کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
391234 661361 2006 9 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Combinatorics of counting finite fuzzy subsets
موضوعات مرتبط
مهندسی و علوم پایه مهندسی کامپیوتر هوش مصنوعی
پیش نمایش صفحه اول مقاله
Combinatorics of counting finite fuzzy subsets
چکیده انگلیسی

Let F(n) denote the number of equivalence classes of fuzzy subsets of a finite set of n elements under a natural equivalence generalizing equality of subsets in the crisp case. Applying results from integer partitions, and partitions of a set, a formula was developed for F(n) recently using the ideas of flags, keychains and pinned-flags. In this paper, F(n) is re-examined through an interpretation of equivalence classes of fuzzy subsets as ordered partitions or chains in the Boolean Algebra of the power set of a set. We derive some recurrence relations, an infinite series as a closed form and a generating function for F(n) for any natural number n.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Fuzzy Sets and Systems - Volume 157, Issue 17, 1 September 2006, Pages 2403-2411