University of Sistan and BaluchestanIranian Journal of Fuzzy Systems1735-065416420190820Fuzzy universal algebras on $L$-sets175187479010.22111/ijfs.2019.4790ENX.WeiDepartment of Mathematics, Ocean University of China, 238 Songling Road, 266100, Qingdao, P.R.ChinaY.YueDepartment of Mathematics, Ocean University of China, 238 Songling Road, 266100, Qingdao, P.R.ChinaJournal Article20171101This paper attempts to generalize universal algebras on classical sets to $L$-sets when $L$ is a GL-quantale. Some basic notions of fuzzy universal algebra on an $L$-set are introduced, such as subalgebra, quotient algebra, homomorphism, congruence, and direct product etc. The properties of them are studied. $L$-valued power algebra is also introduced and it is shown there is an onto homomorphism from $P(A)/R^{+}$ to $P(A/R)$ for any congruence $R$ on $L$-set $A$.https://ijfs.usb.ac.ir/article_4790_412f1336f3fe0b6517f44e76f17396e6.pdf