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Consistency Test And Weight Generation For Additive Interval Fuzzy Preference Relations, Yejun Xu, Kevin Li, Huimin Wang
Consistency Test And Weight Generation For Additive Interval Fuzzy Preference Relations, Yejun Xu, Kevin Li, Huimin Wang
Odette School of Business Publications
Some simple yet pragmatic methods of consistency test are developed to check whether an interval fuzzy preference relation is consistent. Based on the definition of additive consistent fuzzy preference relations proposed by Tanino (Fuzzy Sets Syst 12:117–131, 1984), a study is carried out to examine the correspondence between the element and weight vector of a fuzzy preference relation. Then, a revised approach is proposed to obtain priority weights from a fuzzy preference relation. A revised definition is put forward for additive consistent interval fuzzy preference relations. Subsequently, linear programming models are established to generate interval priority weights for additive …
Incomplete Interval Fuzzy Preference Relations And Their Applications, Yejun Xu, Kevin Li, Huimin Wang
Incomplete Interval Fuzzy Preference Relations And Their Applications, Yejun Xu, Kevin Li, Huimin Wang
Odette School of Business Publications
This paper investigates incomplete interval fuzzy preference relations. A characterization, which is proposed by Herrera-Viedma et al. (2004), of the additive consistency property of the fuzzy preference relations is extended to a more general case. This property is further generalized to interval fuzzy preference relations (IFPRs) based on additive transitivity. Subsequently, we examine how to characterize IFPR. Using these new characterizations, we propose a method to construct an additive consistent IFPR from a set of n − 1 preference data and an estimation algorithm for acceptable incomplete IFPRs with more known elements. Numerical examples are provided to illustrate the effectiveness …