Algebraic fuzzy directed-complete posets

In this paper, as a special case of fuzzy domains, algebraic fuzzy directed-complete posets (shortly, algebraic fuzzy dcpos) are discussed. Throughout the algebraic fuzzy dcpos, some equivalent characterizations of fuzzy domains are given. Then, the construction of new algebraic fuzzy dcpos (resp., fuzzy domains) from known ones by means of forming products, taking some special subsets, and taking images under maps with appropriate operations is investigated. Finally, a new kind of fuzzy continuous section retraction pairs is proposed. Moreover, it is proved that every fuzzy domain is a fuzzy continuous retraction of an algebraic fuzzy dcpo, and the fuzzy continuous retraction of a fuzzy domain is also a fuzzy domain.