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Arrow Index of a Fuzzy Choice Function

Georgescu I.

Fundamenta Informaticae

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2010

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Vol. 99, nr 3

245-261

EN

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.

2

Revealed Preference, Congruence and Rationality: A Fuzzy Approach

Georgescu I.

Fundamenta Informaticae

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2005

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Vol. 65, nr 4

307--328

EN

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].

3

Detection system for survey of the professional exposed personnel

Stosioiu A., Mihai F., Georgescu I.

Prace Naukowe GIG. Górnictwo i Środowisko / Główny Instytut Górnictwa

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2004

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nr 1

61-62

4

Consistency Conditions in Fuzzy Consumers Theory

Georgescu I.

Fundamenta Informaticae

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2004

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Vol. 61, nr 3,4

223--245

EN

This paper is concerned with consistency properties for fuzzy consumers. We introduce the consistency conditions Fα, Fβ, Fδ as fuzzy forms of Sen's properties α, β and δ. Other consistency conditions are also studied: Fα2, Fβ(+), Fγ2 and FPI. The main results are: (1) A fuzzy consumer verifies Fα, Fβ if and only if the congruence axiom WFCA holds; (2) If h is a normal fuzzy consumer then Fδ holds if and only if the associated fuzzy preference relation R is quasi-transitive; (3) A fuzzy consumer is normal if and only if conditions Fα2, Fγ2 hold.