Chi-square ranking method for the fuzzy judgement matrix

A chi-square method is presented for ranking alternatives based on a kind of fuzzy judgement matrix about the alternatives provided by the decision maker. Firstly, structure of fuzzy judgement matrix and its consistency are introduced. Then, an optimization model is constructed to obtain ranking values of the alternatives. The theory and the algorithms for solving the model are also discussed. The ranking values of alternatives can be obtained by the model and the rankings of alternatives can reflect the subjective preference of the decision maker accurately. Finally, a numerical example is given to illustrate the effectiveness of the proposed method.