Affiliations: Turku Centre for Computer Science, Institute for
Advanced Management Systems Research, Åbo Akademi University,
Lemminkäisenkatu 14, FIN-20520 Turku, Finland.
irina.georgescu@abo.fi
Note: [] Address for correspondence: Turku Centre for Computer Science,
Institute for Advanced Management Systems Research, Lemminkäisenkatu 14,
FIN-20520 Turku, Finland
Abstract: In a previous paper connections between the congruence axioms WFCA,
SFCA and the revealed preference axioms WAFRP, SAFRP for fuzzy choice functions
whose domain contains the characteristic functions of pairs and of triples of
alternatives have been studied. The first objective of this paper is to establish such connections
for the case of arbitrary fuzzy choice functions. We introduce the new revealed
preference axioms WAFRP^o, SAFRP^o, HAFRP
and we prove two main theorems: 1. The axioms WFCA and WAFRP^o are equivalent;
2. The axioms SFCA and HAFRP are equivalent. Our second objective is to define G-rational, M-rational, G-normal
and M-normal fuzzy choice functions and to investigate some of their
properties. The notions and the results are formulated in terms of the residuum
of the Gödel t-norm and the proofs use the residuated lattice structure of
the interval [0,1].
