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Decision Analysis with the Set of Normalized Triangular Fuzzy Weight Vectors in Fuzzy AHP

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Integrated Uncertainty in Knowledge Modelling and Decision Making (IUKM 2022)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 13199))

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Abstract

Intervals and fuzzy numbers have been introduced to the analytic hierarchy process (AHP) reflecting the vagueness of the decision maker. In this paper, we propose a fuzzy AHP approach to multiple criteria decision analysis. First we investigate the normalized fuzzy weight vector estimation problem under a given fuzzy pairwise comparison matrix (PCM). After reviewing a previous approach to the estimation problem, we show the non-uniqueness of the normalized fuzzy weight vector associated with a consistent fuzzy PCM. Those normalized fuzzy weight vectors associated with the same consistent fuzzy PCM are at the same distance from the given PCM. Therefore, we require that all such fuzzy weight vectors should be the solutions to the estimation problem. As the previous estimation method does not satisfy this requirement, the estimation method is modified so that all such normalized fuzzy weight vectors are estimated. Then a decision analysis with all such normalized fuzzy weight vectors is proposed. The stability of the best alternative can be scrutable as the range of alternative orderings is analyzed by the proposed approach.

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Acknowledgements

This work is supported by JSPS KAKENHI Grant Number JP18H01658.

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Authors and Affiliations

  1. Graduate School of Engineering Science, Osaka University Toyonaka, Osaka, Japan

    Shigeaki Innan & Masahiro Inuiguchi

Authors
  1. Shigeaki Innan
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  2. Masahiro Inuiguchi
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Corresponding author

Correspondence to Shigeaki Innan .

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Editors and Affiliations

  1. Osaka Prefecture University, Sakai, Osaka, Japan

    Katsuhiro Honda

  2. University of Hyogo, Kobe, Japan

    Tomoe Entani

  3. Osaka Prefecture University, Sakai, Japan

    Seiki Ubukata

  4. Japan Advanced Institute of Science and Technology, Nomi, Japan

    Van-Nam Huynh

  5. Osaka University, Toyonaka, Osaka, Japan

    Masahiro Inuiguchi

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Innan, S., Inuiguchi, M. (2022). Decision Analysis with the Set of Normalized Triangular Fuzzy Weight Vectors in Fuzzy AHP. In: Honda, K., Entani, T., Ubukata, S., Huynh, VN., Inuiguchi, M. (eds) Integrated Uncertainty in Knowledge Modelling and Decision Making. IUKM 2022. Lecture Notes in Computer Science(), vol 13199. Springer, Cham. https://doi.org/10.1007/978-3-030-98018-4_6

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  • DOI: https://doi.org/10.1007/978-3-030-98018-4_6

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-98017-7

  • Online ISBN: 978-3-030-98018-4

  • eBook Packages: Computer ScienceComputer Science (R0)

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