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International Journal of Machine Learning and Cybernetics

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01-12-2013 | Original Article

Intuitionistic fuzzy filter theory of BL-algebras

Published in: International Journal of Machine Learning and Cybernetics | Issue 6/2013

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Abstract

In this paper, the intuitionistic fuzzy filter theory of BL-algebras is researched. The basic knowledge of BL-algebras and intuitionistic fuzzy sets is firstly reviewed. The notions of intuitionistic fuzzy filters, lattice filters, prime filters, Boolean filters, implicative filters, positive implicative filters, ultra filters and obstinate filters are introduced, respectively. Their important properties are investigated. In intuitionistic fuzzy sets, intuitionistic fuzzy filters, Boolean filters, ultra filters are proved to be equivalent to lattice filters, implicative filters, obstinate filters, respectively. Each intuitionistic fuzzy Boolean filter is an intuitionistic fuzzy positive implicative filter, but the converse may not be true in BL-algebras. The conditions under an intuitionistic fuzzy positive implicative filter being an intuitionistic fuzzy Boolean filter are constructed. Finally, the concepts of the intuitionistic fuzzy ultra and obstinate filters are introduced, and the intuitionistic fuzzy ultra filter is proved to be equivalent to the intuitionistic fuzzy obstinate filter in BL-algebras.

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Title: Intuitionistic fuzzy filter theory of BL-algebras
Publication date: 01-12-2013
Published in: International Journal of Machine Learning and Cybernetics / Issue 6/2013
Print ISSN: 1868-8071
Electronic ISSN: 1868-808X
DOI: https://doi.org/10.1007/s13042-012-0130-8

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