Research On Methods For Grey Multiple Attribute Decision Making

The researching objective of grey systems theory is the uncertain system whose information is partly knowable and partly unknowable. Its character is missing information. We can find its regularity using the knowable information. Due to the ubiquity of missing information uncertain systems, Grey system theories are more prosperous in the future. Furthermore, grey multiple attribute decision making is an important field in present decision sciences, and it can be applied widely to society, economics, management, military affairs and engineering. This paper is to do a research on problems of grey multiple attribute decision making with interval grey numbers, or interval grey numbers and linguistic variables, respectively. The research results are below:(1) Using the operation principle of the standard interval gery number and computing interval grey numbers of overall value of alternatives, ranking method based on the minimax regret approach is proposed for grey multiple attribute decision making problems, including grey multiple attribute group decision making problems, in which the attribute values take interval grey numbers, and the weight information is known, or known partially.Concepts of interval grey number of positive ideal point and negative ideal point are introduced and multiple attribute decision making method marching on ideal point is generalized to grey multiple attribute decision making.(2) The definition of deviation degree between two interval grey numbers is given from the essence of normalized interval grey number as well as the concept and formula. The incidence degree coefficient formula and relative incidence degree coefficient formula are constructed from an analytical technique based on deviation degree for interval grey numbers. Incidence degree decision making approach is put, in which decision-maker'preferences to alternatives are interval grey number with partial weight information.The TOPSIS method of multiple attribute group decision making is generalized to grey multiple attribute group decision making. Two nonlinear programming models and incidence degree decision making approach are established under the situations where decision maker has (or has no) preference information on alternatives for the case of the unknown attribute weight. For grey multiple attribute decision making problems without the attribute weight, according to essence of grey incidence coefficient, the concepts and formulas for predominance strength and predominance comparative matrix between alternatives are introduced and the alternative is ranked according to the priority method of fuzzy complementary judgment matrix. For grey multiple attribute group decision making problems without the attribute weight, according to essence of grey incidence degree, ideal expert, assessment matrix of group incidence degree, and formulas for group predominance strength and group predominance comparative matrix between alternatives are introduced and two methods of ranking alternatives are given by the priority method of fuzzy complementary judgment matrix and by the eigenvector algorithm based on projection.(3) For the case of the known attribute weight, the evidential reasoning approaches are proposed for hybrid grey multiple attribute (or group) decision making problems in which the attribute values are interval grey numbers and linguistic variables, respectively; the grade interval evidential reasoning approach is proposed for hybrid grey multiple attribute decision making problems in which the attribute values are interval grey numbers and uncertain linguistic variables. For hybrid grey multiple attribute decision making problems, in which the information on the attribute's weight is known partially and the attribute values are interval grey numbers and linguistic variables, or the attribute values are interval grey numbers and uncertain linguistic variables, the approaches based on the evidential reasoning are proposed, respectively. In these approaches, through evidential reasoning algorithms, the attribute values are aggregated and two nonlinear programming models are developed. Because classic programming methods are hard to solve the nonlinear programming models, using genetic algorithms to solve the nonlinear programming models, the attribute's weight, the maximum, minimum, and average expected values are gained. So the ranking of the alternatives can be attained. Also, selecting the risk-preferences of the decision maker is a very important, because changing the points of discontinuity in the piecewise linear utility function and choosing whitenization methods of grey information may affect the choice of the best alternative.(4) The research on the application of compromise method for hybrid grey multiple attribute decision making is given.For hybrid grey multiple attribute decision making problems, in which the information on the attribute's weight is unknown,or known and the attribute values are interval grey numbers and linguistic variables, VIKOR method is proposed. Meanwhile, the range of VIKOR is developed.