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On the axioms of revealed preference in fuzzy consumer theory

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Abstract

The revealed preference is a central subject in classical consumer theory. Authors like Samuelson, Arrow, Richter, Sen, Uzawa and others have proposed an axiomatic setting of revealed preference theory.

Consequently revealed preference axioms WARP and SARP and congruence axioms WCA and SCA have been considered.

An important theorem of Sen establishes the equivalence between these axioms provided the family of budgets includes all non-empty finite sets of bundles.

Fuzzy consumer theory (=fuzzy choice functions) is a topic that appears in a lot of papers. Particularly, Banerjee studies in fuzzy context axioms of revealed preference and congruence extending some results of Arrow and Sen.

In this paper we modify the Banerjee definition of a fuzzy choice function (=fuzzy consumer) and we study some fuzzy versions of the axioms of revealed preference and congruence. Banerjee fuzzifies only the range of a consumer; we use a fuzzification of both the domain and the range of a consumer. The axioms WAFRP, SAFRP, WFCA, SFCA generalize to fuzzy consumer theory the well-known axioms WARP, SARP, WCA, SCA. Our main result establishes some connections between WAFRP, SAFRP, WFCA, SFCA extending a significant part of Sen theorem.

Generally, we work in a fuzzy set theory based on a continuous t-norm, but some results are obtained for Gödel t-norm and others are obtained for Lukasiewicz t-norm.

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Authors and Affiliations

  1. Turku Centre for Computer Science, Institute for Advanced Management Systems Research, Lemminkäisenkatu 14, FIN-20520, Turku, Finland

    Irina Georgescu

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  1. Irina Georgescu
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Irina Georgescu received her B.S. degree in cybernetics and the M.Sc. degree in quantitative economics, both from the Academy of Economic Studies, Bucharest, Romania, in 1999 and 2000 respectively.

She is currently working toward the PhD degree in Business Administration with Turku Centre for Computer Science, Institute for Advanced Management Systems Research, Turku, Finland. Her research interests include the areas of fuzzy sets and systems, social choice and welfare economics.

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Georgescu, I. On the axioms of revealed preference in fuzzy consumer theory. J. Syst. Sci. Syst. Eng. 13, 279–296 (2004). https://doi.org/10.1007/s11518-006-0165-z

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