Fuzzy Boolean and positive implicative filters of BL-algebras

Authors:
Liu Lianzhen;Li Kaitai
Affiliations:
College of Science, Xi'an Jiaotong University, 710049 Xi'an, China and College of Science, Southern Yangtze University, 214036 Wuxi, China;College of Science, Xi'an Jiaotong University, 710049 Xi'an, China
Venue:
Fuzzy Sets and Systems
Year:
2005

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Abstract

The aim of this paper is to introduce the notions of fuzzy Boolean filters and fuzzy positive implicative filters in BL-algebras and to investigate their properties. Several characterizations of fuzzy Boolean filters and fuzzy positive implicative filters are derived. The extension theorems of fuzzy Boolean filters and fuzzy positive implicative filters are obtained. The relation between fuzzy Boolean filters and fuzzy positive implicative filters is investigated and it is proved that every fuzzy Boolean filter is a fuzzy positive implicative filter, but the converse may not be true. Furthermore, the conditions under which a fuzzy positive implicative filter is a fuzzy Boolean filter are established.