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On extension of multiplicative consistency to interval fuzzy preference relations

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  • Jana Krejčí

    (University of Trento
    University of Bayreuth)

Abstract

Various definitions of consistency for interval fuzzy preference relations have been proposed in the literature. The aim of this paper is to review the definitions of multiplicative consistency based on the extension of Tanino’s multiplicative-transitivity property and to point out their drawbacks. In particular, some of the definitions proposed in the literature are not invariant under permutation of objects in interval fuzzy preference relations and some of them violate reciprocity of the pairwise comparisons of objects, which is not acceptable. The weak form of multiplicative-consistency defined by Xu and Chen (Eur J Oper Res 184:266–280, 2008) is approved as the only one appropriate among all definitions examined in the paper. Further, a new definition of multiplicative consistency that is much stronger than the definition proposed by Xu and Chen (Eur J Oper Res 184:266–280, 2008) is introduced. Tools for verifying both the multiplicative consistency defined in this paper and the multiplicative weak consistency defined by Xu and Chen (Eur J Oper Res 184:266–280, 2008) are proposed, and some interesting properties of both multiplicatively consistent and multiplicatively weakly consistent interval fuzzy preference relations are demonstrated. Finally, numerical examples are provided in order to illustrate and compare both types of consistency.

Suggested Citation

  • Jana Krejčí, 2019. "On extension of multiplicative consistency to interval fuzzy preference relations," Operational Research, Springer, vol. 19(3), pages 783-815, September.
    • Handle: RePEc:spr:operea:v:19:y:2019:i:3:d:10.1007_s12351-017-0307-8
    DOI: 10.1007/s12351-017-0307-8
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    References listed on IDEAS

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    1. Matteo Brunelli & Michele Fedrizzi, 2015. "Axiomatic properties of inconsistency indices for pairwise comparisons," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 66(1), pages 1-15, January.
    2. Xu, Zeshui & Chen, Jian, 2008. "Some models for deriving the priority weights from interval fuzzy preference relations," European Journal of Operational Research, Elsevier, vol. 184(1), pages 266-280, January.
    3. Meimei Xia & Zeshui Xu, 2011. "Some Issues On Multiplicative Consistency Of Interval Reciprocal Relations," International Journal of Information Technology & Decision Making (IJITDM), World Scientific Publishing Co. Pte. Ltd., vol. 10(06), pages 1043-1065.
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