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On Q-rationality of Fuzzy Choice Functions on Base Domains

Desai S. S., Chaudhari S. R.

Fundamenta Informaticae

2015

Vol. 139, nr 2

127--151

Many researchers have studied the rationality of fuzzy choice functions with transitive rationalization. However, not much is known when transitivity is weakened to quasi-transitivity or any other weaker property of the preference relation. In the present paper we study the rationality of fuzzy choice functions with quasi-transitive rationalization for the domains that contain characteristic functions of all single and two element subsets of the universal set.

Arrow Index of a Fuzzy Choice Function

Georgescu I.

Fundamenta Informaticae

2010

Vol. 99, nr 3

245-261

The Arrow index of a fuzzy choice function C is a measure of the degree to which C satisfies the Fuzzy Arrow Axiom, a fuzzy version of the classical Arrow Axiom. The main result of this paper shows that A(C) characterizes the degree to which C is full rational. We also obtain a method for computing A(C). The Arrow index allows to rank the fuzzy choice functions with respect to their rationality. Thus, if for solving a decision problem several fuzzy choice functions are proposed, by the Arrow index the most rational one will be chosen.

Revealed Preference, Congruence and Rationality: A Fuzzy Approach

Georgescu I.

Fundamenta Informaticae

2005

Vol. 65, nr 4

307--328

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°, SAFRP°, HAFRP and we prove two main theorems: 1. The axioms WFCA and WAFRP° 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].