Journal
MATHEMATICAL LOGIC QUARTERLY
Volume 55, Issue 5, Pages 493-508Publisher
WILEY-V C H VERLAG GMBH
DOI: 10.1002/malq.200810022
Keywords
Boolean (implicative) filter; (is an element of, is an element of boolean OR q)-fuzzy Boolean (implicative) filter; ((is an element of)over-bar, (is an element of)over-bar boolean OR (q)over-bar)-fuzzy Boolean; (implicative) filter; implication-based fuzzy Boolean (implicative) filter; R-0-algebra
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Funding
- National Natural Science Foundation of China [60875034]
- Natural Science Foundation of Education Committee of Hubei Province, China [D20092905, Q20092901, D20082903, B200529001]
- Natural Science Foundation of Hubei Province, China [2008CDB341]
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In this paper, we introduce the notions of (is an element of, is an element of V q)-fuzzy filters and (is an element of, is an element of V q)-fuzzy Boolean (implicative) filters in R-0-algebras and investigate some of their related properties. Some characterization theorems of these generalized fuzzy filters are derived. In particular, we prove that a fuzzy set in R-0-algebras is an (is an element of, is an element of V q)-fuzzy Boolean filter if and only if it is an (is an element of, is an element of V q)-fuzzy implicative filter. Finally, we consider the concepts of implication-based fuzzy Boolean (implicative) filters of R-0-algebras. (c) 2009 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
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