Incomplete Fuzzy Preference Relations Research Articles

A NOTE ON THE ESTIMATION OF MISSING PAIRWISE PREFERENCE VALUES: A UNINORM CONSISTENCY BASED METHOD

Dealing with incomplete information is an important problem in decision making. In this paper, we present a short discussion on this topic and a new estimation method of missing values in an incomplete fuzzy preference relation which is based on the modelling of consistency of preferences via a representable uninorm.

AN APPROACH TO GROUP DECISION MAKING BASED ON INCOMPLETE FUZZY PREFERENCE RELATIONS

In this paper, a new approach is proposed to solve group decision making (GDM) problems where the preference information on alternatives provided by decision makers (DMs) is represented in incomplete fuzzy preference relations. In order to make the collective opinion close each decision maker's opinion as near as possible, an optimization model is constructed to integrate the incomplete fuzzy preference relations and to compute the collective ranking values of alternatives. The ranking of alternatives or selection of the most desirable alternative(s) is directly obtained from the derived collective ranking values. A numerical example is also used to illustrate the applicability of the proposed approach.

A Consensus Model for Group Decision Making With Incomplete Fuzzy Preference Relations

Two processes are necessary to solve group decision making problems: A consensus process and a selection process. The consensus reaching process is necessary to obtain a final solution with a certain level of agreement between the experts; and the selection process is necessary to obtain such a final solution. In a previous paper, we present a selection process to deal with group decision making problems with incomplete fuzzy preference relations, which uses consistency measures to estimate the incomplete fuzzy preference relations. In this paper we present a consensus model. The main novelty of this consensus model is that of being guided by both consensus and consistency measures. Also, the consensus reaching process is guided automatically, without moderator, through both consensus and consistency criteria. To do that, a feedback mechanism is developed to generate advice on how experts should change or complete their preferences in order to reach a solution with high consensus and consistency degrees. In each consensus round, experts are given information on how to change their preferences, and to estimate missing values if their corresponding preference relation is incomplete. Additionally, a consensus and consistency based induced ordered weighted averaging operator to aggregate the experts' preferences is introduced, which can be used in consensus models as well as in selection processes. The main improvement of this consensus model is that it supports the management of incomplete information and it allows to achieve consistent solutions with a great level of agreement.

Group Decision-Making Model With Incomplete Fuzzy Preference Relations Based on Additive Consistency

In decision-making problems there may be cases in which experts do not have an in-depth knowledge of the problem to be solved. In such cases, experts may not put their opinion forward about certain aspects of the problem, and as a result they may present incomplete preferences, i.e., some preference values may not be given or may be missing. In this paper, we present a new model for group decision making in which experts' preferences can be expressed as incomplete fuzzy preference relations. As part of this decision model, we propose an iterative procedure to estimate the missing information in an expert's incomplete fuzzy preference relation. This procedure is guided by the additive-consistency (AC) property and only uses the preference values the expert provides. The AC property is also used to measure the level of consistency of the information provided by the experts and also to propose a new induced ordered weighted averaging (IOWA) operator, the AC-IOWA operator, which permits the aggregation of the experts' preferences in such a way that more importance is given to the most consistent ones. Finally, the selection of the solution set of alternatives according to the fuzzy majority of the experts is based on two quantifier-guided choice degrees: the dominance and the nondominance degree.

A Procedure for Decision Making Based on Incomplete Fuzzy Preference Relation

In this paper, we investigate the decision making problem based on fuzzy preference relation with incomplete information. We first introduce incomplete fuzzy preference relation and present some of...

Goal programming models for obtaining the priority vector of incomplete fuzzy preference relation

In this paper, we first define the concepts of incomplete fuzzy preference relation, additive consistent incomplete fuzzy preference relation and multiplicative consistent incomplete fuzzy preference relation, and then propose two goal programming models, based on additive consistent incomplete fuzzy preference relation and multiplicative consistent incomplete fuzzy preference relation respectively, for obtaining the priority vector of incomplete fuzzy preference relation. These two goal programming models are also extended to obtain the collective priority vector of several incomplete fuzzy preference relations. Finally, two illustrative numerical examples are given to verify the developed models.