2016 | 11 | 125-136
Article title

A New Fuzzy Measure for the Analytic Hierarchy Process with the Choquet Integral

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A new fuzzy measure is presented in this paper. Using the assumption that the decision maker is able to provide the pairwise additivity degree between attributes, our method uses Zimmerman’s approach to solve the fuzzy multiobjective problem: a simple problem for computing fuzzy density is derived. Having done that, we use this new fuzzy measure to implement an analytic hierarchy process (AHP) with dependent attributes using the Choquet integral. Our identification procedure for fuzzy density is much easier because it reduces the resolution complexity using a linear programming problem rather than the complicated power form used traditionally.
Physical description
  • IIUM University. Department of Business Administration. Kulliyyah of Economics and Management Sciences. Jalan Gombak. Malaysia
  • Da-Yeh University. Institute of Industrial Engineering and Management. Da-Tsuen. Chang-Hwa. Taiwan
  • Bortot S., Marques Pereira R.A. (2013), Inconsistency and Non-additive Capacities: The Analytic Hierarchy Process in the Framework of Choquet Integration, Fuzzy Sets and Systems, Vol. 213, 6-26.
  • Chen Y.W. (2001), Implementing an Analytic Hierarchy Process by Fuzzy Integral, International Journal of Fuzzy Systems, Vol. 3, No. 3, 493-502.
  • Chen Y.W., Larbani M. (2006), On a Generalization of AHP Method to the Case of Interdependent Attributes by λ-Fuzzy Measure, Proceeding of MOPGP'06: 7th Int. Conf. on Multiobjective Programming and Goal Programming, Tours, France.
  • Chen Y.W., Tzeng G.H. (2001), Using Fuzzy Integral for Evaluating Subjectively Perceived Travel Costs in a Traffic Assignment Model, European Journal of Operational Research, Vol. 130, No. 3, 653-664.
  • Corrente S., Greco S., Ishizaka A. (2016), Combining Analytical Hierarchy Process and Choquet Integral within Non-additive Robust Ordinal Regression, Omega, Vol. 61, 2-18.
  • Grabisch M. (1995), Fuzzy Integral in Multicriteria Decision Making, Fuzzy Sets and Systems, Vol. 69, No. 3, 279-298.
  • Grabisch M., Kojadinovic I., Meyer P. (2008), A Review of Methods for Capacity Identification in Choquet Integral Based Multi-attribute Utility Theory, European Journal of Operational Research, Vol. 186, No. 2, 766-785.
  • Grabisch M., Labreuche C. (2010), A Decade of Application of the Choquet and Sugeno Integrals in Multi-criteria Decision Aid, Annals of Operations Research, Vol. 175, No. 1, 247-286.
  • Greco S., Slowinski R., Figueira J.R., Mousseau V. (2010), Robust Ordinal Regression [in:] M. Ehrgott J.R. Figueira, S. Greco (eds.): Trends in Multiple Criteria Decision Analysis, Springer, New York, Heidelberg, Berlin, 241-284.
  • Ishii K., Sugeno M. (1985), A Model of Human Evaluation Process Using Fuzzy Integral, International Journal of Man-Machine Studies, Vol. 22, No. 1, 19-38.
  • Kambara H., Matsushita Y., Miyakoshi J. (1997), Partition Type of Fuzzy Integral Model for Subjective Evaluation Processes, Journal of Japan Society for Fuzzy Theory and Systems, Vol. 9, No. 1, 52-61.
  • Keeney R.L., Raiffa H. (1976), Decisions with Multiple Objectives, Preferences and Value Trade offs, Cambridge University Press.
  • Larbani M., Huang C.-Y., Tzeng G.-H. (2011), A Novel Method for Fuzzy Measure Identification, International Journal of Fuzzy Systems, Vol. 13, No. 1, 24-34.
  • Lee K.M., Leekwang H. (1995), Identification of λ-fuzzy Measure by Genetic Algorithm, Fuzzy Sets and Systems, Vol. 75, No. 3, 301-309.
  • Liou J.H., Tzeng G.H. (2007), A Non-additive Model for Evaluating Airline Service Quality, Journal of Air Transport, Vol. 13, No. 3, 131-138.
  • Saaty T.L. (1980), The Analytic Hierarchy Process, McGraw-Hill, New York.
  • Sugeno M. (1974), Theory of Fuzzy Integral and Its Application, Doctoral Dissertation, Tokyo Institute of Technology.
  • Takahagi E. (2000), On Identification Methods of λ-fuzzy Measures Using Weights and λ, Japanese Journal of Fuzzy Sets and Systems, Vol. 12, No. 5, 665-676.
  • Tzeng G.-H., Yang Y.-P., Lin C.-T., Chen C.-B. (2005), Hierarchical MADM with Fuzzy Integral for Evaluating Enterprise Intranet Web Sites, Information Sciences, Vol. 169, No. 3/4, 409-426.
  • Wang J.-C., Chen T.-Y. (2005), Experimental Analysis of λ-Fuzzy Measure Identification by Evolutionary Algorithms, International Journal of Fuzzy Systems, Vol. 7, No. 1, 1-10.
  • Yang J.L., Chiu H.N., Tzeng G.H. (2008), Vendor Selection by Integrated Fuzzy MCDM Techniques with Independent and Interdependent Relationships, Information Sciences, Vol. 178, No. 21, 4166-4183.
  • Zeleny M. (1982), Multiple Criteria Decision Making, McGraw-Hill, New York.
  • Zimmerman H.J. (1985), Fuzzy Set Theory and Its Applications, Kluwer-Nijhoff, Boston.
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