In this paper we study L-fuzzy proximity spaces, where L represents a completely distributive lattice.We shall investigate the level decomposition of L-fuzzy proximity on X and the corresponding L-fuzzy proximity continuous maps. In addition, we shall establish the representation theorems of L-fuzzy proximity on X.
We introduce the concept of L-fuzzy neighborhood systems using complete MV-algebras and present important links with the theory of L-fuzzy topological spaces. We investigate the relationships among the degrees of L-fuzzy r-adherent points (r-convergent, r-cluster, and r-limit, resp.) in an L-fuzzy topological spaces. Also, we investigate the concept of LF-continuous functions and their properties.
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