Closure operators and concept equations in non-commutative fuzzy logic

Rok, strany: 2003, 67 - 90

We introduce the notions of closure operator and closure system in a non-commutative fuzzy framework, where the structure of truth values is a generalized residuated lattice, $L$. We investigate the relationship between $L$-Galois connections and a weakened form of $L$-closure operators, which will eventually lead us to three ways of indicating a hierarchy of formal concepts: by means of relations, of Galois connections and of closure operators. So the situation from the classical case (as well as the one from the commutative fuzzy case) is recovered (of course, with some loses, expressed by the notions of strong $L$-Galois connection and weak $L$-closure operator, loses generated by the existence of two residua for the conjunction in the structure of truth values). Finally, we study systems of concept equations, which are in fact a form of (sometimes incomplete) specification of a conceptual hierarchy.

ISO 690:

Georgescu, G., Popescu, A. 2003. Closure operators and concept equations in non-commutative fuzzy logic. In Tatra Mountains Mathematical Publications, vol. 27, no.3, pp. 67-90. 1210-3195.

APA:

Georgescu, G., Popescu, A. (2003). Closure operators and concept equations in non-commutative fuzzy logic. Tatra Mountains Mathematical Publications, 27(3), 67-90. 1210-3195.