Research On The Consistency Of Distributed Preference Relations And Its Application In Decision Making

As a kind of typical presentation for preference information of decision makers,preference relation is widely applied to many multiple attribute decision making problems under uncertain environment.The traditional preference relations are constructed from the comparison relations between pairwise alteratives with single grade,such as analytic hierarchy process(AHP)and fuzzy preference relation(FPR)and intuitionistic fuzzy preference relation(IFPR),etc.Different from traditional method of comparing pairwise alteratives,distributed preference relation(DPR)generates the comparison relations between pairwise alteratives with multiple grades,which can simultaneously characterize the preferred,non-preferred,indifferent,and uncertain degrees of one alternative over another on a set of grades.Compared with the traditional methods,DPR describes the comparison relations between pairwise alteratives more comprehensively and flexibly,and solve decision making problems with the high complexity and large scale more appropriately.Because DPR remain in the primary stage of its development,it is necessary to analyze and research FPR its in depth and further discuss its transitivity and consistency conditions,which promote the scientific decision making under dynamic and uncertain environment.At first,the consistency condition of FPRs is researched.The transitivity issues of FPRs are descributed systematically from multiple aspects,such as triangle condition,weak transitivity,max-min transitivity,max-max transitivity,restricted max-min transitivity and restricted max-max transitivity.Under the condition of satisfying restricted max-max transitivity,the comparison possibility degrees of DPRs and gives the corresponding proof are analyzed.Then,based on the transitivity conditions of FPRs,the analysis and research of consistency issues of FPR are discussed.Given DPRs between neighboring alternatives,grade scores based combination rule of grades is constructed and its properties are analyzed.The criterion for determining the consistency of DPRs is defined on the basis of the combination rule of grades.Then,a multiple attribute decision making method based on DPRs is researched.In view of the constructed criterion for determining the consistency of DPRs,the combination rule of DPRs between different pairs of alternatives with the satisfaction of consistency can be developed.By regarding the rule as a core,the procedure of the MADA method is designed to make solutions satisfying consistency of DPRs.By using a problem of evaluating the strategic emerging industries of Wuhu,a city of Anhui Province,is analysed and studied to verify the validity and applicability of the related research.The above research has enriched and perfected the theoretical knowledge of DPRs.It has also added scientificity and rationality for the development of decision making problems with uncertainty which is modelled by DPRs.