an:01274620
Zbl 0919.04004
De Baets, B.; Mare??, M.; Mesiar, R.
\(\mathcal T\)-partitions of the real line generated by idempotent shapes
EN
Fuzzy Sets Syst. 91, No. 2, 177-184 (1997).
00056055
1997
j
03E72
\({\mathcal T}\)-idempotent; scale; t-norm; fuzzy numbers; equivalence classes; \({\mathcal T}\)-equivalences on the real line; generators; shape; fuzzy relations; \({\mathcal T}\)-addition
Summary: The idea of generating fuzzy numbers as equivalence classes of particular \({\mathcal T}\)-equivalences on the real line \(\mathbb{R}\) is fully exploited. Scales (or generators) are used to define certain (pseudo-)metrics on \(\mathbb{R}\). By means of a shape (function), these (pseudo-)metrics are then transformed into binary fuzzy relations on \(\mathbb{R}\). Shapes leading to \({\mathcal T}\)-equivalences, and hence to a class of fuzzy numbers forming a \({\mathcal T}\)-partition of \(\mathbb{R}\), are completely characterized in the case of a continuous generator. This characterization problem is shown to be closely related to determining the idempotents w.r.t. the \({\mathcal T}\)-addition of fuzzy numbers.