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Iranian Journal of Fuzzy Systems، جلد ۱۰، شماره ۳، صفحات ۱۲۵-۱۳۶
عنوان فارسی representation theorems of $L-$subsets and $L-$families on complete residuated lattice
چکیده فارسی مقاله 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.
کلیدواژه‌های فارسی مقاله Complete residuated lattices، $L-$subsets، $L-$nested systems، $L-$families، Level $L-$subsets، Representation theorems،
عنوان انگلیسی representation theorems of $L-$subsets and $L-$families on complete residuated lattice
چکیده انگلیسی مقاله 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.
کلیدواژه‌های انگلیسی مقاله Complete residuated lattices, $L-$subsets, $L-$nested systems, $L-$families, Level $L-$subsets, Representation theorems
نویسندگان مقاله هیو هانیه |
department of mathematics, ocean university of china, 266100 qingdao, p.r. china

jinming fang |
department of mathematics, ocean university of china, 266100 qing- dao, p.r. china

نشانی اینترنتی http://ijfs.usb.ac.ir/article_866_34e66093d052f7fc3dc927be495d286b.pdf
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