Some lattices associated with LM-fuzzy topological spaces

Abstract

This paper studies the closure and interior operators in LM-fuzzy topological spaces. The algebraic structures associated with various collections of closed sets and open sets are identified. Further, certain lattices formed by these algebraic structures are obtained and some lattice theoretic properties of the same are investigated. Corresponding to every element in M, the study associates a lattice of monoids which is determined by various types of closed sets and open sets.