Journal
INFORMATION SCIENCES
Volume 180, Issue 19, Pages 3614-3632Publisher
ELSEVIER SCIENCE INC
DOI: 10.1016/j.ins.2010.05.034
Keywords
(Regular) residuated lattice; (Fuzzy) filter; Regular (fuzzy) filter; (Fuzzy) Boolean (implicative positive implicative and fantastic) filter
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Funding
- Natural Science Foundation of P. R. China [60875034]
- Research Foundation of Guangzhou Maritime University [0912001]
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The aim of this paper is to develop the filter theory of general residuated lattices. First, we extend some particular types of filters and fuzzy filters in BL-algebras and MTL-algebras naturally to general residuated lattices, and further enumerate some relative results obtained in BL-algebras or MTL-algebras, which still hold in general residuated lattices. Next, we introduce the concepts of regular filters and fuzzy regular filters to general residuated lattices, which are two new types of filters and fuzzy filters, and derive some of their characterizations. Finally, we discuss the relations between (fuzzy) regular filters and several other special (fuzzy) filters, and also characterize some special classes of residuated lattices by filters or fuzzy filters. (C) 2010 Elsevier Inc. All rights reserved.
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