Fuzzy 1-type and 2-type positive implicative filters of pseudo- BCK algebras 1

Abstract

The notions of fuzzy 1-type (2-type) positive implicative filter and fuzzy normal filter of pseudo-BCK algebras are introduced, some properties and equivalent conditions are given. By using the new notions, the characterizations of 1-type positive implicative pseudo-BCK algebra and 2-type positive implicative pseudo-BCK algebra (positive implicative BCK-algebra) are displayed. Moreover, some conclusions related with positive implicative filters in previous literature are revised. Finally, the concepts of fuzzy commutative filter and fuzzy implicative filter are proposed, and the relationships among fuzzy 1-type (2-type) positive implicative filters, fuzzy commutative filters and fuzzy implicative filters of pseudo-BCK algebras are investigated.