کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
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389297 | 661126 | 2014 | 16 صفحه PDF | دانلود رایگان |
Filters play an important role in studying logical systems and the related algebraic structures. Various filters have been proposed in the literature. In this paper, we aim to develop a unifying definition for some specific filters called II-filters which provide us with a meaningful method to study these filters and corresponding logical algebras. In particular, trivial characterizations of II-filters, non-trivial characterizations of classes of II-filters, such as implicative, fantastic and Boolean filters, and characterizations of homologous logical algebras are obtained. Next, three new types of II-filters named divisible filters, strong and n-contractive filters in residuated lattices are introduced. Particularly, it is verified that n-fold implicative BL-algebras and n -contractive BL-algebras coincide. Finally, we investigate the relationships between these specific II-filters. It is shown that a filter is a fantastic filter if and only if it is both a divisible filter and a regular filter.
Journal: Fuzzy Sets and Systems - Volume 247, 16 July 2014, Pages 92–107