## On the transitivity of fuzzy indifference relations.(English)Zbl 1132.68768

Bilgiç, Taner (ed.) et al., Fuzzy sets and systems — IFSA 2003. 10th international Fuzzy Systems Association world congress, Istanbul, Turkey, June 30 – July 2, 2003. Proceedings. Berlin: Springer (ISBN 3-540-40383-3/pbk). Lect. Notes Comput. Sci. 2715, 87-94 (2003).
Summary: 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 $$I$$.
For the entire collection see [Zbl 1029.00022].

### MSC:

 68T37 Reasoning under uncertainty in the context of artificial intelligence
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