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Construction of Fuzzy Utility Functions in Group Decision Making

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Part of the book series: International Series in Intelligent Technologies ((ISIT,volume 10))

Abstract

This paper discusses a method for group decision making through fuzzy decision analysis. Decision problems in the real-world include complex and ambiguous properties one of whose major sources comes from group decision situations. Some people are pursuing fuzzy set-aggregation approaches using fuzzy connectives and fuzzy integrals for treating this situations, where no concern is with identifying the individual preference functions. This paper intends to present a method for deriving the fuzzy utility function and its multiobjective extensions in the group decision environments. Representation theorems of the fuzzy utility function and the fuzzy multiattribute utility function are discussed in the possibilistic decision analysis.

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References

  • Bellman, R. E. and L. A. Zadeh: Decision-making in a fuzzy environment, Management Sciences 17 1970, 141–164.

    Article  Google Scholar 

  • Cholewa, W.: Aggregation of fuzzy opinions — an axiomatic approach, Fuzzy Sets and Systems 17, 248–258, 1985.

    Article  Google Scholar 

  • Davidson, D. and P. Suppes: A finitistic axiomatization of subjective probability and utility, Econometrica 28, 1956, 264–275.

    Article  Google Scholar 

  • DeGroot, M. H.: Optimal Statistical Decisions, McGraw-Hill, New York 1970

    Google Scholar 

  • Dubois, D. and Prade, H.: Operations on fuzzy number, International Journal of Systems Science, 9(6), 1978, 613–626.

    Article  Google Scholar 

  • Dubois, D. and Prade, H.: Fuzzy Sets and Systems, Theory and Applications, Academic Press New York 1980.

    Google Scholar 

  • Dubois, D. and H. Prade: A Review of fuzzy set aggregation connectives, Information Sciences 36, 85–121.

    Google Scholar 

  • Fishburn, P. C.: Decision And Value Theory, Wiley, New York 1964.

    Google Scholar 

  • Fishburn, P. C.: Utility Theory for Decision Making, John Wiley, 1970.

    Google Scholar 

  • Fishburn, P. C.: Nonlinear preference and Utility Theory, The John Hopkins University Press, Baltimore 1988.

    Google Scholar 

  • Grabisch, M.: integral in multicriteria decision making, Fuzzy Set and Fuzzy Systems 69, 1995, 279–298.

    Article  Google Scholar 

  • Keeney, R. L.: Multiplicative utility functions, Operations Research 22, 1974, 22–34.

    Article  Google Scholar 

  • Keeney, R. L. and Raiffa, H.: Decisions with Multiple Objectives; Preferences and Value Tradeoffs, Wiley, New York, 1976.

    Google Scholar 

  • Luce, R. D. and Raiffa, H.: Games and Decision, Wiley, New York, 1957.

    Google Scholar 

  • Mathieu-Nicot, B.: Fuzzy expected utility, Fuzzy Sets and Systems 20, 1986, 163–173.

    Article  Google Scholar 

  • Murofushi, T. and M. Sugeno: An interpretation of fuzzy measures and the Choquet integral as an integral with respect to a fuzzy measure, Fuzzy Sets and Systems 28, 1989, 201–227.

    Article  Google Scholar 

  • Nishizaki, I. and F. Seo: Interactive support for fuzzy trade-off evaluation in group decision making, Fuzzy Sets and Systems 68, 1994, 309–325.

    Article  Google Scholar 

  • Ponsard, C.: Fuzzy mathematical models in economics, Fuzzy Sets and Systems 28, 1988, 273–283.

    Article  Google Scholar 

  • Pratt, J., Raiffa W. H. and R O. Schlaifer: Introduction to Statistical Decision Theory, McGraw-Hill, New York 1965.

    Google Scholar 

  • Pratt, J., Raiffa, W. H. and R. O. Schlaifer: The foundations of decision under uncertainty: an elementary exposition, Journal of the American Statistical Association, 59, 1964.

    Google Scholar 

  • Raiffa, H.: Decision Analysis, Addition Wesley, Mass. 1968. Reprinted by Random House, New York.

    Google Scholar 

  • Savage, L. J.: The Foundation of Statistics, Wiley, 1954.

    Google Scholar 

  • Schmeidler, D.: Subjective probability and expected utility without additivity, Econometrica 57(3), 1989 571–587.

    Article  Google Scholar 

  • Schlaifer, R.: Analysis of Decisions under Uncertainty, McGraw-Hill, New York 1969. Reprinted by Robert E. Krieger Publishing Co. Florida.

    Google Scholar 

  • Seo, F.: Fundamentals of intelligent support systems for fuzzy multiobjective decision analysis. In: G. H. Tzeng, H. F. Wang, U. P. Wen and P. L. Yu (eds.): Multiple Criteria Decision Making, Springer-Verlag, 1994, pp. 209–218.

    Google Scholar 

  • Seo, F. and M. Sakawa: Fuzzy multiattribute utility analysis for collective choice, IEEE Transactions on Systems, Man, and Cybernetics SMC-15, 1985, 45–53.

    Article  Google Scholar 

  • Seo. F. and M. Sakawa: Multiple Criteria Decision Analysis in Regional Planning: Concepts, Methods, Applications, D. Reidel, 1988.

    Google Scholar 

  • Thole, U., H.-J. Zimmermann and P. Zysno: On the suitability of minimum and product operators for the intersection of fuzzy sets, Fuzzy Sets and Systems 2, 167–189, 1979.

    Article  Google Scholar 

  • von Neumann, J. and Morgenstern, O.: Theory of Games and Economic Behavior, Wiley, 1944 2nd. 1947, 3rd, 1953.

    Google Scholar 

  • Zadeh, L. A.: Fuzzy sets, Information and Control, 8, 1965, 338–353.

    Article  Google Scholar 

  • Zadeh, L. A.: Fuzzy sets as a base for a theory of possibility, Fuzzy sets and Systems 1, 1978, 3–28.

    Article  Google Scholar 

  • Zadeh, L. A.: The concept of a linguistic variables and its application to approximate reasoning, Information Sciences 8, 199–249, 301-357; 9, 43-80, 1975.

    Google Scholar 

  • Zimmermann, H. J., and P. Zysno: Latent connectives in human decision making, Fuzzy sets and Systems 4, 37–51,1980.

    Article  Google Scholar 

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© 1997 Springer Science+Business Media New York

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Seo, F. (1997). Construction of Fuzzy Utility Functions in Group Decision Making. In: Kacprzyk, J., Nurmi, H., Fedrizzi, M. (eds) Consensus Under Fuzziness. International Series in Intelligent Technologies, vol 10. Springer, Boston, MA. https://doi.org/10.1007/978-1-4615-6333-4_12

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  • DOI: https://doi.org/10.1007/978-1-4615-6333-4_12

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-1-4613-7908-9

  • Online ISBN: 978-1-4615-6333-4

  • eBook Packages: Springer Book Archive

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