On the relationship between fuzzy topological ordered spaces and fuzzy bitopological spaces

Abstract

The parallel between the theory of bitopological spaces and the theory of topological ordered spaces was given by M.J. Canfell in his thesis “Semialgebras and rings of continuous functions”, but he left the question open when a bitopological space may be treated as a topological ordered space. More precisely, if (X, T₁, T₂) is a bitopological space and T = T₁ + T₂ is the coarest topology containing T₁ and T₂, to find conditions under which there exists a partial order ≤ on X such that T₁ coincides with the upper topology and T₂ with the lower topology of (X, T , ≤). In this paper we give a solution to this problem in the fuzzy setting.