On choosing rationally when preferences are fuzzy
Fuzzy Sets and Systems
Fuzzy choice functions, revealed preference and rationality
Fuzzy Sets and Systems
Fuzzy set theory—and its applications (3rd ed.)
Fuzzy set theory—and its applications (3rd ed.)
Fuzzy Reasoning in Decision Making and Optimization
Fuzzy Reasoning in Decision Making and Optimization
Fuzzy Relational Systems: Foundations and Principles
Fuzzy Relational Systems: Foundations and Principles
Acyclic rationality indicators of fuzzy choice functions
Fuzzy Sets and Systems
Degree of dominance and congruence axioms for fuzzy choice functions
Fuzzy Sets and Systems
Reducing adverse selection by fuzzy choices
International Journal of Modelling and Simulation
ECSQARU'05 Proceedings of the 8th European conference on Symbolic and Quantitative Approaches to Reasoning with Uncertainty
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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$^o$, SAFRP$^o4, HAFRPand we prove two main theorems: 1. The axioms WFCA and WAFRP$^o$ 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].