciprocal relation and a pairwise comparison matrix

We propose two straightforward methods for deriving the priority vector associated with a reciprocal relation, by some authors called fuzzy preference relation. Then, using transformations between pairwise comparison matrices and reciprocal relations, we study the relationships between the priority vectors associated with these two types of preference relations. Eventually, we show a brief example involving the newly introduced characterizations.

A survey of preference relations

Preference Relations are a popular and powerful tool used by decision makers to provide their preference information in the process of decision making. Over the last decades, various types of preference relations have been developed, but they are scattered through the literature. The purpose of this paper is to present a comprehensive survey of preference relations. We also briefly discuss their properties and introduce some new preference relations. Finally, we put forward the directions of future research.

Scoring rule and majority agreements for large electorates with arbitrary preferences

This paper examines elections among three candidates when the electorate is large and voters can have any of the 26 nontrivial asymmetric binary relations on the candidates as their preference relations. Comparisons are made between rule-λ rankings based on rank-order ballots and simple majorities based on the preference relations. The rule-λ ranking is the decreasing point total order obtained when 1, λ and 0 points are assigned to the candidates ranked first, second and third on each voter's ballot, with 0 ⩽ λ ⩽ 1. Limit probabilities as the number of voters gets large are computed for events such as ‘the first-ranked rule-λ candidate has a majority over the second-ranked rule-λ candidate’ and ‘the rule-λ winner is the Condorcet candidate, given that there is a Condorcet candidate’. The probabilities are expressed as functions of λ and the distribution of voters over types of preference relations. In general, they are maximized at λ = 1/2 (Borda) and minimized at λ = 0 (plurality) and at λ = 1 for any fixed distribution of voters over preference types. The effects of more indifference and increased intransitivity in voter's preference relations are analyzed when λ is fixed.

An axiomatic system for multidimensional preferences

An axiomatic system TP is developed which allows the amalgamation of linear preferences (preferences in respect to different criteria) according to the weights of those criteria. Section 1 deals with linear preferences. In Section 2 an axiomatic system for the ordering of classes of criteria is formulated. Section 3 explains the development of system TP. Two TP-systems are distinguished, based on two different linear preference systems. The preference relation of TP is shown to be nontransitive, while the linear preference relation is transitive. In 3.7 an alternative-system TP′ is given. Section 3.8 deals with formulas concerning the disjunction of alternatives, which are not valid in TP, even though they are valid in a linear preference system. In Section 4 types of preference relations and types of alternatives are distinguished to get the opportunity to express preferences between preferences.