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Note on " Fuzzy universal algebras on L-sets" | ||
| Iranian Journal of Fuzzy Systems | ||
| دوره 18، شماره 2، خرداد و تیر 2021، صفحه 175-186 اصل مقاله (415.68 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22111/ijfs.2021.5922 | ||
| نویسنده | ||
| Y. Yue* | ||
| Department of Mathematics, Ocean University of China, Qingdao, 266100, P. R. China | ||
| چکیده | ||
| This note is the continuation of the paper entitled ``Fuzzy universal algebras on $L$-sets"(IJFS, Volume 16, Number 4, (2019), pp. 175--187) and it focuses on $\mathcal{Q}$-valued (universal) algebras on $\mathcal{Q}$-typed sets. When $\mathcal{Q}$ is an involutive quantaloid, some basic related notions in $\mathcal{Q}$-valued algebra such as subalgebra, quotient algebra, homomorphism, congruence, direct product and variety etc are given and the properties of them are studied. When $\mathcal{Q}$ is still a symmetric quantaloid, the $\mathcal{Q}$-valued algebra is lifted to $\mathcal{Q}$-valued power algebra, and the power isomorphism theorem is given. As a special case of $\mathcal{Q}$-valued algebra, the fuzzy universal algebra on $L$-set is presented naturally when $L$ is a commutative and divisible quantale. | ||
| کلیدواژه‌ها | ||
| $mathcal{Q}$-typed set؛ universal algebra؛ $mathcal{Q}$-valued algebra؛ congruence؛ power algebra | ||
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آمار تعداد مشاهده مقاله: 193 تعداد دریافت فایل اصل مقاله: 312 |
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