L-fuzzy closure systems

This paper studies the generalization of fuzzy closure operators and fuzzy closure systems, introduced by Bělohlávek in 2001, and introduces the concepts of strong L-fuzzy closure systems and strong L-fuzzy closure operators. It is shown that a strong L-fuzzy closure system is precisely the fuzzy system in opposition to the crisp system, and a strong L-fuzzy closure operator is a suitable closure operator that has a close relation to a strong L-fuzzy closure system. It is also shown that there is a Galois correspondence between the category of (strong) L-fuzzy closure system spaces and that of (strong) L-fuzzy closure spaces.