A Novel Method for Fuzzy Multi-Criteria Decision Making

To determine the weight vector and to aggregate the individual opinions are necessary steps in the classical methods for multi-criteria group decision-making problems in which the weight vectors of the decision makers and the criteria are incompletely known. In this paper, we propose a simple but efficient approach which can avoid these steps by establishing some optimal models. To get the optimal group decision matrix, we first propose two kinds of models among which the former focuses on minimizing the deviations between individual decision matrix and the ideal group one, while the latter aims at minimizing the deviations between the estimated group opinion and the ideal group one. To get the overall performances of alternatives, another two types of models are further established, one of which is to minimize the distance between the evaluation value under each criterion and the ideal overall value for each alternative, and the other is to minimize the distance between the estimated overall value and the ideal overall one. The proposed models can be used to deal with group decision-making under intuitionistic fuzzy, interval-valued fuzzy or other fuzzy environments, and can also provide the decision makers more choices by containing the parameter which can be assigned different values according to different actual situations. Several examples illustrate the practicability of the proposed methods.