Dealing with Imprecision in Consumer Theory: A New Approach to Fuzzy Utility Theory

Chapter
Part of the Studies in Computational Intelligence book series (SCI, volume 502)

Abstract

This chapter presents a new approach to dealing with imprecision in the Classical Consumer Utility Theory based on the concept of Marginal Rate of Substitution (MRS) and using the concept of fuzzy sets and fuzzy numbers. The methodology developed applies imprecision to MRS, whereas previous studies placed the imprecision factor on final utility values and functions. The chapter considers fuzzy elements applied to MRS and uses the necessary formulations to obtain the results in Utility Theory. In this fuzzy environment, the final consumer decision problem is framed as a fuzzy nonlinear programming problem, maintaining the classical structure in which consumers maximize their fuzzy utility subject to budget constraints, and showing that the consumer optimum choice is a fuzzy set. The chapter will also address the problem of aggregation of utility functions in order to offer a multi-criteria approach.

Keywords

New directions of decision analysis under uncertainty Muti-criteria decision making 

References

  1. 1.
    Aliev, R., Pedrycz, W., et al.: Fuzzy logic-based generalized decision theory with imperfect information. Inf. Sci. 189, 18–42 (2012)MathSciNetCrossRefMATHGoogle Scholar
  2. 2.
    Banerjee, A.: Fuzzy choice functions, revealed preference rationality. Fuzzy Sets Syst. 70, 13–43 (1995)CrossRefGoogle Scholar
  3. 3.
    Buckley, J.J., Feuring, T.: Introduction to fuzzy partial differential equations. Fuzzy Sets. Syst. 105(2), 241–248 (1999)MathSciNetCrossRefMATHGoogle Scholar
  4. 4.
    Buckley, J.J., Feuring, T.: Fuzzy differential equations. Fuzzy Sets Syst. 110, 43–54 (2000)MathSciNetCrossRefMATHGoogle Scholar
  5. 5.
    Chuoo, E.U., Shoner, B., Wedley, W.C.: Interpretation of criteria weights in multicriteria decision making. Comput. Ind. Eng. 37, 527–541 (1999)CrossRefGoogle Scholar
  6. 6.
    Colin, A., Trivedi, P.: Microeconometrics: Methods and Applications. Cambridge University Press, Cambridge (2005)Google Scholar
  7. 7.
    van Kooten, C., et al.: Preference uncertainty in non-market valuation: a fuzzy aproach. Am. J. Agric. Econ. 83(3), 487–500 (2001)CrossRefMATHGoogle Scholar
  8. 8.
    Dean, P.-K., et al.: Product and cost estimation with fuzzy multi-attribute utility theory. Eng. Econ. 44(4), 303–331 (1999)MathSciNetCrossRefGoogle Scholar
  9. 9.
    Debreu, G.: Topological methods in cardinal utility theory. Math. Methods Soc. Sci. 1959, 16–26 (1960) (Cowles Foundation paper 156).Google Scholar
  10. 10.
    De Wilde, P.: Fuzzy utility and equilibria. IEEE Trans. Syst. Man Cybern. 34(4), 1774–1785 (2004)CrossRefGoogle Scholar
  11. 11.
    Dubois, D., Prade, H.: Additions of interactive fuzzy numbers. IEEE Trans. Autom. Control 26(4), 926–936 (1981)MathSciNetCrossRefGoogle Scholar
  12. 12.
    Duncan, R., Tukey, J.W.: Simultaneous conjoint measurement: a new type of fundamental measurement. J. Math. Psychol. 1, 1–27 (1964)CrossRefGoogle Scholar
  13. 13.
    Figueira, J., Greco, S., Ehrgott, M. (eds.): Multiple Criteria Decision Analysis. State of the Art Surveys. Springer, Berlin (2005)MATHGoogle Scholar
  14. 14.
    Fishburn, P.: Independence in utility theory with whole product sets. Operat. Res. 13(3), 28–45 (1965)MathSciNetCrossRefGoogle Scholar
  15. 15.
    Fodor, J., De Baets, B., Perny, P. (eds.): Preferences and Decisions Under Incomplete Knowledge. Springer, Berlin (2000)MATHGoogle Scholar
  16. 16.
    Gálvez, D. and Pino, J.L.: The extension of Buckley-Feuring solutions for non-polynomial fuzzy partial differential equations. Application to Microeconomics Utility Theory. In: Proceedings of NAFIPS (The 28th North American Fuzzy Information Processing Society Annual Conference). IEEE, 2009.Google Scholar
  17. 17.
    Gálvez, D. and Pino, J.L.: The extension of Buckley-Feuring solutions for non-polynomial fuzzy partial differential equations. Application to Microeconomics Utility Theory and consumer decision. In: Proceedings of Fuzz-IEEE (2009 IEEE International Conference on Fuzzy Systems). IEEE, 2009.Google Scholar
