Closure systems and L-subalgebras. (English) Zbl 0562.06004

A subset of a complete lattice is called a closure system if it is closed under the inf-operation. In the lattice of L-fuzzy sets [cf. J. A. Goguen, J. Math. Anal. Appl. 18, 145-174 (1967; Zbl 0145.244)] many closure systems can be described by systems of inequalities, which lead to the simple computation of the respective closure operation. The authors have collected a long list of L-fuzzy subalgebras which are defined by suitable systems of inequalities (and therefore form closure systems), and they have obtained certain formulas for the determination of the respective generated L-fuzzy algebras.
Reviewer: J.Drewniak


06B23 Complete lattices, completions
06A15 Galois correspondences, closure operators (in relation to ordered sets)
08A30 Subalgebras, congruence relations


Zbl 0145.244
Full Text: DOI


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