剩余格上的n-维模糊滤子

The n-dimensional Fuzzy Filters in Residuated Lattices

在剩余格上提出n-维模糊滤子,n-维模糊EIMTL-滤子和n-维模糊t-滤子概念并研究它们的一些性质。给出n-维模糊滤子,n-维模糊EIMTL-滤子和n-维模糊t-滤子的一些等价刻画。证明了n-维模糊集f是n-维模糊滤子(n-维模糊EIMTL-滤子,n-维模糊t-滤子)当且仅当对任意的λ∈[0,1],fλ是1-维模糊滤子(1-维模糊EIMTL-滤子,1-维模糊t-滤子)。此外,得到了剩余格上n-维模糊Divisible滤子和n-维模糊Strong滤子的等价刻画。

In this paper,we introduce the notions of n-dimensional fuzzy filters,n-dimensional fuzzy EIMTL-filters and n-dimensional fuzzy t-filters in residuated lattices and investigate some of their properties.Some characteristics of n-dimensional fuzzy filters,n-dimensional fuzzy EIMTL-filters and n-dimensional fuzzy t-filters are given,respectively.Furthermore,we prove that a n-dimensional fuzzy set is a n-dimensional fuzzy filter（an-dimensional fuzzy EIMTL-filter,an-dimensional fuzzy t-filter）if and only if fλis a n-dimensional fuzzy filter（an-dimensional fuzzy EIMTL-filter,an-dimensional fuzzy t-filter）for anyλ∈[0,1].In addition,we obtain some characteristics of n-dimensional fuzzy Divisible filters and n-dimensional fuzzy Strong filters.