Summary: Based on the notion of an -fuzzy partially ordered set [see L. Fan, Q.-Y. Zhang, W.-Y. Xiang and C. Y. Zheng, “An -fuzzy approach to quantitative domain. I. Generalized ordered set valued in frame and adjunction theory”, Fuzzy Syst. Math. 14, 6–7 (2000)] and by introducing the concepts of an -fuzzy directed set and the join of an -fuzzy set w.r.t. the -fuzzy partial order, -fuzzy domains are defined and the generalized Scott topology on an -fuzzy domain is built. This approach is similar to Flagg’s logic approach to quantitative domain theory [B. Flagg, P. Sünderhauf, and K. Wagner, A logical approach to quantitative domain theory, Preprint (1996), submitted for publication]. In addition, the concepts of stratified approximation and a basis for an -fuzzy domain are proposed, and a notion of a continuous -fuzzy domain is developed. It is proved that if is a completely distributive lattice in which 1 is -irreducible and the well-below relation is multiplicative, then the stratified interpolation property holds in a continuous -fuzzy domain , and , is a base for the generalized Scott topology on .
|06B35||Continuous lattices and posets, applications|