Consistency test and weight generation for additive interval fuzzy preference relations
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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 interval fuzzy preference relations. A practical procedure is proposed to solve group decision problems with additive interval fuzzy preference relations. Theoretic analysis and numerical examples demonstrate that the proposed methods are more accurate than those in Xu and Chen (Eur J Oper Res 184:266–280, 2008b).
KeywordsMultiple criteria decision analysis Interval fuzzy preference relation Consistency test Weight generation Additive consistent Linear programming
The authors are very grateful to the Associate Editor and the two anonymous reviewers for their constructive comments and suggestions that have further helped to improve the quality and presentation of this paper. Yejun Xu would like to acknowledge the financial support of a Grant (No. 71101043) from National Natural Science of China. Kevin W. Li would like to acknowledge the financial support of a Natural Sciences and Engineering Research Council of Canada (NSERC) Discovery Grant, and Grants (No. 71272129 and 71271188) from National Natural Science Foundation of China. Huimin Wang would like to acknowledge the financial support of a Grant (No. 12&ZD214) from Major Program of the National Social Science Foundation of China.
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