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

Díaz, Susana; De Baets, Bernard; Montes, Susana

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.