Incomplete Information Gray Fuzzy Multi-criteria Decision Making Methods

In the social and economic activities, it is common that people will encounter a lot of grey fuzzy multi-criteria decision-making problems. These problems are the problem of selecting and ranking alternatives where their evaluations are grey fuzzy numbers on multi-criteria. Because of vagueness, grey and indeterminacy of the problems to be decided, it is normal that people will encounter a lot of grey fuzzy multi-criteria decision-making problems whose information of the decision-making factors, such as the weights and the preference values given by the decision-maker, may be incomplete. Recently, few people focus on these problems. Therefore it is significant and meaningful to do some systemic research on the theory and methods of the grey fuzzy multi-criteria decision-making problems, which having incomplete information about the decision making factors being represented by grey fuzzy number.Based on comprehensive research on the current domestic and international situation of grey fuzzy multi-criteria decision-making research, according to grey fuzzy sets, this paper defines interval grey fuzzy numbers and interval grey trapezoidal fuzzy number. Taking their properties into consideration, the studies on theories or methods for multi-criteria decision-making are put to use in the domain of grey fuzzy multi-criteria decision-making to propose corresponding methods. And they are solved on the basis of the optimization theories and algorithms. And the main productions are as follows:(1) The definition, distance and operation principle of interval grey fuzzy numbers are given. Some studies are made on multi-criteria decision-making problems with certain or uncertain weights of criteria and the criteria values in the forms of interval grey fuzzy numbers. For the decision-making problems with certain criteria, a decision-making approach with certain weights of criteria and the criteria values in the forms of interval grey fuzzy numbers is proposed. According to the gradation of criteria values, the criteria values are aggregated by OWA operator. Then ranking alternatives is finished by it. For the decision-making problems with incomplete certain criteria, a decision-making approach with incomeplete certain weights of criteria and the criteria values in the forms of interval grey fuzzy numbers is proposed. An objective programming model is constructed in order to work out optimum weight vector. Based on possibility degree method of interval numbers, ranking alternatives come out.(2) The definitions , distances, measures and operation principle of interval grey trapezoidal fuzzy numbers is given. Some studies are made on multi-criteria decision-making problems with certain or complete unkown weights of criteria and the criteria values in the forms of interval grey trapezoidal fuzzy numbers. For the decision-making problems with certain criteria, a decision-making approach with certain weights of criteria and the criteria values in the forms of interval grey fuzzy trapezoidal numbers is proposed. Expand the TOPSIS method to the decision-making model with the criteria weights and criteria values in the forms of interval grey trapezoidal fuzzy numbers. According to interval grey trapezoidal fuzzy numbers' distance formula, the distance between criteria values and ideal solution is computed, thus obtains the ranking alternatives.For the decision-making problems with complete unkown criteria, a decision-making approach with incomeplete certain weights of criteria and the criteria values in the forms of interval grey fuzzy numbers is proposed. The optimum weight vector of the problem is got by maximal deviation method. The intervals of synthetic criteria values are aggregated by C-OWA operator, and ranking alternatives is given on the basis of interval numbers theory with possibility degree.(3)The definition of interval grey fuzzy judgement matrix is given. And preference information is represented by grey fuzzy judgement matrix. According to minimum deviation method, a linear programming model is constructed to get optimum weight vector, then ranking alternatives is obtained based on C-OWA operator and possibility degree method of interval numbers.