University of Sistan and BaluchestanIranian Journal of Fuzzy Systems1735-065414220170429ON THE SYSTEM OF LEVEL-ELEMENTS INDUCED BY AN L-SUBSET93105313510.22111/ijfs.2017.3135ENJinmingFangDepartment of Mathematics, Ocean University of China, Qing Dao
266071, PR ChinaYouyanLiDepartment of Mathematics, Ocean University of China, Qing Dao
266071, PR ChinaWenyiChenDepartment of Mathematics, Ocean University of China, Qing Dao
266071, PR ChinaJournal Article20141022This 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.http://ijfs.usb.ac.ir/article_3135_8463d3b272c307c070fd6fde0df0c457.pdf