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Fuzzy Decision Theory

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Uncertain Decisions
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Abstract

The main purpose of the fuzzy approach of individual preferences is to introduce some new behaviors inside the standard theory. The existing literature is generally divided in two schools, according to the position authors adopt relatively to the axiom of Independence of Irrelevant Alternatives (IIA).1 Actually, most of the works using fuzzy preferences are based on additive measures of satisfaction (Bazu 1984, Butnariu 1987, Orlovsky 1980, Ovchinnikov & Roubens 1992).

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References

  • d’Aspremont C. & Gevers L. 1977. ‘Equity and the Informational Basis of Collective Choice’, Review of Economic Studies, 44, 199–209.

    Article  Google Scholar 

  • Barret C.R., Pattanaik P.K. & Salles M. 1985. ‘On the Structure of Fuzzy Social Welfare Functions’, Séminaire de l’Institut de Mathématiques Economiques, Université de Dijon.

    Google Scholar 

  • Barret C.R., Pattanaik P.K. & Salles M. 1992. ‘Rationality and Aggregation of Preferences in an Ordinally Fuzzy Framework’, Fuzzy Sets and Systems, 49, 9–15.

    Article  Google Scholar 

  • Bazu K. 1984. ‘Fuzzy Revealed Preference Theory’, Journal of Economic Theory, 32, 212–227.

    Article  Google Scholar 

  • Bellman R.E. & Zadeh L.A. 1970. ‘Decision-making in a Fuzzy Environment’, Management Science, 17, 141–154.

    Article  Google Scholar 

  • Billot A. 1987. Préférences et Utilités Floues, Presses Universitaires de France, Paris.

    Google Scholar 

  • Billot A. 1991. ‘Aggregation of Preferences: The Fuzzy Case’, Theory and Decision, 30, 51–93.

    Article  Google Scholar 

  • Billot A. 1992. ‘From Fuzzy Set Theory to NonAdditive Probabilities: How Have Economists Reacted ?’, Fuzzy Sets and Systems, 49, 75–90.

    Article  Google Scholar 

  • Billot A. 1995a. ‘Fuzzy Continuous Utility Function: A New Elementary Proof’, Fuzzy Sets and Systems, 74, 271–276.

    Article  Google Scholar 

  • Billot A. 1995b. Economic Theory of Fuzzy Equilibria, 2nd Edition, Springer-Verlag, Berlin, New York.

    Book  Google Scholar 

  • Butnariu D. 1987. ‘Values and Cores of Fuzzy Games with Infinitely Many Players’, International Journal of Game Theory, 16, 43–68.

    Article  Google Scholar 

  • Chang C.L. 1968. ‘Fuzzy Topological Spaces’, Journal of Mathematical Analysis and Applications, 24 182–190.

    Article  Google Scholar 

  • Chichilinsky G. 1982. ‘Social Aggregation and Continuity’, The Quarterly Journal of Economics, 97, 337–352.

    Article  Google Scholar 

  • Debreu G. 1954. ‘Representation of Preference Ordering by a Numerical function’ in ‘Decision Processes, Thrall R.M., Coombs C.H. & R.L. Davis Eds, Wiley, New York, 159–165.

    Google Scholar 

  • Debreu G. 1959. Theory of Value, Wiley, New York.

    Google Scholar 

  • Dubois D. 1983. Modéles Mathématiques de l’Imprécis et de l’Incertain en vue d’Applications aux Techniques d’Aide à la Décision, Thése de Doctorat d’Etat es Sciences, Mathématiques Appliquées, Grenoble.

    Google Scholar 

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

    Google Scholar 

  • Fishburn P.C. 1973. The Theory of Social Choice, Princeton University Press.

    Google Scholar 

  • Grandmont J.M. 1978. ‘Intermediate Preferences and the Majority Rule’, Econometrica, 46, 317–330.

    Article  Google Scholar 

  • Guilbaud G.T. 1952. ‘Les Théories de L’intérêt Général et le Probléme Logique de l’Agrégation’, Economie Appliquée, 5, 502–584.

    Google Scholar 

  • Haak S. 1974. Deviant Logic, Cambridge University Press.

    Google Scholar 

  • Harsanyi J.C. 1973. ‘Can the Maximin Principle Serve as a Basis for Morality: A Critique of John Rawls’s Theory’, American Political Science Review, 69(2), 594–606.

    Article  Google Scholar 

  • Kacprzyk J., Fedrizzi M. & Nurmi H. 1992. ‘Group Decision Making and Consensus under Fuzzy Preferences and Fuzzy Majority’, Fuzzy Sets and Systems, 49, 21–33.

