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Some characterizations of pseudo-BL-chains

Walendziak A., Wojciechowska-Rysiawa M.

Commentationes Mathematicae

2011

Vol. 51, [Z] 2

121-124

Pseudo-BL-chains are linearly ordered pseudo-BL-algebras. Characterizations of them in terms of concepts of lattice theory are given.

Anti Fuzzy filters of pseudo-BL-algebras

Wojciechowska-Rysiawa M.

Commentationes Mathematicae

2011

Vol. 51, [Z] 2

155-165

Characterizations of anti fuzzy filters in a pseudo-BL-algebra are established. Conditions for a fuzzy set to be an anti fuzzy filter are given. Finally, a study anti of fuzzy prime filters and characterizations of linearly ordered pseudo-BL-algebras via anti fuzzy filters are given.

Bipartite pseudo-BL algebras

Walendziak A., Wojciechowska-Rysiawa M.

Demonstratio Mathematica

2010

Vol. 43, nr 3

487-496

The class of bipartite pseudo-BL algebras (denoted by BP) and the class of strongly bipartite pseudo-BL algebras (denoted by BP0) are investigated. We prove that the class BP0 is a variety and show that BP is closed under subalgebras and arbitrary direct products but it is not a variety. We also study connections between bipartite pseudo-BL algebras and other classes of pseudo-BL algebras.