scholarly journals Research on Bounded Rationality of Fuzzy Choice Functions

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Xinlin Wu ◽  
Yong Zhao
Keyword(s):  
Fuzzy Sets ◽  
Bounded Rationality ◽  
Choice Function ◽  
Research Topic ◽  
Choice Functions ◽  
Fuzzy Choice Functions ◽  
Fuzzy Choice Function

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.

Quasi-Transitive Rationality of Fuzzy Choice Functions Through Indicators

2016 ◽  
Vol 12 (03) ◽  
pp. 191-208 ◽  
Author(s):  
S. S. Desai ◽  
A. S. Desai
Keyword(s):  
Choice Function ◽  
Choice Functions ◽  
Fuzzy Choice Functions ◽  
Independent Property ◽  
Fuzzy Choice Function ◽  
Text Condition

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.

THE RATIONALITY OF FUZZY CHOICE FUNCTIONS

2008 ◽  
Vol 04 (03) ◽  
pp. 309-327 ◽  
Author(s):  
JOHN N. MORDESON ◽  
KIRAN R. BHUTANI ◽  
TERRY D. CLARK
Keyword(s):  
Choice Function ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Choice Rule ◽  
Choice Functions ◽  
Political Actors ◽  
Necessary And Sufficient ◽  
Fuzzy Choice Functions ◽  
Fuzzy Choice Function

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.

Distances of Fuzzy Choice Functions

2015 ◽  
Vol 11 (03) ◽  
pp. 249-265 ◽  
Author(s):  
Irina Georgescu ◽  
Jani Kinnunen
Keyword(s):  
Choice Function ◽  
Fuzzy Relations ◽  
Choice Functions ◽  
Fuzzy Preferences ◽  
Fuzzy Choice Functions ◽  
Finite Choice ◽  
Fuzzy Choice Function ◽  
The Way

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.

Full Rationality of Fuzzy Choice Functions on Base Domain Through Indicators

2016 ◽  
Vol 12 (03) ◽  
pp. 175-189
Author(s):  
Santosh Desai ◽  
Rupali Potdar
Keyword(s):  
Choice Function ◽  
Choice Functions ◽  
Full Rationality ◽  
Fuzzy Choice Functions ◽  
Fuzzy Choice Function ◽  
Base Domain

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.

NEW REVEALED PREFERENCE INDICATORS OF FUZZY CHOICE FUNCTIONS

2012 ◽  
Vol 08 (02) ◽  
pp. 239-256
Author(s):  
IRINA GEORGESCU
Keyword(s):  
Choice Function ◽  
Revealed Preference ◽  
Choice Functions ◽  
Preference Theory ◽  
Classic Theory ◽  
Fuzzy Choice Functions ◽  
Revealed Preference Theory ◽  
Fuzzy Choice Function

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.

A Comment on Arrow’s Impossibility Theorem

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Alec Sandroni ◽  
Alvaro Sandroni
Keyword(s):  
Social Choice ◽  
Choice Function ◽  
Social Preference ◽  
Social Choice Function ◽  
Individual Preference ◽  
Impossibility Theorem ◽  
Preference Order ◽  
Individual Choice ◽  
Choice Functions ◽  
Preference Orders

AbstractArrow (1950) famously showed the impossibility of aggregating individual preference orders into a social preference order (together with basic desiderata). This paper shows that it is possible to aggregate individual choice functions, that satisfy almost any condition weaker than WARP, into a social choice function that satisfy the same condition (and also Arrow’s desiderata).

Smooth approximations by continuous choice-functions

2021 ◽  
Author(s):  
Mihai Prunescu
Keyword(s):  
Error Bound ◽  
Common Sense ◽  
Choice Function ◽  
Continuous Functions ◽  
Ordered Sets ◽  
Choice Functions ◽  
Continuous Choice ◽  
Functions Of Two Variables ◽  
Smooth Approximations

Abstract We explore the existence of rational-valued approximation processes by continuous functions of two variables, such that the output continuously depends of the imposed error-bound. To this sake we prove that the theory of densely ordered sets with generic predicates is ℵ0- categorical. A model of the theory and a particular continuous choice-function are constructed. This function transfers to all other models by the respective isomorphisms. If some common-sense conditions are fulfilled, the processes are computable. As a byproduct, other functions with surprising properties can be constructed.

scholarly journals On a correspondence between probabilistic and fuzzy choice functions

2017 ◽  
Vol 17 (3) ◽  
pp. 247-264 ◽  
Author(s):  
Davide Martinetti ◽  
Susana Montes ◽  
Susana Díaz ◽  
Bernard De Baets
Keyword(s):  
Choice Functions ◽  
Fuzzy Choice Functions
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