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On Consistency in AHP and Fuzzy AHP

Author

Listed:
  • Liu Fang

    (School of Mathematics and Information Science, Guangxi University, Nanning 530004, China)

  • Peng Yanan

    (School of Mathematics and Information Science, Guangxi University, Nanning 530004, China)

  • Zhang Weiguo

    (School of Business Administration, South China University of Technology, Guangzhou 510641, China)

  • Pedrycz Witold

    (Department of Electrical and Computer Engineering, University of Alberta, Edmonton T6R 2V4 AB, Canada)

Abstract

The analytic hierarchy process (AHP) is used widely for analyzing decisions made in various real-world applications. Its basic idea is to construct a hierarchy of concepts encountered in a given decision problem and to choose the best alternative according to pairwise comparison matrices given by the decision maker. Under the assumption of fully rational economics, a reasonable decision should be consistent. It becomes an important issue on how to analyze and ensure the consistency of comparison matrices together with the judgments of the decision maker. The main objectives of the present paper are threefold. First, we review the basic idea and methods used to define the consistency and the transitivity of multiplicative reciprocal matrices, additive reciprocal matrices and comparison matrices with fuzzy interval and triangular fuzzy numbers. The existing controversy behind the applications of fuzzy set theory to the AHP in the literature is presented. Second, the consistency of the collective comparison matrices in group decision making based on AHP and fuzzy AHP is further analyzed. We point out that the weak consistency of preference relations with fuzzy numbers in fuzzy AHP and group decision making should be investigated comprehensively. Third, under the consideration of the vagueness in the process of evaluating the judgements, a new concept of fuzzy consistency of comparison matrices in the AHP is given.

Suggested Citation

  • Liu Fang & Peng Yanan & Zhang Weiguo & Pedrycz Witold, 2017. "On Consistency in AHP and Fuzzy AHP," Journal of Systems Science and Information, De Gruyter, vol. 5(2), pages 128-147, April.
    • Handle: RePEc:bpj:jossai:v:5:y:2017:i:2:p:128-147:n:3
    DOI: 10.21078/JSSI-2017-128-20
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    References listed on IDEAS

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