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.

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.

scholarly journals Necessary and sufficient conditions for pairwise majority decisions on path-connected domains

2021 ◽  
Author(s):  
Madhuparna Karmokar ◽  
Souvik Roy ◽  
Ton Storcken
Keyword(s):  
Connected Domain ◽  
Majority Rule ◽  
Choice Function ◽  
Sufficient Conditions ◽  
Choice Functions ◽  
Group Strategy ◽  
Median Rule ◽  
Strategy Proof ◽  
Necessary And Sufficient ◽  
Path Connected

AbstractIn this paper, we consider choice functions that are unanimous, anonymous, symmetric, and group strategy-proof and consider domains that are single-peaked on some tree. We prove the following three results in this setting. First, there exists a unanimous, anonymous, symmetric, and group strategy-proof choice function on a path-connected domain if and only if the domain is single-peaked on a tree and the number of agents is odd. Second, a choice function is unanimous, anonymous, symmetric, and group strategy-proof on a single-peaked domain on a tree if and only if it is the pairwise majority rule (also known as the tree-median rule) and the number of agents is odd. Third, there exists a unanimous, anonymous, symmetric, and strategy-proof choice function on a strongly path-connected domain if and only if the domain is single-peaked on a tree and the number of agents is odd. As a corollary of these results, we obtain that there exists no unanimous, anonymous, symmetric, and group strategy-proof choice function on a path-connected domain if the number of agents is even.

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.

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.

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.

The extinction time of a general birth and death process with catastrophes

1986 ◽  
Vol 23 (04) ◽  
pp. 851-858 ◽  
Author(s):  
P. J. Brockwell
Keyword(s):  
Laplace Transform ◽  
Size Distribution ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Death Process ◽  
Extinction Time ◽  
Birth And Death Process ◽  
Different Types ◽  
The Laplace Transform ◽  
Necessary And Sufficient

The Laplace transform of the extinction time is determined for a general birth and death process with arbitrary catastrophe rate and catastrophe size distribution. It is assumed only that the birth rates satisfyλ0= 0,λj> 0 for eachj> 0, and. Necessary and sufficient conditions for certain extinction of the population are derived. The results are applied to the linear birth and death process (λj=jλ, µj=jμ) with catastrophes of several different types.

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