On the transitivity of fuzzy indifference relations

Authors:
Susana Díaz;Bernard De Baets;Susana Montes
Affiliations:
Department of Statistics and O.R., Faculty of Geology, University of Oviedo, Oviedo, Spain;Department of Applied Mathematics, Biometrics and Process Control, Ghent University, Gent, Belgium;Department of Statistics and O.R., University of Oviedo, Gijón, Spain
Venue:
IFSA'03 Proceedings of the 10th international fuzzy systems association World Congress conference on Fuzzy sets and systems
Year:
2003

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Abstract

Transitivity is an essential property in preference modelling. In this work we study this property in the framework of fuzzy preference structures. In particular, we discuss the relationship between the transitivity of a fuzzy large preference relation R and the transitivity of the fuzzy indifference relation I obtained from R by some of the most important generators employed in the literature. We consider different types of transitivity for the fuzzy large preference relation R and identify the strongest type of transitivity of the corresponding fuzzy indifference relation I.