Section-retraction-pairs between fuzzy domains

In this paper we give the concepts of fuzzy monotone and fuzzy continuous section-retraction-pairs between fuzzy domains defined in [Q.-Y. Zhang, C.-Y. Zheng, L-fuzzy domain and its related properties, Fuzzy Systems and Math. 18 (2004) 1–7 (in chinese); Q.-Y. Zhang, L. Fan, Continuity in quantitative domains, Fuzzy Sets and Systems 154 (2005) 118–131], discuss some properties about them, and prove that the fuzzy monotone retract of a fuzzy domain is also a fuzzy domain, the fuzzy continuous retract of a continuous fuzzy domain is also a continuous fuzzy domain when L is a completely distributive lattice in which is multiplicative, and every continuous fuzzy domain is a fuzzy continuous retract of an algebraic fuzzy domain when L is a completely distributive lattice in which 1 is ∨-irreducible and is multiplicative.