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.
Qimei Xiao. Qingguo Li. "Generalized Lower and Upper Approximations in Quantales." J. Appl. Math. 2012 1 - 11, 2012. https://doi.org/10.1155/2012/648983