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Non-uniqueness of Interval Weight Vector to Consistent Interval Pairwise Comparison Matrix and Logarithmic Estimation Methods

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Integrated Uncertainty in Knowledge Modelling and Decision Making (IUKM 2016)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 9978))

Abstract

In this paper we investigate the interval priority weight estimation from a given interval pairwise comparison matrix. The lower and upper models as well as goal programming model were proposed. It has been expected that the sum of widths of interval weights estimated by lower model is not greater than that estimated by upper model. We show that this expectation is not always hold. Especially when the given interval comparison matrix is totally consistent, it is possible that the solution is not unique and the reverse inequality relation holds. We investigate uniqueness conditions of interval comparison matrices and the influence of non-uniqueness in the comparison of alternatives. Based on the results of investigation above, we propose interval weight estimation methods from interval pairwise comparison matrix.

This work was partially supported by JSPS KAKENHI Grant Number 26350423.

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Authors and Affiliations

  1. Graduate School of Engineering Science, Osaka University, Toyonaka, Osaka, 560-8531, Japan

    Masahiro Inuiguchi

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  1. Masahiro Inuiguchi
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Correspondence to Masahiro Inuiguchi .

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Editors and Affiliations

  1. Japan Advanced Institute of Science and Technology, Nomi, Ishikawa, Japan

    Van-Nam Huynh

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

    Masahiro Inuiguchi

  3. University of Science, Ho Chi Minh City, Vietnam

    Bac Le

  4. Duy Tan University, Da Nang, Vietnam

    Bao Nguyen Le

  5. Université de Technologie de Compiègne , Compiègne, France

    Thierry Denoeux

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Inuiguchi, M. (2016). Non-uniqueness of Interval Weight Vector to Consistent Interval Pairwise Comparison Matrix and Logarithmic Estimation Methods. In: Huynh, VN., Inuiguchi, M., Le, B., Le, B., Denoeux, T. (eds) Integrated Uncertainty in Knowledge Modelling and Decision Making. IUKM 2016. Lecture Notes in Computer Science(), vol 9978. Springer, Cham. https://doi.org/10.1007/978-3-319-49046-5_4

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  • DOI: https://doi.org/10.1007/978-3-319-49046-5_4

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-49045-8

  • Online ISBN: 978-3-319-49046-5

  • eBook Packages: Computer ScienceComputer Science (R0)

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