Multi-Attributes Decision Making Under Uncertainty With The Dempster-Shafer Theory

The Multi-Criteria Decision Making (MCDM) is one of the most important parts of Decision Science. A MCDM problem with countable alternatives is called Multi-Attribute Decision Making (MADM) problem, theories of which hav been developed a lot in the past thirty years especially when making decisions with complete information. However, problems always turn out to be huge and complex in reality and Decision Makers can only be able to get incomplete, imprecise decision information because of time pressure or limitations on capabilities, and so on. Decision information usually exists as fuzzy data, interval data or completely ignorance. A number of approaches have been proposed to solve MADM problems with uncertain information and this paper will focus on one of the most efficient method named Dempster-Shafer theory (DS theory).DS theory is an evidence reasoning approach extended from Bayesian statistics theory and is used widely in various fields because of being able to express uncertainty and ignorance. Researches on DS Theory mainly focus on the following aspects:â‘ Theory researches, such as rules of dealing with conflicting evidence and extension of DS theory;â‘¡Combination with other methods, for example of DS/AHP method and BP-DST method;â‘¢Applications in realities, such as military affairs, Artificial Intelligence, evaluations on risk and credit, and so on. This paper will be arranged referring to the above three points.This paper is organized as follows: Chapter 1 mainly expatiates on the background and purposes of this paper; According to different reasons of conflicting, a few typical rules of combining conflicting evidence are reviewed in Chapter 2. Also, cases of the application of DS theory are introduced. Chapter 3 deals with a recursion method based on DS theory and the application of it in different situations is discussed, including MADM problems with uncertain attributes and known weights of attributes, MADM problems with both uncertain attributes and weights of attributes, MADM problems with interval uncertainties and known weights of attributes, MADM problems with interval uncertainties and uncertain weights of attributes, and so on. At the end of this chapter, a use of DS theory in MADM problems with incomplete preference relations between alternatives is put forward. Chapter 4 focuses on the DS/AHP method. The traditional DS/AHP method and its new development are introduced at first. Then, an Interval DS/AHP method is proposed to solve the problem of interval uncertainty with utility functions unknown in MADM problems base on the interval DS theory and traditional DS/AHP method. A numerical example is taken and proved the method to be efficient and reasonable. Chapter 5 discussed some blanks and limitations of the existing theories of DS.DS theory deals with incomplete information better than other method and is used widely in realities. However, limitations exist, too. For example, the combination of conflicting evidence may create results which are counter-intuitive behaviors; the process of calculation is quite complex, and so on. Further researches are quite necessary.