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Strong reciprocity and strong consistency in pairwise comparison matrix with fuzzy elements

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  • Jaroslav Ramík

    (Silesian University in Opava)

Abstract

The decision making problem considered in this paper is to rank n alternatives from the best to the worst, using the information given by the decision maker in the form of an $$n\times n$$ n × n pairwise comparison matrix. Here, we deal with pairwise comparison matrices with fuzzy elements. Fuzzy elements of the pairwise comparison matrix are applied whenever the decision maker is not sure about the value of his/her evaluation of the relative importance of elements in question. We investigate pairwise comparison matrices with elements from abelian linearly ordered group (alo-group) over a real interval. The concept of reciprocity and consistency of pairwise comparison matrices with fuzzy elements have been already studied in the literature. Here, we define stronger concepts, namely the strong reciprocity and strong consistency of pairwise comparison matrices with fuzzy intervals as the matrix elements (PCF matrices), derive the necessary and sufficient conditions for strong reciprocity and strong consistency and investigate their properties as well as some consequences to the problem of ranking the alternatives.

Suggested Citation

  • Jaroslav Ramík, 2018. "Strong reciprocity and strong consistency in pairwise comparison matrix with fuzzy elements," Fuzzy Optimization and Decision Making, Springer, vol. 17(3), pages 337-355, September.
    • Handle: RePEc:spr:fuzodm:v:17:y:2018:i:3:d:10.1007_s10700-017-9273-0
    DOI: 10.1007/s10700-017-9273-0
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    References listed on IDEAS

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    1. Leung, L. C. & Cao, D., 2000. "On consistency and ranking of alternatives in fuzzy AHP," European Journal of Operational Research, Elsevier, vol. 124(1), pages 102-113, July.
    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. Mikhailov, L., 2004. "A fuzzy approach to deriving priorities from interval pairwise comparison judgements," European Journal of Operational Research, Elsevier, vol. 159(3), pages 687-704, December.
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