Generalizations of pseudo MV-algebras and generalized pseudo effect algebras

Pseudo Mv-algebras and Pseudo Bl-algebras

This material is studying MV-algebras and BL-algebras in terms of applicability in Boole algebra. Boole algebras are expanded use in fuzzy logic.

Semirings and pseudo MV algebras

In this paper, we describe the relationships between pseudo MV algebras and semirings. We also give definitions of automata on lattice ordered semirings, prove that the family of K-Languages is closed under union, and discuss the conditions for the closedness of families of K-languages under intersection, generalized intersection and reversal operations.

Pseudo-BL algebras and pseudo-effect algebras

Pseudo-BL algebras and pseudo-effect algebras arose in two rather different fields: fuzzy logics and quantum logics. In this paper, by introducing the notion of pseudo-weak MV-effect algebra which is non-commutative generalization of weak MV-effect algebra, we investigate the mutual relationship between pseudo-BL algebras and pseudo-effect algebras. We prove that dual pseudo-BL algebra under ce...

Unitizing generalized pseudo effect algebras

IDEALS OF PSEUDO MV-ALGEBRAS BASED ON VAGUE SET THEORY

The notion of vague ideals in pseudo MV-algebras is introduced,and several properties are investigated. Conditions for a vague set to be avague ideal are provided. Conditions for a vague ideal to be implicative aregiven. Characterizations of (implicative, prime) vague ideals are discussed.The smallest vague ideal containing a given vague set is established. Primeand implicative extension proper...