    Article  Google Scholar 

  • Kalai E. & Ritz Z. 1980. ‘Characterization of the Private Alternatives Domains Admitting Arrow Social Welfare Functions’, Journal of Economic Theory, 22, 12–22.

    Article  Google Scholar 

  • Kaufmann A. 1973–1980. Introduction à la Théorie des Sous-Ensembles Flous, Tomes I and IV, Masson, Paris.

    Google Scholar 

  • Luo C.Z. 1986. ‘Fuzzy Relation Equation on Infinite Sets’, Busefal, 26, 57–66.

    Google Scholar 

  • May K.O. 1952. ‘A Set of Independent, Necessary and Sufficient Conditions for Simple Majority Decision’, Econometrica, 20, 680–684.

    Article  Google Scholar 

  • Negoita C.V. & Ralescu D.A. 1978. ‘Applications of Fuzzy Sets to System Analysis’, Fuzzy Sets and Systems, 1, 155–167.

    Article  Google Scholar 

  • Orlovsky S.A. 1978. ‘Decision Making with Fuzzy Preference Relation’, Fuzzy Sets and Systems, 4, 155–167.

    Article  Google Scholar 

  • Orlovsky S.A. 1980. ‘On Formalization of a General Fuzzy Mathematical Problem’, Fuzzy Sets and Systems, 3, 311–321.

    Article  Google Scholar 

  • Ovchinnikov S.V. 1981. ‘Structure of Fuzzy Binary Relations’, Fuzzy Sets and Systems, 6, 169–195.

    Article  Google Scholar 

  • Ovchinnikov S.V. & Roubens M. 1992. ‘On Fuzzy Strict Preference, Indifference, and Incomparability Relations’, Fuzzy Sets and Systems, 49, 15–21.

    Article  Google Scholar 

  • Pattanaik P.K. & Salles M. Eds 1983. Social Choice and Welfare, Contributions to Economic Analysis 145, North-Holland, Amsterdam.

    Google Scholar 

  • Ponsard C. 1986. ‘Foundations of Soft Decision Theory’, in Management Decision Support Systems Using Fuzzy Sets and Possibility Theory, J. Kacprzyk & R.R. Yager Eds, Verlag T.U.V., Rheinland, 27–37.

    Google Scholar 

  • Ponsard C. 1987. ‘Fuzzy Mathematical Models in Economics’, Fuzzy Sets andSystems.

    Google Scholar 

  • Prevôt M. 1977. Sous-Ensembles Flous: Une Approche Théorique, Sirey, Collection de l’Institut de Mathématiques Economiques, Paris.

    Google Scholar 

  • Rawls J. 1971, 1987. Théorie de la Justice, Seuil, Paris.

    Google Scholar 

  • Roubens M. & Vincke P. 1986. Preferences Modelling, Lecture Notes in Economics and Mathematical Systems 250, Springer Verlag, Berlin, New-York.

    Google Scholar 

  • Sen A.K. 1974. “Information Basis of Alternative Welfare Approaches, Agregation and Income Distribution”, Journal of PublicEconomics, 3, 387–403.

    Google Scholar 

  • Sen A.K. 1977. “Social Choice Theory: A Re-Examination”, Econometrica, 45, 53–89.

    Article  Google Scholar 

  • Strasnick S. 1976. “The Problem of Social Choice: Arrow to Rawls”, Philosophy and Public Affairs, 5, 241–273.

    Google Scholar 

  • Usawa H. 1960. “Preference and Rational Choice in the Theory of Consumption”, Proceedings of a Symposium on Mathematical Methods In Social Sciences, Stanford University Press.

    Google Scholar 

  • Zadeh L.A. 1965. “Fuzzy Sets”, Information and Control 8, 338–353.

    Article  Google Scholar 

  • Zadeh L.A. 1971. “Similarity Relations and Fuzzy Orderings”, Information Sciences, 3, 177–200.

    Article  Google Scholar 

  • Zimmermann H.J. 1985. Fuzzy Set Theory, and its Applications, Klüwer, Nijhoff Publishing, Boston.

    Google Scholar 

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Billot, A. (1999). Fuzzy Decision Theory. In: Luini, L. (eds) Uncertain Decisions. Springer, Boston, MA. https://doi.org/10.1007/978-1-4615-5083-9_9

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  • DOI: https://doi.org/10.1007/978-1-4615-5083-9_9

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