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

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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.

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Authors and Affiliations

  1. Department of Industrial Engineering, University of Trento, Via Sommarive 9, 38122, Trento, Italy

    Jana Krejčí

  2. Department of Mathematical Analysis and Applications of Mathematics, Faculty of Science, Palacký University Olomouc, 17. listopadu 12, 771 46, Olomouc, Czech Republic

    Ondřej Pavlačka & Jana Talašová

Authors
  1. Jana Krejčí
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  2. Ondřej Pavlačka
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  3. Jana Talašová
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Corresponding author

Correspondence to Ondřej Pavlačka.

Additional information

Research has been supported by the project No. GA 14-02424S Methods of operations research for decision support under uncertainty of the Grant Agency of the Czech Republic.

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Krejčí, J., Pavlačka, O. & Talašová, J. A fuzzy extension of Analytic Hierarchy Process based on the constrained fuzzy arithmetic. Fuzzy Optim Decis Making 16, 89–110 (2017). https://doi.org/10.1007/s10700-016-9241-0

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