%0 Journal Article %T Generalized Lower and Upper Approximations in Quantales %A Qimei Xiao %A Qingguo Li %J Journal of Applied Mathematics %D 2012 %I Hindawi Publishing Corporation %R 10.1155/2012/648983 %X 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. %U http://www.hindawi.com/journals/jam/2012/648983/