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

Lexicographic Effect Algebras

In the paper we investigate a class of effect algebras which can be represented in the form of the lexicographic product \Gamma(H\lex G,(u,0)), where $(H,u)$ is an Abelian unital po-group and $G$ is an Abelian directed po-group. We study algebraic conditions when an effect algebra is of this form. Fixing a unital po-group $(H,u)$, the category of strong $(H,u)$-perfect effect algebra is introduced and it is shown that it is categorically equivalent to the category of directed po-group with interpolation. We show some representation theorems including a subdirect product representation by antilattice lexicographic effect algebras

Prime ideals and Godel ideals of BL-algebras

In this paper we give further properties of ideals of a BL-algebra. The concepts of prime ideals, irreducible ideals and Godel ideals are introduced. We prove that the concept of prime ideals coincides with one of irreducible ideals, and establish the Prime Ideal Theorem in BL-algebras. As applications of Prime ideal Theorem we give several representation and decomposition properties of ideals in BL-algebras. In particular, we give some equivalent conditions of Godel ideals and prove that a BL-algebra A satisfying condition (C) is a Godel algebra i the ideal f0g is a Godel ideal i all ideals of A are Godel ideals if and only if      for any &nbsp

Pseudo MV-algebras and Lexicographic Product

We study algebraic conditions when a pseudo MV-algebra is an interval in the lexicographic product of an Abelian unital $\ell$-group and an $\ell$-group that is not necessary Abelian. We introduce $(H,u)$-perfect pseudo MV-algebras and strong $(H,u)$-perfect pseudo MV-algebras, the latter ones will have a representation by a lexicographic product. Fixing a unital $\ell$-group $(H,u)$, the category of strong $(H,u)$-perfect pseudo MV-algebras is categorically equivalent to the category of $\ell$-groups.Comment: arXiv admin note: text overlap with arXiv:1304.074