A Fuzzy Weights Representation for Inner Dependence  AHP

Shin-ichi Ohnishi; Takahiro Yamanoi; Hideyuki Imai

doi:10.20965/jaciii.2011.p0329

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JACIII Vol.15 No.3 pp. 329-335

doi: 10.20965/jaciii.2011.p0329

(2011)

Paper:

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A Fuzzy Weights Representation for Inner Dependence AHP

Shin-ichi Ohnishi^, Takahiro Yamanoi^, and Hideyuki Imai^**

^*Faculty of Engineering, Hokkai-Gakuen University, W11-1-1, S26, Chuo-ku, Sapporo, Hokkaido 064-0926, Japan

^**Graduate School of Information Science and Technology, Hokkaido University, W9, N14, Kita-ku, Sapporo, Hokkaido 060-0814, Japan

Received:

October 30, 2010

Accepted:

December 21, 2010

Published:

May 20, 2011

Keywords:

decision-making, analytic hierarchy process (AHP), fuzzy sets, sensitivity analysis

Abstract

The Analytic Hierarchy Process (AHP) proposed by T. L. Saaty has been widely used in decision making. Inner dependence method AHP is used for cases in which criteria are not independent enough. Using the original AHP or inner dependence AHP may cause results to lose reliability because the comparison matrix is not necessarily sufficiently consistent. In such cases, fuzzy representation for weighting criteria using results from sensitivity analysis is useful. We present weights of normal AHP criteria via fuzzy sets, then calculate modified fuzzy weights of inner dependence methods. We also get overall weights of alternatives based on certain assumptions. Results show the fuzziness of inner dependence AHP if the comparison matrix is not sufficiently consistent and individual criterion do not have enough independence.

Cite this article as:

S. Ohnishi, T. Yamanoi, and H. Imai, “A Fuzzy Weights Representation for Inner Dependence AHP,” J. Adv. Comput. Intell. Intell. Inform., Vol.15, No.3, pp. 329-335, 2011.

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References

[1] T. L. Saaty, “A Scaling Method for Priorities in Hierarchical Structures,” J. Math. Psy., Vol.15, No.3, pp. 234-281, 1977.
[2] T. L. Saaty, “The Analytic Hierarchy Process,” McGraw-Hill, New York, 1980.
[3] T. L. Saaty, “Scaling the Membership Function,” European J. of O.R., Vol.25, pp. 320-329, 1986.
[4] T. L. Saaty, “Inner and Outer Dependence in AHP,” University of Pittsburgh, 1991.
[5] S. Ohnishi, D. Dubois, H. Prade, and T. Yamanoi, “A Fuzzy Constraint-Based Approach to the Analytic Hierarchy Process,” Uncertainty and Intelligent Information Systems, pp. 217-228, 2008.
[6] S. Ohnishi, H. Imai, and T. Yamanoi, “Weights Representation of Analytic Hierarchy Process by Use of Sensitivity Analysis,” IPMU 2000 Proc, 2000.
[7] S. Ohnishi, T. Yamanoi, and H. Imai, “A Fuzzy Representation for Weights of Alternatives in AHP,” New Dimensions in Fuzzy Logic and Related Technologies, Vol.2, pp.311-316, 2007.
[8] S. Ohnishi, T. Yamanoi, and H. Imai, “A Fuzzy Weight Representation for Inner Dependence Method AHP,” 2009 IFSA World congress / EUSFLAT Conf. (IFSA-EUSFLAT 2009), pp. 1612-1617, 2009.
[9] Y. Tanaka, “Recent Advance in Sensitivity Analysis in Multivariate Statistical Methods,” J. Japanese Soc. Comp. Stat., Vol.7, No.1, pp. 1-25, 1994.
[10] S. Ohnishi, H. Imai, and M. Kawaguchi, “Evaluation of a Stability on Weights of Fuzzy Analytic Hierarchy Process Using a Sensitivity Analysis,” J. of Japan Society for Fuzzy Theory and Systems, Vol.9, No.1, pp. 140-147, 1997.
[11] M. Saito, “An Introduction to Linear Algebra,” Tokyo University Press, 1966.
[12] D. Dubois and H. Prade, “Possibility Theory an Approach to Computerized Processing of Uncertainty,” Plenum Press, New York, 1988.
[13] K. Tone, “The Game Feeling Decision Making,” Nikka-giren Press, Tokyo, 1986.

This article is published under a Creative Commons Attribution-NoDerivatives 4.0 Internationa License.

[1] [1] T. L. Saaty, “A Scaling Method for Priorities in Hierarchical Structures,” J. Math. Psy., Vol.15, No.3, pp. 234-281, 1977.

[2] [2] T. L. Saaty, “The Analytic Hierarchy Process,” McGraw-Hill, New York, 1980.

[3] [3] T. L. Saaty, “Scaling the Membership Function,” European J. of O.R., Vol.25, pp. 320-329, 1986.

[4] [4] T. L. Saaty, “Inner and Outer Dependence in AHP,” University of Pittsburgh, 1991.

[5] [5] S. Ohnishi, D. Dubois, H. Prade, and T. Yamanoi, “A Fuzzy Constraint-Based Approach to the Analytic Hierarchy Process,” Uncertainty and Intelligent Information Systems, pp. 217-228, 2008.

[6] [6] S. Ohnishi, H. Imai, and T. Yamanoi, “Weights Representation of Analytic Hierarchy Process by Use of Sensitivity Analysis,” IPMU 2000 Proc, 2000.

[7] [7] S. Ohnishi, T. Yamanoi, and H. Imai, “A Fuzzy Representation for Weights of Alternatives in AHP,” New Dimensions in Fuzzy Logic and Related Technologies, Vol.2, pp.311-316, 2007.

[8] [8] S. Ohnishi, T. Yamanoi, and H. Imai, “A Fuzzy Weight Representation for Inner Dependence Method AHP,” 2009 IFSA World congress / EUSFLAT Conf. (IFSA-EUSFLAT 2009), pp. 1612-1617, 2009.

[9] [9] Y. Tanaka, “Recent Advance in Sensitivity Analysis in Multivariate Statistical Methods,” J. Japanese Soc. Comp. Stat., Vol.7, No.1, pp. 1-25, 1994.

[10] [10] S. Ohnishi, H. Imai, and M. Kawaguchi, “Evaluation of a Stability on Weights of Fuzzy Analytic Hierarchy Process Using a Sensitivity Analysis,” J. of Japan Society for Fuzzy Theory and Systems, Vol.9, No.1, pp. 140-147, 1997.

[11] [11] M. Saito, “An Introduction to Linear Algebra,” Tokyo University Press, 1966.

[12] [12] D. Dubois and H. Prade, “Possibility Theory an Approach to Computerized Processing of Uncertainty,” Plenum Press, New York, 1988.

[13] [13] K. Tone, “The Game Feeling Decision Making,” Nikka-giren Press, Tokyo, 1986.

A Fuzzy Weights Representation for Inner Dependence AHP

Shin-ichi Ohnishi*, Takahiro Yamanoi*, and Hideyuki Imai**

Shin-ichi Ohnishi^, Takahiro Yamanoi^, and Hideyuki Imai^**