Solid weak BCC-algebras

We characterize weak BCC-algebras in which the identity $(xy)z=(xz)y$ is satisfied only in the case when elements $x,y$ belong to the same branch

New generalizations of BCI, BCK and Hilbert algebras

We introduce more generalizations of BCI, BCK and of Hilbert algebras, with proper examples, and show the hierarchies existing between all these algebras, old and new ones. Namely, we found thirty one new generalizations of BCI and BCK algebras and twenty generalizations of Hilbert algebras.Comment: Open problems 11.3 (1), (2), (3) were solved. New (20'), (21''), Theorems 2.4,2.6, Cor. 2.5, 5.5 adde

Interval valued (\in,\ivq)-fuzzy filters of pseudo BLBL-algebras

We introduce the concept of quasi-coincidence of a fuzzy interval value with an interval valued fuzzy set. By using this new idea, we introduce the notions of interval valued (\in,\ivq)-fuzzy filters of pseudo $BL$-algebras and investigate some of their related properties. Some characterization theorems of these generalized interval valued fuzzy filters are derived. The relationship among these generalized interval valued fuzzy filters of pseudo $BL$-algebras is considered. Finally, we consider the concept of implication-based interval valued fuzzy implicative filters of pseudo $BL$-algebras, in particular, the implication operators in Lukasiewicz system of continuous-valued logic are discussed