Soc Choice Welf DOI 10.1007/s00355-013-0729-z ORIGINAL PAPER Transitive and acyclic rationality indicators of fuzzy choice functions on base domain S. R. Chaudhari · S. S. Desai Received: 26 April 2011 / Accepted: 12 February 2013 © Springer-Verlag Berlin Heidelberg 2013 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. 1 Introduction Rational choice theory is a mathematical approach used by social scientists to under- stand the human behaviour. To study the rationality of consumers Samuelson (1938) introduced the theory of revealed preference through a preference relation associ- ated with a demand function. Uzawa (1956) and Arrow (1959) have developed the revealed preference theory in the abstract setting of a choice function. In their work they assumed that the domain of the choice function contains all non-empty finite sets S. R. Chaudhari · S. S. Desai (B ) Department of Mathematics, Shivaji University, Vidyanagar, Kolhapur 416004, Maharashtra, India e-mail: santosh_desai21@rediffmail.com S. R. Chaudhari e-mail: shrikant_chaudhari@yahoo.com 123