Since all the algebras connected to logic have, more or less explicitely, an associated order relation, it follows that they have two presentations, dual to each other. We classify these dual presentations in ”left” and ”right” ones and we consider that, when dealing with several algebras in the same research, it is useful to present them unitarily, either as ”left” algebras or as ”right” algeb...

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...

In this note, by using the concept of Bipolar-valued fuzzy set, the notion of bipolar-valued fuzzy BCK/BCI-algebra is introduced. Moreover, the notions of (strong) negative s-cut (strong) positive t-cut are introduced and the relationship between these notions and crisp subalgebras are studied.

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...

Processing of the certain information, especially inferences based on certain information. Is based on classical two-valued logic. Due to strict and complete logical foundation (classical logic), making inference levels. Thus, it is natural and necessary to attempt to establish some rational logic system as the logical foundation for uncertain information processing. It is evident that this kin...

BCK and BCI-algebras, two classes of algebras of logic, were introduced by Imai and Iseki [1], Iseki [2] and Iseki and Tanaka [3] and have been extensively studied by various other researchers [4, 5]. It is known that the class of BCK-algebras is a proper subclass of the class of BCI-algebras. In [6, 7] a wider class of abstract algebras was introduced by Q.P.Hu and X.Li.They have shown that th...