Fuzzy closure systems onL-ordered sets

Abstract

MSC (2010) 03E72, 06A15In this paper, notions of fuzzy closure system and fuzzy closure L-system on L-ordered sets are introduced from the fuzzy point of view. We first explore the fundamental properties of fuzzy closure systems. Then the correspondence between fuzzy closure systems (fuzzy closure L-systems) and fuzzy closure operators is established. Finally, we study the connections between fuzzy closure systems and fuzzy Galois connections.

Fuzzy -Continuous Posets

“…Theorem 32 (see [33]). Let ( , ) be a fuzzy poset, : → a fuzzy monotone map, and ∘ : → ( ) the corestriction to the image.…”

“…In [33], the authors studied fuzzy closure systems onorder sets, where the -order sets are really fuzzy posets, and discussed their relationship with fuzzy closure operators.…”

“…Definition 31 (see [33]). If ( , ) is a fuzzy poset, a fuzzy closure system on is a subset of such that for each ∈ , min{↑ * 1 } exists, where 1 is the constant fuzzy set with the value 1 on .…”

Closure Systems as a Fuzzy Extension of Meet-subsemilattices

“…We can find distinct definitions of closure system depending on the ordered structure on which the fuzzy closure operator is defined. As a consequence, the notion of fuzzy closure system has been defined on L-ordered sets [14], on fuzzy preposets [8] and fuzzy preordered structures [9]. This paper is a continuation on the study of fuzzy closure systems done in [19], where the underlying structure was a Heyting algebra.…”

Fuzzy Closure Systems on Complete Residuated Lattices

“…Recently, Bělohlávek [2] investigate the properties of fuzzy closure systems and fuzzy closure operators on residual lattices which supports part of foundation of theoretic computer science. Guo et.al [6] introduced fuzzy closure systems in a sense as the least upper bound on fuzzy partial ordered sets. It is a generalization of Bělohlávek's fuzzy closure system.…”