Separation axioms in fuzzy topological ordered spaces

Abstract Since the fuzzy topological space ( X , τ ) may be considered as a fuzzy topological ordered space when it is realised that the non-empty set X is partially ordered by agreeing that x ⩽ y in X if and only if x = y . Then the study of the fuzzy topological ordered spaces not only includes the study of the abstract fuzzy topological spaces but also reveals many generalizations of well-known results concerning the abstract fuzzy topological spaces. This paper provides a certain number of separation axioms for fuzzy topological ordered spaces, which we label FT i -order separation axioms (for i = 1,2,3,4). The relationships between some of the FT i -order separation axioms are studied.