Class of Sheffer stroke BCK-algebras

Abstract

In this paper, Sheffer stroke BCK-algebra is defined and its features are investigated. It is indicated that the axioms of a Sheffer stroke BCK-algebra are independent. The relationship between a Sheffer stroke BCK-algebra and a BCK-algebra is stated. After describing a commutative, an implicative and an involutory Sheffer stroke BCK-algebras, some of important properties are proved. The relationship of this structures is demonstrated. A Sheffer stroke BCK-algebra with condition (S) is described and the connection with other structures is shown. Finally, it is proved that for a Sheffer stroke BCK-algebra to be a Boolean lattice, it must be an implicative Sheffer stroke BCK-algebra.

Neutrosophic N−Ideals on Sheffer Stroke BCK-Algebras

“…Lemma 2.3. [14] Let (A, |, 0) be a Sheffer stroke BCK-algebra. Then the following properties hold for all x, y, z ∈ A:…”

“…Example 3.2. Consider the Sheffer stroke BCK-algebra A where A = {0, x, y, 1} and Sheffer stroke | on A has the Cayley table [14] in Table 1:…”

“…BCK-algebras have been applied to many mathematical areas such as group theory, functional analysis, probability theory and topology. Recently, some types of BCK-algebras with Sheffer stroke are defined and relationships between other Sheffer stroke algebras and these algebraic structures are examined ( [12], [14]).…”

Fuzzy set approach to ideal theory on Sheffer stroke BE-algebras

“…Sheffer stroke (Sheffer operation), which is one of the two operators that can be used by itself without any other logical operators, was originally introduced by Sheffer to build a logical formal system [13]. Since it offers novel axiom systems that are straightforward and easily adaptable for a variety of algebraic structures owing to its commutative property, there are numerous uses for this operation in algebraic structures, such as Sheffer Stroke Hilbert algebras [8], Sheffer stroke BCK-algebras [9], Sheffer stroke BCH-algebras [5], strong Sheffer stroke nonassociative MV-algebras [6], Sheffer stroke BL-algebras [10], Sheffer stroke UP-algebras [7], and Sheffer stroke BE-algebras [1,2,11,12].…”

M-polar Q-hesitant Anti-fuzzy Set in BCK/BCI-algebras

“…Also, in recent years have witnessed a growing interest in the application of (hesitant) fuzzy sets to various algebraic structures. Notable contributions to this field have been made by researchers [11][12][13]18]. Their studies have shed light on the potential of (hesitant) fuzzy sets in the context of algebraic structures and opened up new avenues for research and application.…”