Math. Dept., Faculty of Science, Assiut Univ., Assiut, Egypt
Our idea in this paper prompts to deal with problems that represent typical interplays between topology and domain theory via the fuzzy theory. Based on the notion of a fuzzy ordered set due to Beg, I. [4], we introduce the concepts a fuzzy directed set and the join of a fuzzy set w.r.t. the fuzzy order; and the fuzzy domain is defined. The concepts of a μ-approximation and a basis for a fuzzy domain are proposed; and the notions of continuous and algebraic fuzzy domains are developed. We construct generalized Scott and Lawson topologies on fuzzy domains and some their properties are explored.
fuzzy directed set, fuzzy domain, a μ-approximation relation, continuous and algebraic fuzzy domains, interpolation property, generalized Scott and Lawson topologies
