In many decision-making problems the decision maker’s judgments are not crisp, and it is relatively difficult for the decision maker to provide precise numerical values for the criteria or attributes. These kinds of criteria make the evaluation process hard and vague. To deal with vagueness of human thought Zadeh  first introduced the fuzzy set theory, which was oriented to the rationality of uncertainty due to imprecision or vagueness. A major contribution of fuzzy set theory is its capability of representing vague data. In a classical set, an element belongs to, or does not belong to, a set whereas an element of a fuzzy set naturally belongs to the set with a membership value from the interval [0,1]. In this chapter, the procedure of the PROMETHEE method described in Chap. 5 will be applied making the assumption that the performance of alternative solutions are fuzzy while the preferences of the decision-maker, such as the parameters of generalized criteria and the weighting factors, are not. That is, the performance of alternative solutions can be determined only approximately and therefore is introduced into the calculations as a fuzzy number.
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