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
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات ریاضیات گسسته و ترکیبات
چکیده انگلیسی
Let n and m be integers, n>m≥2, and let A={A1,…,Am} be a partition of [n], where [n]={1,…,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 Ai∩X≠∅ and Ai∩([n]∖X)≠∅. 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
نویسندگان
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