Reasonable properties for the ordering of fuzzy quantities (II)

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.

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

Linear programming with fuzzy parameters: an interactive method resolution

Ranking fuzzy numbers plays an very important role in linguistic decision making and some other fuzzy application systems. Several strategies have been proposed for ranking of fuzzy numbers. Each of these techniques have been shown to produce non-intuitive results in certain cases. In this paper, we will introduce a new approach for ranking of trapezoidal fuzzy numbers based on the left and the right spreads at some @a-levels of trapezoidal fuzzy numbers. The calculation of the proposed method is far simpler and easier. Finally, some comparative examples are used to illustrate the advantage of the proposed method.

A new approach for ranking of trapezoidal fuzzy numbers

Fuzzy data envelopment analysis (DEA): a possibility approach☆

Preliminaries.- Basics of Fuzzy Sets.- Fuzzy Relations.- Extension Principle and Fuzzy Numbers.- A Brief Introduction to Some Pure Mathematical Topics.- Fuzzy Inference and Fuzzy Control.

Mathematics of Fuzziness―Basic Issues

In this paper, we classify all the approaches to order fuzzy quantities into three classes. Then we focus our attention on the investigation of dependency among the elements of the first class of ordering approaches.

On the Classification and the Dependencies of the Ordering Methods

An investigation into relations between some transitivity-related concepts

In this paper we introduce a definition of consistency of the judgement matrix in the fuzzy Analytic Hierarchy Process (AHP) and give a general expression of all fuzzy weights under the condition of consistency. Finally, based on our discussion, the geometric average method is suggested for fuzzy weights calculation in the practical decision-making situation.

Xuzhu Wang

Papers

Reasonable properties for the ordering of fuzzy quantities (II)

Mathematics of Fuzziness―Basic Issues

On the Classification and the Dependencies of the Ordering Methods

An investigation into relations between some transitivity-related concepts

Consistency of judgement matrix and fuzzy weights in fuzzy analytic hierarchy process