representation theorems of $L-$subsets and $L-$families on complete residuated lattice

Document Type : Research Paper

Authors

1 Department of Mathematics, Ocean University of China, 266100 Qingdao, P.R. China

2 Department of Mathematics, Ocean University of China, 266100 Qing- dao, P.R. China

Abstract

In this paper, our purpose is twofold. Firstly, the tensor and
residuum operations on $L-$nested systems are introduced under the
condition of complete residuated lattice. Then we show that
$L-$nested systems form a complete residuated lattice, which is
precisely the classical isomorphic object of complete residuated
power set lattice. Thus the new representation theorem of
$L-$subsets on complete residuated lattice is obtained. Secondly, we
introduce the concepts of $L-$family and the system of $L-$subsets,
then with the tool of the system of $L-$subsets, we obtain the
representation theorem of intersection-preserving $L-$families on
complete residuated lattice.

Keywords

References

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Iranian Journal of Fuzzy Systems
Volume 10, Issue 3 - Serial Number 3
May and June 2013
Pages 125-136

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