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A fuzzy extension of Analytic Hierarchy Process based on the constrained fuzzy arithmetic

Author

Listed:
  • Jana Krejčí

    (University of Trento)

  • Ondřej Pavlačka

    (Palacký University Olomouc)

  • Jana Talašová

    (Palacký University Olomouc)

Abstract

The aim of the paper is to highlight the necessity of applying the concept of constrained fuzzy arithmetic instead of the concept of standard fuzzy arithmetic in a fuzzy extension of Analytic Hierarchy Process (AHP). Emphasis is put on preserving the reciprocity of pairwise comparisons during the computations. For deriving fuzzy weights from a fuzzy pairwise comparison matrix, we consider a fuzzy extension of the geometric mean method and simplify the formulas proposed by Enea and Piazza (Fuzzy Optim Decis Mak 3:39–62, 2004). As for the computation of the overall fuzzy weights of alternatives, we reveal the inappropriateness of applying the concept of standard fuzzy arithmetic and propose the proper formulas where the interactions among the fuzzy weights are taken into account. The advantage of our approach is elimination of the false increase of uncertainty of the overall fuzzy weights. Finally, we advocate the validity of the proposed fuzzy extension of AHP; we show by an illustrative example that by neglecting the information about uncertainty of intensity of preferences we lose an important part of knowledge about the decision making problem which can cause the change in ordering of alternatives.

Suggested Citation

  • Jana Krejčí & Ondřej Pavlačka & Jana Talašová, 2017. "A fuzzy extension of Analytic Hierarchy Process based on the constrained fuzzy arithmetic," Fuzzy Optimization and Decision Making, Springer, vol. 16(1), pages 89-110, March.
    • Handle: RePEc:spr:fuzodm:v:16:y:2017:i:1:d:10.1007_s10700-016-9241-0
    DOI: 10.1007/s10700-016-9241-0
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    References listed on IDEAS

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    1. Wang, Ying-Ming & Luo, Ying & Hua, Zhongsheng, 2008. "On the extent analysis method for fuzzy AHP and its applications," European Journal of Operational Research, Elsevier, vol. 186(2), pages 735-747, April.
    2. Yoram Wind & Thomas L. Saaty, 1980. "Marketing Applications of the Analytic Hierarchy Process," Management Science, INFORMS, vol. 26(7), pages 641-658, July.
    3. Chang, Da-Yong, 1996. "Applications of the extent analysis method on fuzzy AHP," European Journal of Operational Research, Elsevier, vol. 95(3), pages 649-655, December.
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