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.
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Acknowledgments
The second author sincerely acknowledges the financial support by the UGC New Delhi (India) in the form of “Research fellowship in Science for Meritorious Students”. The authors would like to thank the anonymous referees for their valuable comments and useful advice to improve the paper linguistically as well as technically.
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Chaudhari, S.R., Desai, S.S. Transitive and acyclic rationality indicators of fuzzy choice functions on base domain. Soc Choice Welf 42, 341–365 (2014). https://doi.org/10.1007/s00355-013-0729-z
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DOI: https://doi.org/10.1007/s00355-013-0729-z