LL-fuzzy interior systems

The aim of this work is to introduce the concept of LL-fuzzy interior systems and LL-fuzzy interior operators. We start by establishing a connection between LL-fuzzy interior systems and LL-fuzzy interior operators. It is shown that an LL-fuzzy interior system is precisely the fuzzy system in opposition to the crisp system, and an LL-fuzzy interior operator is a suitable interior operator that has a close relation to an LL-fuzzy interior system. It is also shown that there is a Galois correspondence between the category of LL-fuzzy interior system spaces and that of LL-fuzzy interior spaces.