TY - JOUR
ID - 3135
TI - ON THE SYSTEM OF LEVEL-ELEMENTS INDUCED BY AN L-SUBSET
JO - Iranian Journal of Fuzzy Systems
JA - IJFS
LA - en
SN - 1735-0654
AU - Fang, Jinming
AU - Li, Youyan
AU - Chen, Wenyi
AD - Department of Mathematics, Ocean University of China, Qing Dao
266071, PR China
Y1 - 2017
PY - 2017
VL - 14
IS - 2
SP - 93
EP - 105
KW - Complete residuated lattice
KW - $L$-partially ordered set
KW - $L$-subset
KW - System of level-elements
KW - Union-preserving system of elements
KW - Compatible union-preserving system of elements
KW - Representation theorem
DO - 10.22111/ijfs.2017.3135
N2 - 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.
UR - http://ijfs.usb.ac.ir/article_3135.html
L1 - http://ijfs.usb.ac.ir/article_3135_8463d3b272c307c070fd6fde0df0c457.pdf
ER -