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.

Research on Bounded Rationality of Fuzzy Choice Functions

The rationality of a fuzzy choice function is a hot research topic in the study of fuzzy choice functions. In this paper, two common fuzzy sets are studied and analyzed in the framework of the Banerjee choice function. The complete rationality and bounded rationality of fuzzy choice functions are defined based on the two fuzzy sets. An assumption is presented to study the fuzzy choice function, and especially the fuzzy choice function with bounded rationality is studied combined with some rationality conditions. Results show that the fuzzy choice function with bounded rationality also satisfies some important rationality conditions, but not vice versa. The research gives supplements to the investigation in the framework of the Banerjee choice function.

Research on a Fuzzy Choice Function in Multi-Objective Fuzzy Decision

In the multi-objective fuzzy decision-making system, the decision-making problems will be encountered in the multi-objective and multi-evaluation process, so that it does not achieve effective decision-making results. How to solve this multi-objective decision making problems, a fuzzy choice function is proposed, that will be proved an effective method of fuzzy evaluation. The multi-objective decision making problem in the selection and evaluation is effectively solved in a decision-making system by using of the fuzzy choice function.

NEW REVEALED PREFERENCE INDICATORS OF FUZZY CHOICE FUNCTIONS

The axioms WAFRP, SAFRP (resp. WFCA, SFCA) are fuzzy versions of the axioms of revealed preference WARP, SARP (resp. of the congruence axioms WCA, SCA) of classic theory of revealed preference. The revealed preference indicators WAFRP(C), SAFRP(C), WFCA(C) and SFCA(C) of a fuzzy choice function C were introduced in a previous paper in order to express the degree to which C verifies the axioms WAFRP, SAFRP, WFCA, SFCA. In this paper, we shall define the new revealed preference indicators WAFRP°(C), HAFRP(C) corresponding to the axioms WAFRP°, HAFRP from fuzzy revealed preference theory. We shall prove two main results: (1) WAFRP°(C) = WFCA(C); (2) HAFRP(C) = SFCA(C). They extend in terms of numerical indicators two known theorems of Hansson and Suzumura of classic theory of choice functions.

THE RATIONALITY OF FUZZY CHOICE FUNCTIONS

If we assume that the preferences of a set of political actors are not cyclic, we would like to know if their collective choices are rationalizable. Given a fuzzy choice rule, do they collectively choose an alternative from the set of undominated alternatives? We consider necessary and sufficient conditions for a partially acyclic fuzzy choice function to be rationalizable. We find that certain fuzzy choice functions that satisfy conditions α and β are rationalizable. Furthermore, any fuzzy choice function that satisfies these two conditions also satisfies Arrow and Warp.