Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
389297 | Fuzzy Sets and Systems | 2014 | 16 Pages |
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.