TY - JOUR
ID - 866
TI - representation theorems of $L-$subsets and $L-$families on complete residuated lattice
JO - Iranian Journal of Fuzzy Systems
JA - IJFS
LA - en
SN - 1735-0654
AU - Han, Hui
AU - Fang, Jinming
AD - Department of Mathematics, Ocean University of China, 266100 Qingdao,
P.R. China
AD - Department of Mathematics, Ocean University of China, 266100 Qing-
dao, P.R. China
Y1 - 2013
PY - 2013
VL - 10
IS - 3
SP - 125
EP - 136
KW - Complete residuated lattices
KW - $L-$subsets
KW - $L-$nested systems
KW - $L-$families
KW - Level $L-$subsets
KW - Representation theorems
DO - 10.22111/ijfs.2013.866
N2 - In this paper, our purpose is twofold. Firstly, the tensor andresiduum operations on $L-$nested systems are introduced under thecondition of complete residuated lattice. Then we show that$L-$nested systems form a complete residuated lattice, which isprecisely the classical isomorphic object of complete residuatedpower set lattice. Thus the new representation theorem of$L-$subsets on complete residuated lattice is obtained. Secondly, weintroduce the concepts of $L-$family and the system of $L-$subsets,then with the tool of the system of $L-$subsets, we obtain therepresentation theorem of intersection-preserving $L-$families oncomplete residuated lattice.
UR - https://ijfs.usb.ac.ir/article_866.html
L1 - https://ijfs.usb.ac.ir/article_866_34e66093d052f7fc3dc927be495d286b.pdf
ER -