%0 Journal Article
%T representation theorems of $L-$subsets and $L-$families on complete residuated lattice
%J Iranian Journal of Fuzzy Systems
%I University of Sistan and Baluchestan
%Z 1735-0654
%A Han, Hui
%A Fang, Jinming
%D 2013
%\ 06/01/2013
%V 10
%N 3
%P 125-136
%! representation theorems of $L-$subsets and $L-$families on complete residuated lattice
%K Complete residuated lattices
%K $L-$subsets
%K $L-$nested systems
%K $L-$families
%K Level $L-$subsets
%K Representation theorems
%R 10.22111/ijfs.2013.866
%X 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.
%U https://ijfs.usb.ac.ir/article_866_34e66093d052f7fc3dc927be495d286b.pdf