Irina Georgescu

Possibilistic risk aversion

Risk theory is usually developed within probability theory. The aim of this paper is to propose an approach of the risk aversion by possibility theory, initiated by Zadeh in 1978. The main notion studied in this paper is the possibilistic risk premium associated with a fuzzy number A and a utility function u. Under the hypothesis that the utility function u verifies certain hypotheses, one proves a formula to evaluate the possibilistic risk premium in terms of u and of some possibilistic indicators.

Similarity of fuzzy choice functions

In this paper two new concepts are introduced: the similarity and the (*,@d)-equality of fuzzy choice functions. We investigate the way the similarity and (*,@d)-equality behave with respect to some fundamental concepts of fuzzy revealed preference theory.

Acyclic rationality indicators of fuzzy choice functions

We introduce the degree of acyclicity of a fuzzy preference relation and two acyclic rationality indicators of a fuzzy choice function C. These two indicators measure the degree to which the choice function C is acyclic G-rational, respectively, acyclic M-rational. We study the fuzzy Condorcet property of a fuzzy choice function and the corresponding indicators. We express the indicator of G-rationality in terms of the Condorcet property and the indicator of @a-consistency.

Degree of dominance and congruence axioms for fuzzy choice functions

In this paper we introduce the degree of dominance of an alternative x with respect to an available fuzzy set of alternatives. Interpreting an available fuzzy set of alternatives as a criterion in decision making the degree of dominance establishes a hierarchy of alternatives with respect to this criterion. With the degree of dominance new congruence axioms for fuzzy choice functions are formulated.

Arrow Index of a Fuzzy Choice Function

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.

On the notion of dominance of fuzzy choice functions and its application in multicriteria decision making

The aim of this paper is twofold: The first objective is to study the degree of dominance of fuzzy choice functions, a notion that generalizes Banerjees concept of dominance. The second objective is to use the degree of dominance as a tool for solving multicriteria decision making problems. These types of problems describe concrete economic situations where partial information or human subjectivity appears. The mathematical modelling is done by formulating fuzzy choice problems where criteria are represented by fuzzy available sets of alternatives.

Consistency Conditions for Fuzzy Choice Functions

We introduce the consistency conditions Fα, Fβ, Fδ as fuzzy forms of Sen’s properties α, β and δ. One first result shows that a fuzzy choice function satisfies Fα, Fβ if and only if the congruence axiom WFCA holds. The second one shows that if h is a normal fuzzy choice function then Fδ holds if and only if the associated preference relation R is quasi-transitive.