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ON THE SYSTEM OF LEVEL-ELEMENTS INDUCED BY AN L-SUBSET | ||
| Iranian Journal of Fuzzy Systems | ||
| مقاله 6، دوره 14، شماره 2، تیر 2017، صفحه 93-105 اصل مقاله (356.97 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22111/ijfs.2017.3135 | ||
| نویسندگان | ||
| Jinming Fang؛ Youyan Li* ؛ Wenyi Chen | ||
| Department of Mathematics, Ocean University of China, Qing Dao 266071, PR China | ||
| چکیده | ||
| This paper focuses on the relationship between an $L$-subset and the system of level-elements induced by it, where the underlying lattice $L$ is a complete residuated lattice and the domain set of $L$-subset is an $L$-partially ordered set $(X,P)$. Firstly, we obtain the sufficient and necessary condition that an $L$-subset is represented by its system of level-elements. Then, a new representation theorem of intersection-preserving $L$-subsets is shown by using union-preserving system of elements. At last, another representation theorem of compatible intersection-preserving $L$-subsets is obtained by means of compatible union-preserving system of elements. | ||
| کلیدواژه‌ها | ||
| Complete residuated lattice؛ $L$-partially ordered set؛ $L$-subset؛ System of level-elements؛ Union-preserving system of elements؛ Compatible union-preserving system of elements؛ Representation theorem | ||
| مراجع | ||
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