Research On Multiple Attribute Decision Making Under Linguistic Environment

Multiple attribute decision making (MADM) is an essential part of modern decision science and has been extensively applied to various areas such as project management, management, military, economics, society, etc. The multiple attribute decision making is to select the best alternative from a finite set of alternatives by evaluating a group of predetermined attribute value. When dealing with the problems of multiple attribute decision making in the real world, due to time pressure, lack of knowledge, the vague of human thinking, the uncertainty of human thinking and complexity of objective things, etc., it is more suitable to provide decision makers’ preference relations in their own words. For example, when evaluating the "comfortable" of a house, terms such as "good","bad", and "fair" are frequently used instead of numeric values. The problems of multiple attribute decision making under linguistic environment have attracted more and more researchers’ interest. In the process of the qualitative linguistic information, obtaining the overall values of the alternatives according to based on max operator, min operator and the combination of max operator and min operator has some common defects, which are related to strict Pareto-dominance, the restricted compensation and focus effect. In this thesis, some problems of multiple attribute decision making with linguistic information have been researched. (1) An induced linguistic set is presented for expressing the linguistic information. Based on max operator, min operator, the ideas of triangular norm and triangular co-norm, some new operational laws of linguistic variables are defined. Some properties of the operational laws are studied.(2) According to the numerical encodings of max operator, min operator, the set of linguistic variables is induced to an induced linguistic set. Based on the new qualitative operational laws, some new aggregation operations are employed to refine the max operator, min operator, and their properties are studied to prove their efficiency and rationality. The refinements of max and min operators are used to refine max-min operators under linguistic environment.(3) Based on the proposed operational laws, the ordered weighted averaging (OWA) operator is extended to linguistic environment. The induced linguistic ordered weighted averaging (ILOWA) operator is proposed. Some desirable properties of the ILOWA operator are investigated. The qualitative model of multiple attribute decision making based on the ILOWA operator is presented.(4) On the basis of the new qualitative operational laws, the simple weighted averaging (SAW) operator is developed to the induced linguistic simple weighted averaging (ILSAW) operator in the linguistic environment. Some properties and theorems of the ILSAW operator are studied. A new method of multiple attribute decision making about linguistic information is given.