TY - JOUR
ID - 4790
TI - Fuzzy universal algebras on $L$-sets
JO - Iranian Journal of Fuzzy Systems
JA - IJFS
LA - en
SN - 1735-0654
AU - Wei, X.
AU - Yue, Y.
AD - Department of Mathematics, Ocean University of China, 238 Songling Road, 266100, Qingdao, P.R.China
Y1 - 2019
PY - 2019
VL - 16
IS - 4
SP - 175
EP - 187
KW - $L$-valued relation
KW - congruence
KW - subalgebra
KW - homomorphism
KW - $L$-valued power algebra
DO - 10.22111/ijfs.2019.4790
N2 - This 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 $A$.
UR - https://ijfs.usb.ac.ir/article_4790.html
L1 - https://ijfs.usb.ac.ir/article_4790_412f1336f3fe0b6517f44e76f17396e6.pdf
ER -