%0 Journal Article
%T ON THE SYSTEM OF LEVEL-ELEMENTS INDUCED BY AN L-SUBSET
%J Iranian Journal of Fuzzy Systems
%I University of Sistan and Baluchestan
%Z 1735-0654
%A Fang, Jinming
%A Li, Youyan
%A Chen, Wenyi
%D 2017
%\ 04/29/2017
%V 14
%N 2
%P 93-105
%! ON THE SYSTEM OF LEVEL-ELEMENTS INDUCED BY AN L-SUBSET
%K Complete residuated lattice
%K $L$-partially ordered set
%K $L$-subset
%K System of level-elements
%K Union-preserving system of elements
%K Compatible union-preserving system of elements
%K Representation theorem
%R 10.22111/ijfs.2017.3135
%X 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.
%U https://ijfs.usb.ac.ir/article_3135_8463d3b272c307c070fd6fde0df0c457.pdf