Several 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 and several grey fuzzy numbers which have been defined, 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) Some studies are made on multi-criteria decision-making problems with certain,uncertain or complete unkown weights of criteria and the criteria values in the forms of grey interval fuzzy numbers and interval grey trapezoidal fuzzy numbers by respectively use SPA(Set Pair Analysis) and F-OWA (Fuzzy Ordered Weighted Averaging) operator. For the multi-criteria decision-making problems with certain and uncertain weights of criteria and the criteria values in the forms of grey interval fuzzy numbers, the decision-making approach based on SPA(Set Pair Analysis) and the decision-making TOPSIS approach based on SPA(Set Pair Analysis) are respectively proposed. Some studies are made on multi-criteria decision-making problems with certain and complete unkown weights of criteria and the criteria values in the forms of interval grey trapezoidal fuzzy numbers by use F-OWA (Fuzzy Ordered Weighted Averaging) operator.(2) Some studies are made on multi-criteria decision-making problems with certain weights of criteria and the criteria values in the forms of interval grey interval fuzzy numbers by use PROMETHEE approach, use each scheme with ideal scheme's closeness degree deviation as variable of Preference Function,and then calculate fuzzy outflow,fuzzy inflow and fuzzy net flow, the ranking of alternatives is expressed according to fuzzy net flow. For the multi-criteria decision-making problems with certain weights of criteria and the criteria values in the forms of interval grey interval fuzzy numbers,the degree sorting method is proposed, use each scheme with ideal scheme's closeness degree deviation as variable of Degree Function, building degree matrix, calculate scheme's global degree flow,and then to sort schemes according to degree flow. For the multi-criteria decision-making problems with complete unkown weights of criteria and the criteria values in the forms of interval grey interval fuzzy numbers, the optimum weight vector of the problem is got by maximal deviation method, and then calculate scheme's global degree flow, then to sort schemes according to degree flow.(3) Some studies are made on multi-criteria decision-making problems with preference information are interval grey interval fuzzy numbers and interval grey fuzzy judgement matrix which given by the decision maker. The deviation of preference information given by the decision maker with synthetic criteria values is introduced. The optimum weight vector of the problem is got by minimum deviation method. And then synthetic criteria values of each scheme is obtained, finally the alternative ranking is obtained.