Journal of Applied Mathematics
Volume 2013 (2013), Article ID 427250, 10 pages
http://dx.doi.org/10.1155/2013/427250
Research Article

Fuzzy Bases of Fuzzy Domains

Sanping Rao1,2 and Qingguo Li1

1College of Mathematics and Econometrics, Hunan University, Changsha 410082, China
2School of Science, Nanchang Institute of Technology, Nanchang 330099, China

Received 21 November 2012; Accepted 26 April 2013

Academic Editor: Jianming Zhan

Copyright © 2013 Sanping Rao and Qingguo Li. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

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.