Fuzzy Sets and Systems 155 (2005) 390 – 407 www.elsevier.com/locate/fss Degree of dominance and congruence axioms for fuzzy choice functions Irina Georgescu ∗ Turku Centre for Computer Science, ˚ Abo Akademi University, Institute for Advanced Management Systems Research, Lemminkäisenkatu 14, FIN-20520 Turku, Finland Received 28 October 2004; received in revised form 3 February 2005; accepted 19 April 2005 Available online 25 May 2005 Abstract In this paper we introduce the degree of dominance of an alternative x with respect to an available fuzzy set of alternatives. Interpreting an available fuzzy set of alternatives as a criterion in decision making the degree of dominance establishes a hierarchy of alternatives with respect to this criterion. With the degree of dominance new congruence axioms for fuzzy choice functions are formulated. © 2005 Elsevier B.V. All rights reserved. Keywords: Fuzzy choice function; Degree of dominance; Congruence axiom; Decision making 1. Introduction Fuzzy preference relations are a topic a vast literature has been dedicated to. Most authors admit that the preferences that appear in social choice are vague (hence modelled through fuzzy binary relations), but the act of choice is exact (hence choice functions are crisp) [3–5]. In [2] Banerjee admits the vagueness of the act of choice and studies choice functions with a fuzzy behaviour. The domain of a Banerjee choice function C is made of all non-empty finite subsets of a set of alternatives X and its range is made of non-zero fuzzy subsets of X. In [8,9] we have considered choice functions C for which the domain and the range are made of fuzzy subsets of X. Banerjee fuzzifies only the range of a choice function; we use a fuzzification of both the ∗ Tel.: +358 2 2153339; fax: +358 2 215 4809. E-mail address: irina.georgescu@abo.fi. 0165-0114/$ - see front matter © 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.fss.2005.04.018