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Transitive and acyclic rationality indicators of fuzzy choice functions on base domain

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  • S. Chaudhari
  • S. Desai

Abstract

In the present paper we introduce the indicators of the fuzzy transitive congruence axiom, fuzzy direct-revelation axiom and fuzzy acyclic congruence axiom. These indicators measure the degree to which a fuzzy choice function satisfies these axioms. We use the indicators of fuzzy transitive congruence axiom and fuzzy acyclic congruence axiom to calculate the minimum degree to which the direct fuzzy revealed preference relation is the transitive and acyclic respectively. We established that (i) the degree to which the fuzzy choice function is full rational is the degree to which it satisfies fuzzy transitive congruence axiom and (ii) the degree to which the fuzzy choice function is acyclic rational is the minimum degree to which it satisfies fuzzy direct-revelation axiom and its fuzzy revealed preference is acyclic. We show that a similarity relation on the set of fuzzy choice functions preserves the indicators of fuzzy transitive congruence axiom, fuzzy direct-revelation axiom, fuzzy acyclic congruence axiom and (transitive and acyclic) rationality indicators. Copyright Springer-Verlag Berlin Heidelberg 2014

Suggested Citation

  • S. Chaudhari & S. Desai, 2014. "Transitive and acyclic rationality indicators of fuzzy choice functions on base domain," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 42(2), pages 341-365, February.
    • Handle: RePEc:spr:sochwe:v:42:y:2014:i:2:p:341-365
    DOI: 10.1007/s00355-013-0729-z
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    References listed on IDEAS

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    1. Amartya Sen, 1969. "Quasi-Transitivity, Rational Choice and Collective Decisions," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 36(3), pages 381-393.
    2. Barrett, C.R. & Pattanaik, P.K. & Salles, M., 1990. "Rationality and Aggregation of Preferences in an Ordinally Fuzzy Framework," Institut des Mathématiques Economiques – Document de travail de l’I.M.E. (1974-1993) 9006, Institut des Mathématiques Economiques. LATEC, Laboratoire d'Analyse et des Techniques EConomiques, CNRS, Université de Bourgogne.
    3. Walter Bossert & Yves Sprumont & Kotaro Suzumura, 2006. "Rationalizability of choice functions on general domains without full transitivity," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 27(3), pages 435-458, December.
    4. Bartel Van de Walle & Bernard De Baets & Etienne Kerre, 1998. "Characterizable fuzzy preference structures," Annals of Operations Research, Springer, vol. 80(0), pages 105-136, January.
    5. Kotaro Suzumura, 1976. "Rational Choice and Revealed Preference," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 43(1), pages 149-158.
    6. Amartya K. Sen, 1971. "Choice Functions and Revealed Preference," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 38(3), pages 307-317.
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    Cited by:

    1. S. S. Desai & A. S. Desai, 2016. "Quasi-Transitive Rationality of Fuzzy Choice Functions Through Indicators," New Mathematics and Natural Computation (NMNC), World Scientific Publishing Co. Pte. Ltd., vol. 12(03), pages 191-208, November.

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