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Fuzzy universal algebras on $L$-sets | ||
Iranian Journal of Fuzzy Systems | ||
مقاله 13، دوره 16، شماره 4، مهر و آبان 2019، صفحه 175-187 اصل مقاله (187.44 K) | ||
نوع مقاله: Research Paper | ||
شناسه دیجیتال (DOI): 10.22111/ijfs.2019.4790 | ||
نویسندگان | ||
X. Wei* ؛ Y. Yue | ||
Department of Mathematics, Ocean University of China, 238 Songling Road, 266100, Qingdao, P.R.China | ||
چکیده | ||
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 $A$. | ||
کلیدواژهها | ||
$L$-valued relation؛ congruence؛ subalgebra؛ homomorphism؛ $L$-valued power algebra | ||
مراجع | ||
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