Methods Based On Dempster-Shafer Theory For Multi-attribute Decision Making With Incomplete Information

In social life or economic activities, there exist a great many multi-attribute decision making (MADM) problems. Many perfect methods have been proposed to solve MADM problems with complete information. But in the real case of the MADM problems, decision maker (DM) is willing or able to provide only incomplete information because of decision making information's imprecise, incomplete, fuzzy, and or decision maker's limitations of attention and information processing capabilities, etc. Thus it is necessary and significant to find new theories and methods for MADM problem with incomplete information systemically. This paper focuses on MADM problems with incomplete information, and mainly researches some theories and methods based on Dempster- Shafer theory (DST).This paper involves eight chapters, and the main contents are organized as follows.In Chapter 1, the related decision making methods for MADM problems with imcomplete information are reviewed. Then the research significance, the main contents, and the research methods are also given.In Chapter 2, the basic concepts of Dempster-Shafer theory are introduced, and a MADM rule based on belief interval is proposed. The paper first reviews the basic concepts of Dempster-Shafer theory, and then analyzes the deficiency of the existing decision making rules based on evidence structure. Finally the paper synthetically considers the role of belief function (Bel) and plausibility function (Pls) to the alternatives, and proposes a MADM rule based on belief interval.In Chapter 3, an evidential reasoning approach for MADM problem with incomplete information is proposed. The approach converts quantitative values into qualitative values in decision matrix, determines all possible focal elements based on the decision matrix, and calculates the basic utility assignment of each focal element and the utility interval of each decision alternative. Ranking of decision alternative is then obtained by comparing their utility intervals.In Chapter 4, the MADM problems with hierarchical structure under incomplete information are investigated, and a DS-AHP approach for MADM problems is proposed. The approach identifies all possible focal elements from the incomplete decision matrix, then constructs the DS-AHP's hierarchical structure model, calculates the basic probability assignment (bpa) of each focal element and the belief interval of each decision alternative. Preference relations among all decision alternatives are determined by comparing their belief intervals.In Chapter 5, the process of group multi-attribute decision making (GMADM) is analyzed based on Dempster-Shafer theory. A measuring method of similarity degree for two different evidences is given, and the consistency of experts based on the measuring method is analyzed in the process of GMADM. The expert's relative reliability is introduced, Dempster's rule of combination is improved, and a new expertise aggregation approach is proposed.In Chapter 6, hybrid group multi-attribute decision making (GMADM) problems having both quantitative and qualitative attributes under incomplete information are investigated. An approach for hybrid GMADM problems is developed. By dealing with the incomplete decision matrix given by decision makers, the bpa values of attribute's focal elements are computed and integrated according to Dempster's rule of combination. The bpa values of expert's focal elements are integrated, and the values of Bel and Pls are calculated and used to rank all decision alternatives.In Chapter 7, a new approach is developed for GMADM problems with incomplete linguistic information. The approach converts linguistic variables and calculates the basic utility assignment value of each focal element. The values are integrated according to Dempster's rule of combination. Alternatives are then ranked by comparing the values of belief function and plausibility function. The last chapter summarizes all the work of this paper, and gives some useful suggestions for future research.This paper proposes the innovation as follows:(1) The membership function is introduced, and an evidential reasoning approach for MADM problem with incomplete information is proposed.(2) The DS-AHP method for MADM problems with incomplete information is proposed, which incorporates Dempster-Shafer theory of evidence with Analytic Hierarchy Process (AHP).(3) Dempster-Shafer theory of evidence with Fuzzy Theory is incorporated, and two approaches are developed for hybrid GMADM problem with incomplete information and linguistic GMADM problem with incomplete information, respectively.