Consistency Properties for Fuzzy Choice Functions: An Analysis with the Łukasiewicz T-Norm

We focus on the relationships among some consistency axioms in the framework of fuzzy choice functions. In order to help disclose the role of the t-norm in existing analyses, we start to study the situation that arises when we replace the standard t-norm with other t-norms. Our results allow us to conclude that unless we impose further structure on the domain of application for the choices, the use of the Łukasiewicz t-norm as a replacement for the standard t-norm does not guarantee a better performance.

Quasi-Transitive Rationality of Fuzzy Choice Functions Through Indicators

The aim of this paper is to study a quasi-transitive rationality of the fuzzy choice functions through indicators. In this paper, we introduce the indicators of the path independent property, fuzzy Condorcet property and fuzzy [Formula: see text] condition of a fuzzy choice function. These indicators measure the degree to which the fuzzy choice function satisfies the fuzzy path independent, fuzzy Condorcet property and fuzzy [Formula: see text] condition, respectively. We express the indicator of quasi-transitive rationality in terms of the indicator of the path independent, Condorcet property and fuzzy [Formula: see text] condition.

Full Rationality of Fuzzy Choice Functions on Base Domain Through Indicators

This paper introduces indicators of the weak fuzzy T-congruence axiom and the fuzzy Chernoff axiom. These indicators measure the degree to which the fuzzy choice function satisfies the weak fuzzy T-congruence axiom and the fuzzy Chernoff axiom. The indicator of the full rationality is expressed in terms of indicators of weak fuzzy T-congruence axiom and the fuzzy Chernoff axiom.

Distances of Fuzzy Choice Functions

In this paper, we introduce four distances on the set of fuzzy choice functions defined on a finite choice space. They are studied along with four distances on the set of fuzzy relations. The two types of distance allow to investigate the way the changes in fuzzy preferences are reflected in the changes of fuzzy choice associated with them. Also the way the changes in fuzzy choices manifest themselves in changes in fuzzy preferences are studied. The coefficient of normality of a fuzzy choice function is defined as a measure of normality and its variation is evaluated with respect to the variation of fuzzy choices. Finally, the variation of some congruence indicators is evaluated as effect of the changes in fuzzy choices.