Abstract
The AHP (Analytic Hierarchy Process) has been widely used in decision making. Inner dependence method AHP is one technique for the case in which criteria do not have enough independency. However using original AHP or inner dependence method, the data and results often lose their reliability because the comparison matrix does not always have sufficient consistency. In these cases, fuzzy representation for weighting criteria and alternatives using results from a sensitivity analysis is useful. In this paper, we first present weights of criteria of normal AHP by means of fuzzy sets, then modified fuzzy weights is calculated. Overall weights of alternatives can also be calculated by employing some assumptions. The results show how inner dependence AHP has fuzziness when the comparison matrix is not sufficiently consistent and each criterion has not enough independency.
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References
Saaty, T.L.: A scaling method for priorities in hierarchical structures. J. Math. Psy. 15(3), 234–281 (1977)
Saaty, T.L.: The Analytic Hierarchy Process. McGraw-Hill, New York (1980)
Saaty, T.L.: Scaling the membership function. European J. of O.R. 25, 320–329 (1986)
Saito, M.: An Introduction to Linear Algebra. Tokyo University Press (1966)
Tanaka, Y.: Recent advance in sensitivity analysis in multivariate statistical methods. J. Japanese Soc. Comp. Stat. 7(1), 1–25 (1994)
Tone, K.: The Game Feeling Decision Making. Nikka-giren Press, Tokyo (1986)
Ohnishi, S., Imai, H., Kawaguchi, M.: Evaluation of a Stability on Weights of Fuzzy Analytic Hierarchy Process using a sensitivity analysis. J. Japan Soc. for Fuzzy Theory and Sys. 9(1), 140–147 (1997)
Ohnishi, S., Imai, H., Yamanoi, T.: Weights Representation of Analytic Hierarchy Process by use of Sensitivity Analysis. In: IPMU 2000 Proceedings (2000)
Dubois, D., Prade, H.: Possibility Theory An Approach to Computerized Processing of Uncertainty. Plenum Press, New York (1988)
Saaty, T.L.: Inner and Outer Dependence in AHP. University of Pittsburgh (1991)
Ohnishi, S., Yamanoi, T., Imai, H.: A Fuzzy Representation for Weights of Alternatives in AHP. New Dimensions in Fuzzy Logic and Related Technologies II, 311–316 (2007)
Ohnishi, S., Dubois, D., Prade, H., Yamanoi, T.: A Fuzzy Constraint-based Approach to the Analytic Hierarchy Process. Uncertainty and Intelligent Information Systems, 217–228 (2008)
Ohnishi, S., Yamanoi, T., Imai, H.: A Fuzzy Weight Representation for Inner Dependence Method AHP. In: 2009 IFSA World congress/EUSFLAT conference(IFSA-EUSFLAT 2009), pp, 1612—1617 (2009)
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Ohnishi, Si., Yamanoi, T., Imai, H. (2010). On a Fuzzy Weights Representation for Inner Dependence AHP. In: Hüllermeier, E., Kruse, R., Hoffmann, F. (eds) Information Processing and Management of Uncertainty in Knowledge-Based Systems. Applications. IPMU 2010. Communications in Computer and Information Science, vol 81. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-14058-7_29
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DOI: https://doi.org/10.1007/978-3-642-14058-7_29
Publisher Name: Springer, Berlin, Heidelberg
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