Fuzzy multiple attributes group decision-making based on fuzzy preference relations

In this paper, we present a new approach for fuzzy multiple attributes group decision-making based on fuzzy preference relations. First, we construct fuzzy importance matrices for decision-makers with respect to attributes and construct fuzzy evaluating matrices for decision-makers with respect to the attributes of the alternatives. Based on the fuzzy importance matrices and the fuzzy evaluating matrices, we construct fuzzy rating vectors for decision-makers with respect to the alternatives. Then, we defuzzify the trapezoidal fuzzy numbers in the constructed fuzzy rating vectors to get the rating vectors for the decision-makers. Based on the rating vectors, we construct fuzzy preference relations for the decision-makers with respect to the alternatives. Based on the fuzzy preference relations, we calculate the average rating value of each decision-maker with respect to the alternatives. Then, we sort these average rating values in a descending sequence and assign them different scores. Then, we calculate the summation values of the scores of the alternatives with respect to each decision-maker, respectively. The larger the summation values of the scores, the better the choice of the alternative. The proposed method is simpler than Chen’s method (2000) and Li’s method (2007) for handling fuzzy multiple attributes group decision-making problems. It provides us with a useful way to handle fuzzy multiple attributes group decision-making problems.