Journal of Applied Mathematics
Volume 2012 (2012), Article ID 648983, 11 pages
Research Article

Generalized Lower and Upper Approximations in Quantales

1College of Mathematics and Econometrics, Hunan University, Changsha, Hunan 410082, China
2School of Mathematics and Computer Science, Changsha University of Science and Technology, Changsha, Hunan 410004, China

Received 8 August 2011; Revised 21 October 2011; Accepted 30 October 2011

Academic Editor: Jin L. Kuang

Copyright © 2012 Qimei Xiao 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.


We introduce the concepts of set-valued homomorphism and strong set-valued homomorphism of a quantale which are the extended notions of congruence and complete congruence, respectively. The properties of generalized lower and upper approximations, constructed by a set-valued mapping, are discussed.