  18. 18.
    Gálvez, D.: Tratamiento de la imprecisión en la teoría de la utilidad del consumidor. Universidad de Sevilla. 2009.Google Scholar
  19. 19.
    Goetschel, R., Voxman, W.: Elementary fuzzy calculus. Fuzzy Sets Syst. 18, 319–330 (1986)Google Scholar
  20. 20.
    Green, W.: Análisis Econométrico. Prentice hall, New Jersey (2002)Google Scholar
  21. 21.
    Hicks, JR: Value and Capital: An Inquiry into Some fundamental Principles of Economic Theory, pp. 18. Clarendon Press, Oxford (1939).Google Scholar
  22. 22.
    Kaufmann, A., Gupta, M.M.: Introduction to fuzzy arithmetic: theory and applications. Van Nostrand Reinhold, New York (1985)Google Scholar
  23. 23.
    Keeney, R.L., Raiffa, H.: Decisions with Multiple Objectives: Preferences and Value Trade-offs. Wiley, New York (1976)Google Scholar
  24. 24.
    Mathieu-Nicot, B.: Fuzzy expected utility. Fuzzy Sets Syst. 20(2), 163–173 (1986)Google Scholar
  25. 25.
    Mesiar, R.: Fuzzy set approach to the utility, preference relations, and agregation operators. Eur. J. Operat. Res. 176(1), 414–422 (2007)Google Scholar
  26. 26.
    Mora, J. J.: Introducción a la teoría del consumidor : de las preferencias a la estimación. Universidad ICESI (2002).Google Scholar
  27. 27.
    Nakamura, K.: Preference relations on a set of fuzzy utilities as a basis for decision making. Fuzzy Sets Syst. 20(2), 147–162 (1986)Google Scholar
  28. 28.
    Orlovsky, S.A.: Decision making with a fuzzy preference relation. Fuzzy Sets Syst. 1(3), 155–167 (1978)Google Scholar
  29. 29.
    Pareto, V.: Manual of Political Economy. Augustus M, Kelley, New York (1971)Google Scholar
  30. 30.
    Ponsard, C.: Fuzzy mathematical models in economics. Fuzzy Sets Syst. 28(3), 273–283 (1988)Google Scholar
  31. 31.
    Ramík, J., Vlach, M.: Generalized Concavity in Fuzzy Optimization and Decision Analysis. Kluwer Academic Publishers, The Netherlands (2002)Google Scholar
  32. 32.
    Robinson, J.: Economics is a Serious Subject. W. Heffer and Sons, Cambridge (1932)Google Scholar
  33. 33.
    Rothbard, M.N.: History economic thought, vol. 1. Economic thought to Adam Smith, Union Editorial (1999)Google Scholar
  34. 34.
    Rommelfanger, H. J.: Decision Making in fuzzy environment. Ways for getting practical decision models. Paper on line at http://www.uni-frankfurt.de. University of Frankfurt (1999)
  35. 35.
    Salles, M.: Fuzzy utility. In: Barbera, S., et al. (eds.) Handbook of Utility Theory, vol. 1. Springer, Berlin (1999)Google Scholar
  36. 36.
    Stewart, T.J.: Simplified approaches for multi-criteria decision making under uncertainty. J. Multi-Criteria Decis. Anal. 4(4), 246–258 (1995)Google Scholar
  37. 37.
    Stewart, T.J.: Robustness of additive value function methods in MCDM. J. Multi-Criteria Decis. Anal. 5(4), 301–309 (1996)Google Scholar
  38. 38.
    Tenekedjiev, K., Nikolova, N.: Justification and numerical realization of the uniform method for finding point estimates of interval elicited scaling constants. Fuzzy Optim. Decis. Making 7(2), 119–145 (2008)Google Scholar
  39. 39.
    Zadeh, L.A.: Fuzzy Sets. Inf. Control 8, 338–353 (1965)Google Scholar
  40. 40.
    Zadeh, L.A.: The concept of Linguistic variables and its applications to approximate reasoning. Part I Inf. Sci. 8(3), 199–249 (1975)Google Scholar
  41. 41.
    Zadeh, L.A.: The concept of Linguistic variables and its applications to approximate reasoning. Part II Inf. Sci. 8(4), 301–357 (1975)Google Scholar
  42. 42.
    Zadeh, L.A.: The concept of Linguistic variables and its applications to approximate reasoning. Part III Inf. Sci. 9(1), 43–80 (1975)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  • David  Gálvez Ruiz
    • 1
    • 2
  • José Luís Pino Mejías
    • 1
    • 2
  1. 1.Department of Statistics and Operational ResearchFaculty of Mathematics. University of SevilleSevillaSpain
  2. 2.Quantitative Methods on Evaluation Research GroupUniversity of SevilleSevillaSpain

Personalised recommendations