کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
8902873 | 1632395 | 2018 | 13 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
Boundary optimization for rough sets
ترجمه فارسی عنوان
بهینه سازی مرز برای مجموعه های خشن
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کلمات کلیدی
موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
ریاضیات گسسته و ترکیبات
چکیده انگلیسی
Let n and m be integers, n>mâ¥2, and let A={A1,â¦,Am} be a partition of [n], where [n]={1,â¦,n}. For a subset X of [n], its A-boundary region A(X) is defined to be the union of those blocks Ai of A for which Aiâ©Xâ â
and Aiâ©([n]âX)â â
. Partitions A of [n] into m parts are determined such that, in a first case, the expected absolute cardinality and, in a second case, the expected relative cardinality of the A-boundary region of a randomly chosen subset of [n] is minimal and maximal, respectively. The problem can be reduced to an optimization problem for integer partitions of n. In the most difficult case, the concave-convex shape of the corresponding weight function as well as several other inequalities are proved using an integral representation of the weight function. In a modified third setting, there is an analogon to the AZ-identity. The study is motivated by rough set theory.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Discrete Mathematics - Volume 341, Issue 9, September 2018, Pages 2465-2477
Journal: Discrete Mathematics - Volume 341, Issue 9, September 2018, Pages 2465-2477
نویسندگان
Konrad Engel, Tran Dan Thu,