## $$T$$-Ferrers relations versus $$T$$-biorders.(English)Zbl 1132.68769

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, 269-276 (2003).
Summary: In this paper, we study the Ferrers property of relations in the context of fuzzy preference modelling. A logical approach leads us to the notion of $$T$$-Ferrers relations, while a relational approach brings us to $$T$$-biorders. We characterize the t-norms for which both notions coincide. We also describe the kind of completeness exhibited by reflexive $$T$$-Ferrers relations or reflexive $$T$$-biorders. Finally, we investigate the relationship between the $$T$$-Ferrers properties of a reflexive fuzzy relation $$R$$ and the corresponding strict preference relation $$P$$, and the relationship between $$R$$ and $$P$$ being $$T$$-biorders.
For the entire collection see [Zbl 1029.00022].

### MSC:

 68T37 Reasoning under uncertainty in the context of artificial intelligence 03E72 Theory of fuzzy sets, etc.
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