Fuzzy Bases of Fuzzy Domains

Abstract EN

This paper is an attempt to develop quantitative domain theory over frames.

Firstly, we propose the notion of a fuzzy basis, and several equivalent characterizations of fuzzy bases are obtained.

Furthermore, the concept of a fuzzy algebraic domain is introduced, and a relationship between fuzzy algebraic domains and fuzzy domains is discussed from the viewpoint of fuzzy basis.

We finally give an application of fuzzy bases, where the image of a fuzzy domain can be preserved under some special kinds of fuzzy Galois connections.