The New Palgrave Dictionary of Economics

2018 Edition
| Editors: Macmillan Publishers Ltd

Fuzzy Sets

  • Claude Ponsard
Reference work entry
DOI: https://doi.org/10.1057/978-1-349-95189-5_786

Abstract

The scope of fuzzy economics is to bring into play a new body of concepts in which imprecision (or fuzziness) is accepted as a matter of science. Accurate mathematical methods are used; they are based on the concept of fuzzy set. Intuitively, a fuzzy set is compounded of elements which appertain to it more or less. The transition from membership to non-membership is soft rather than crisp, as in the case of an ordinary set. In the same manner, fuzzy logic handles imprecise truths, and fuzzy connectives and rules of inference, contrary to classical two-valued logic.

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Bibliography

  1. Butnariu, D. 1982. Fixed points for fuzzy mappings. Fuzzy Sets and Systems 7(2): 191–207.CrossRefGoogle Scholar
  2. Debreu, G. 1959. Theory of value: An axiomatic analysis of economic equilibrium, Cowles Foundation Monograph, vol. 17. New York: John Wiley & Sons.Google Scholar
  3. Dubois, D., and H. Prade. 1980. Fuzzy sets and systems: Theory and applications. New York: Academic Press.Google Scholar
  4. Goguen, J.A. 1967. L-fuzzy sets. Journal of Mathematical Analysis and Applications 18: 145–174.CrossRefGoogle Scholar
  5. Kaufmann, A. 1975. Introduction to the theory of fuzzy subsets, Fundamental Theoretical Elements, vol. 1. New York: Academic Press. (trans. of French edn of 1973).Google Scholar
  6. Mathieu-Nicot, B. 1985. Espérance mathématique de l’utilité floue, Coll. IME, vol. 29. Dijon: Librairie de l’Universite.Google Scholar
  7. Ponsard, C. 1975. L’imprécision et son traitement en analyse économique. Revue d'Economie Politique 1: 17–37.Google Scholar
  8. Ponsard, C. 1977. Hiérarchie des places centrales et graphes phi-flous. Environment and Planning A 9: 1233–1252.CrossRefGoogle Scholar
  9. Ponsard, C. 1981a. An application of fuzzy subsets theory to the analysis of the consumer’s spatial preferences. Fuzzy Sets and Systems 5(3): 235–244.CrossRefGoogle Scholar
  10. Ponsard, C. 1981b. L’équilibre spatial du consommateur dans un contexte imprécis. Sistemi Urbani 3: 107–133.Google Scholar
  11. Ponsard, C. 1982a. Producer’s spatial equilibrium with a fuzzy constraint. European Journal of Operational Research 10: 302–313.CrossRefGoogle Scholar
  12. Ponsard, C. 1982b. Partial spatial equilibria with fuzzy constraints. Journal of Regional Science 22: 159–175.CrossRefGoogle Scholar
  13. Ponsard, C. 1983. History of spatial economic theory, Texts and Monographs in Economics and Mathematical Systems. Berlin: Springer-Verlag.CrossRefGoogle Scholar
  14. Ponsard, C. 1984. A theory of spatial general equilibrium in a fuzzy economy. Working Paper No. 65, IME. Revised version in Fuzzy economics and spatial analysis, ed. C. Ponsard and B. Fustier, Coll. IME 32. Dijon: Librairie de l’Université, 1986.Google Scholar
  15. Ponsard, C. 1985a. Fuzzy sets in economics: Foundation of soft decision theory. In Management decision support systems using fuzzy sets and possibility theory, Coll. Interdisciplinary Systems Research, vol. 83, ed. J. Kacprzyk and R.R. Yager, 25–37. Cologne: Verlag TUV Rheinland.Google Scholar
  16. Ponsard, C. 1985b. Fuzzy data analysis in a spatial context. In Measuring the unmeasurable, Series D, no. 22, NATO ASI Series, ed. P. Nijkamp, H. Leitner, and N. Wrigley, 487–508. Dordrecht: Martinus Nijhoff.CrossRefGoogle Scholar
  17. Ponsard, C., and P. Tranqui. 1985. Fuzzy economic regions in Europe. Environment and Planning, Series A 17: 873–887.CrossRefGoogle Scholar
  18. Sambuc, R. 1975. Fonctions phi-floues. Application á l’aide au diagnostic en pathologie thyroïdienne. PhD thesis, Université de Marseille.Google Scholar
  19. Tanaka, H., T. Okuda, and K. Asai. 1974. On fuzzy mathematical programming. Journal of Cybernetics 3: 37–46.CrossRefGoogle Scholar
  20. Tranqui, P. 1978. Les régions économiques floues: Application au cas de la France, Coll. IME, vol. 16. Dijon: Librairie de l’Université.Google Scholar
  21. Zadeh, L.A. 1965. Fuzzy sets. Information and Control 8: 338–353.CrossRefGoogle Scholar
  22. Zadeh, L.A. 1968. Probability measures of fuzzy events. Journal of Mathematical Analysis and Applications 23: 421–427.CrossRefGoogle Scholar
  23. Zadeh, L.A. 1975. The concept of a linguistic variable and its application to approximate reasoning. Information Sciences, Part 1: 8, 199–249; Part 2: 8, 301–57; Part 3: 9, 43–80.Google Scholar
  24. Zadeh, L.A. 1978. Fuzzy sets as a basis for a theory of possibility. Fuzzy Sets and Systems 1(1): 3–28.CrossRefGoogle Scholar
  25. Zimmermann, H.J. 1985. Fuzzy set theory and its applications. Dordrecht: Kluwer-Nijhoff.CrossRefGoogle Scholar

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© Macmillan Publishers Ltd. 2018

Authors and Affiliations

  • Claude Ponsard
    • 1
  1. 1.