L-topological derived neighborhood relations and L-topological derived remote neighborhood relations

Abstract

Fuzzy relations and fuzzy derived operators are useful tools to characterize fuzzy mathematical structures such as fuzzy topology, fuzzy convexity, fuzzy matriod and fuzzy convergence structure. In this paper, notions of L-topological neighborhood relation space, L-topological derived neighborhood relation space and L-topological derived neighborhood space are introduced. It is proved that all of these spaces are categorically isomorphic to L-topological internal relation space and L-topological neighborhood space. Also, notions of L-topological remote neighborhood relation space, L-topological derived remote neighborhood relation space and L-topological derived remote neighborhood space are introduced. It is proved that all of these spaces are categorically isomorphic to L-topological enclosed relation space and L-topological remote neighborhood space.