Fuzzy closure operators. II: Induced relations, representation, and examples. (English) Zbl 1027.06008
Author’s abstract: In this paper [a follow up to Part I, J. Math. Anal. Appl. 262, 473-489 (2001; Zbl 0989.54006)], we study relations induced by fuzzy closure operators (fuzzy quasiorders and similarities); factorization of closure systems by similarities and by so-called decrease of logical precision; representation of fuzzy closure operators by (crisp) closure operators; relation to consequence relations; and natural examples illustrating the notions and results.
Reviewer: Bernhard Behrens (Göteborg)
MSC:
06A15 | Galois correspondences, closure operators (in relation to ordered sets) |
68T30 | Knowledge representation |
03B52 | Fuzzy logic; logic of vagueness |
03E72 | Theory of fuzzy sets, etc. |
68T37 | Reasoning under uncertainty in the context of artificial intelligence |