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Logarithmic Conversion Approach to the Estimation of Interval Priority Weights from a Pairwise Comparison Matrix

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Integrated Uncertainty in Knowledge Modelling and Decision Making (IUKM 2015)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 9376))

Abstract

An alternative method for the estimation of interval priority weights in Interval AHP is proposed. The proposed method applies the logarithmic conversion to components of the pairwise comparison matrix and obtains logarithmically-converted interval priority weights so as to minimize the sum of their widths. The logarithmically-converted interval priority weights are estimated as an optimal solution of a linear programming problem. The interval priority weights are obtained by the antilogarithmic conversion of the optimal solution and by the normalization. Numerical experiments are conducted to demonstrate the advantages of the proposed estimation over the conventional estimation.

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References

  1. Saaty, T.L.: The Analytic Hierarchy Process. McGraw-Hill, New York (1980)

    MATH  Google Scholar 

  2. Saaty, T.L., Vargas, C.G.: Comparison of eigenvalue, logarithmic least squares and least squares methods in estimating ratios. Mathematical Modelling 5, 309–324 (1984)

    Article  MathSciNet  MATH  Google Scholar 

  3. van Laarhoven, P.J.M., Pedrycz, W.: A fuzzy extension of Saaty’s priority theory. Fuzzy Sets and Systems 11, 199–227 (1983)

    Article  MathSciNet  MATH  Google Scholar 

  4. Buckley, J.J.: Fuzzy hierarchical analysis. Fuzzy Sets and Systems 17, 233–247 (1985)

    Article  MathSciNet  MATH  Google Scholar 

  5. Wang, Y.-M., Elhag, T.M.S., Hua, Z.: A modified fuzzy logarithmic least squares method for fuzzy analytic hierarchy process. Fuzzy Sets and Systems 157, 3055–3071 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  6. Arbel, A.: Approximate articulation of preference and priority derivation. European Journal of Operational Research 43m, 317–326 (1989)

    Article  MathSciNet  MATH  Google Scholar 

  7. Sugihara, K., Tanaka, H.: Interval evaluations in the analytic hierarchy process by possibilistic analysis. Computational Intelligence 17, 567–579 (2001)

    Article  Google Scholar 

  8. Sugihara, K., Ishii, H., Tanaka, H.: Interval priorities in AHP by interval regression analysis. European Journal of Operational Research 158, 745–754 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  9. Tanaka, H., Nagasaka, K., Hayashi, I.: Interval regression analysis by possibilistic measures (in Japanese). The Japanese Journal of Behaviormetrics 16, 1–7 (1988)

    Article  Google Scholar 

  10. Entani, T., Inuiguchi, M.: Pairwise comparison based interval analysis for group decision aiding with multiple criteria. Fuzzy Sets and Systems 271, 79–96 (2015)

    Article  MathSciNet  Google Scholar 

  11. Guo, P., Tanaka, H.: Decision making with interval probabilities. European Journal of Operational Research 203, 444–454 (2010)

    Article  MathSciNet  MATH  Google Scholar 

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Author information

Authors and Affiliations

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

    Masahiro Inuiguchi & Shigeaki Innan

Authors
  1. Masahiro Inuiguchi
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  2. Shigeaki Innan
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Corresponding author

Correspondence to Masahiro Inuiguchi .

Editor information

Editors and Affiliations

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

    Van-Nam Huynh

  2. Science, Dept of Systems Innovation, Osaka University,Graduate School of, Osaka, Japan

    Masahiro Inuiguchi

  3. Université de Technologie de Compiègne, Compiègne, France

    Thierry Demoeux

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© 2015 Springer International Publishing Switzerland

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Inuiguchi, M., Innan, S. (2015). Logarithmic Conversion Approach to the Estimation of Interval Priority Weights from a Pairwise Comparison Matrix. In: Huynh, VN., Inuiguchi, M., Demoeux, T. (eds) Integrated Uncertainty in Knowledge Modelling and Decision Making. IUKM 2015. Lecture Notes in Computer Science(), vol 9376. Springer, Cham. https://doi.org/10.1007/978-3-319-25135-6_9

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  • DOI: https://doi.org/10.1007/978-3-319-25135-6_9

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-25134-9

  • Online ISBN: 978-3-319-25135-6

  • eBook Packages: Computer ScienceComputer Science (R0)

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