Decision-making problem with the vague criteria based on the fuzzy relation equation

For handling human's subjective thought and judgment quantitatively, fuzzy theory has been utilized in various sphere of science, especially in the field of decision-making. Because the mode of human's thinking is an exceeding vague system, the fuzziness is regarded as the most effective way to reflect it. Therefore, it arrests many researcher's attention in recent years. In this paper, we utilize the fuzzy relation in the famous decision-making method of AHP (analytic hierarchy process) for solving the problem which is difficult to evaluate the alternatives by some vague criteria. We consider to establish the fuzzy relation between the vague criteria and some measurable items and make the decision through evaluating the alternatives by the measurable items.