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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، تابستان 2017، صفحه 93-105
اصل مقاله (357 K)
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نوع مقاله: Research Paper | |||||||||||

نویسندگان | |||||||||||

Jinming Fang؛ Youyan Li^{*} ؛ Wenyi Chen
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^{}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. | |||||||||||

کلیدواژه ها | |||||||||||

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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آمار تعداد مشاهده مقاله: 176 تعداد دریافت فایل اصل مقاله: 230 |
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