Further study on $(L,M)$-fuzzy topologies and $(L,M)$-fuzzy neighborhood systems

Abstract

Following the idea of $L$-fuzzy neighborhood system as introduced byFu-Gui Shi, and its generalization to $(L,M)$-fuzzy neighborhood system, the relationship between $(L,M)$-fuzzy topology and $(L,M)$-fuzzy neighborhood system will be further studied. As an application of the obtained results, we will describe the initial structures of $(L,M)$-fuzzy neighborhood subspaces and $(L,M)$-fuzzy topological product spaces.