期刊
FUZZY SETS AND SYSTEMS
卷 247, 期 -, 页码 92-107出版社
ELSEVIER
DOI: 10.1016/j.fss.2013.11.009
关键词
Non-classical logics; Residuated lattice; I-filter; Divisible filter; Strong filter; n-Contractive filter
资金
- AMEP of Linyi University
- Natural Science Foundation of Shandong Province [ZR2011FL017]
- National Nature Science Foundation of China [61179038]
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 I-filters which provide us with a meaningful method to study these filters and corresponding logical algebras. In particular, trivial characterizations of I-filters, non-trivial characterizations of classes of I-filters, such as implicative, fantastic and Boolean filters, and characterizations of homologous logical algebras are obtained. Next, three new types of I-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 I-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. (C) 2013 Elsevier B.V. All rights reserved.
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