Researches On The Consistency Of Fuzzy Recip-Rocal Judgment Matrix And Methods Aggregating Individual Preferences Into A Group Preference

Analytic hierarchy process (AHP) is a practical and effective decision-making method. It has been widely applied to society, economy, management, engineering systems and so on. With the development of AHP theory and the actual requirements of applications, the fuzzy idea and fuzzy methods are introduced to AHP, so the fuzzy analytic hierarchy process (FAHP) has been shaping, which is just consistent with the fuzziness of men's thought. When we use FAHP to make decisions, we have to construct a compared judgment matrix which is fuzzy reciprocal, and the matrix is reasonable or not will have a direct effect on the decision .Moreover, the important rule which judges the matrix reasonable or not is that whether the matrix is absolute consistent or satisfied consistent. Therefore, the problem of the consistency of fuzzy reciprocal judgment matrix has been one of problems attracting more and more attention. On the other hand, with the development of society, advancement of the technology and increase of the knowledge and information, the decision-making problems are more and more complex. So the cases that many individuals participate in a decision process are more and more, which are called the group decision-making. In group decision-making, the information about the alternatives provided by the experts may be of a diverse nature, so how aggregating the information in different forms into a unified form is a problem worthy of research.This paper studies the consistency of fuzzy reciprocal judgment matrix and the methods aggregating information in different forms in group decision-making. The main research works are as follows:In Chapter 1, the recent researches on the consistency of fuzzy reciprocal judgment matrix and the methods aggregating the different forms information in group decision-making are briefly reviewed. The main research problems in this paper are also involved.In Chapter 2, Firstly, often used conceptions and properties in fuzzy reciprocal judgment matrix are proposed. Secondly, some test standards on additive consistency of fuzzy reciprocal judgment matrix are concluded. Moreover, some of them are improved. Finally, three methods for adjusting the consistency of the fuzzy reciprocal judgment matrix are proposed, the using area separately is indicated, and the convergence of the third method is demonstrated.In Chapter 3,the sensitivity to the consistency-adjusting is analyzed, and the sensitivity changing areas, which make the primary matrix still consistent, are put forward while a pair of elements or a line elements and the elements of the row corresponding the line changing.In Chapter 4, the problem how transform the preference information in different forms into one form information is researched, and the problem how aggregate the preference information from different experts into a group preference information. The existing results are first summarized, the problems needing attention in changing process are pointed, and then a method, which transforms the interval utility value into a fuzzy reciprocal matrix, is proposed. Finally the three aggregating methods are proposed.In the end, this paper is summarized, and the suggestions about the studied contents of group decision-making based on fuzzy reciprocal judgment matrix in the future are proposed.