The aim of this paper is to introduce the notion of fantastic deductive systems on generalizations of fuzzy structures, and to emphasize their role in the probability theory on these algebras. We give a characterization of commutative pseudo-BE algebras and we generalize an axiom system consisting of four identities to the case of commutative pseudo-BE algebras. We define the fantastic deductiv...

Hyperstructure theory was born in 1934 when Marty [9] defined hypergroups, began to analyze their properties and applied them to groups, rational algebraic functions. Now they are widely studied from theoretical point of view and for their applications to many subjects of pure and applied properties. In 1986, Sen and Saha [12] introduced the concept of Γsemigroup as a generalization of semigrou...

We introduce the notion of sensible fuzzy ideals of BCK-algebras with respect to a t-conorm and investigate some of their properties. We give the conditions for a sensible fuzzy subalgebra with respect to a t-conorm to be a sensible fuzzy ideal with respect to a t-conorm. Some properties of the direct product and S-product of fuzzy ideals of BCK-algebras with respect to a t-conorm are also disc...

In this paper, we introduce the concept of doubt intuitionistic fuzzy subalgebras and doubt intuitionistic fuzzy ideals in BCK/BCI-algebras. We show that an intuitionistic fuzzy subset of BCK/BCI-algebras is an intuitionistic fuzzy subalgebra and an intuitionistic fuzzy ideal if and only if the complement of this intuitionistic fuzzy subset is a doubt intuitionistic fuzzy subalgebra and a doubt...

In order to lay a foundation for providing a soft algebraic tool in considering many problems that contain uncertainties, the notion of double-framed soft sets is introduced, and applications in BCK/BCI-algebras are discussed. The notions of double-framed soft algebras in BCK/BCIalgebras are introduced, and related properties are investigated. Characterizations of doubleframed soft algebras are...

The notion of (∈,∈ ∨q)-interval-valued fuzzy prime ideals in commutative BCK-algebras is introduced. Some characterization theorems in (∈,∈ ∨q)-interval-valued fuzzy prime ideals in commutative BCK-algebras are derived. Also we study relation between (∈,∈ ∨q)-interval-valued fuzzy prime ideal and (∈ ∨q)-interval-valued fuzzy level prime ideals. Characterization of interval-valued fuzzy set to b...

for two algebras $a$ and $b$, a linear map $t:a longrightarrow b$ is called separating, if $xcdot y=0$ implies $txcdot ty=0$ for all $x,yin a$. the general form and the automatic continuity of separating maps between various banach algebras have been studied extensively. in this paper, we first extend the notion of separating map for module case and then we give a description of a linear separa...

Recently, L.Rozansky and E.Witten [RW] associated to any hyper-Kähler manifold X an invariant of topological 3-manifolds. In fact, their construction gives a system of weights c Γ (X) associated to 3-valent graphs Γ and the corresponding invariant of a 3-manifold Y is obtained as the sum c Γ (X)I Γ (Y) where I Γ (Y) is the standard integral of the product of linking forms. So the new ingredient...

Recently, L.Rozansky and E.Witten [RW] associated to any hyper-Kähler manifold X an invariant of topological 3-manifolds. In fact, their construction gives a system of weights c Γ (X) associated to 3-valent graphs Γ and the corresponding invariant of a 3-manifold Y is obtained as the sum c Γ (X)I Γ (Y) where I Γ (Y) is the standard integral of the product of linking forms. So the new ingredient...

Starting from quasi-Wajsberg algebras (which are generalizations of Wajsberg algebras), whose regular sets are Wajsberg algebras, we introduce a theory of quasi-algebras versus, in parallel, a theory of regular algebras. We introduce the quasi-RM, quasi-RML, quasi-BCI, (commutative, positive implicative, quasi-implicative, with product) quasi-BCK, quasi-Hilbert and quasi-Boolean algebras as gen...