Consistency test and weight generation for additive interval fuzzy preference relations |
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Authors: | Yejun Xu Kevin W Li Huimin Wang |
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Affiliation: | 1. State Key Laboratory of Hydrology-Water Resources and Hydraulic Engineering, Hohai University, Nanjing, 210098, People’s Republic of China 2. Business School, Hohai University, Jiangning, Nanjing, 211100, People’s Republic of China 3. Odette School of Business, University of Windsor, Windsor, ON, N9B 3P4, Canada
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Abstract: | 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). |
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