Correspondence between Incomplete Fuzzy Preference Relation and Its Priority Vector

Fuzzy preference relations are frequently adopted by decision makers to express their preference tendency toward alternatives. Due to the lack of expertise of knowledge, decision makers may not be able to specify complete preference relation. To deal with incomplete fuzzy preference relations, Xu [26] proposed prioritization methods for incomplete fuzzy preference relations where he postulated a correspondence between priority vector and additive consistent incomplete fuzzy preference relation. In this paper, we are going to prove the correspondence does not always hold.

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