The concepts of (internal, external) cubic soft sets, P-cubic (resp. R-cubic) soft subsets, R-union (resp. R-intersection, P-union, Pintersection) of cubic soft sets, and the complement of a cubic soft set are introduced, and several related properties are investigated. We apply the notion of cubic soft sets to BCK/BCI-algebras, and introduce the notion of cubic soft BCK/BCI-algebras. A charact...

In this paper we show that the K-algebra (G, ·, , e) on an abelian group (G, ·) is equivalent to the p-semisimple BCI-algebra (G; , e). Mathematics Subject Classification: 06F35, 20A05.

Let $X$ be a $BCH$-algebra and $I$ be an ideal of $X$. In this paper, we introduce the concept of $sqrt{I}$. We show that it is an ideal of $X$, when $I$ is closed ideal of $X$. Then we verify some useful properties of it. We prove that it is the ::::union:::: of all $k-$nil ideals of $I$. Moreover, if $I$ is a closed ideal of $X$, then $sqrt{I}$ is a closed translation ideal and so we can cons...

Based on the theory of intuitionistic fuzzy sets, the concepts of intuitionistic fuzzy subalgebras with thresholds (λ, μ) and intuitionistic fuzzy ideals with thresholds (λ, μ) of BCI-algebras are introduced and some properties of them are discussed. Keywords—BCI-algebra, intuitionistic fuzzy set, intuitionistic fuzzy subalgebra with thresholds (λ, μ), intuitionistic fuzzy ideal with thresholds...

The aim of this paper is to introduce the notion of intuitionistic fuzzy implicative ideals with thresholds (λ, μ) of BCI-algebras and to investigate its properties and characterizations. Keywords—BCI-algebra, intuitionistic fuzzy set, intuitionistic fuzzy ideal with thresholds (λ,μ), intuitionistic fuzzy implicative ideal with thresholds (λ,μ).

A new kind of derivation in BCI-algebras is introduced, and related properties are investigated. For a self map dq of a BCI-algebra X, conditions for the kernel of dq to be both a subalgebra and an ideal of X are provided. Mathematics Subject Classification: 06F35, 03G25

In this paper, we apply the concept of an intuitionistic fuzzy set to closed ideals in BCI-algebras. The notion of an intuitionistic fuzzy closed ideal of a BCI-algebra is introduced, and some related properties are investigated. Characterizations of an intuitionistic fuzzy closed ideal are also given.

and Applied Analysis 3 Definition 2.2 see 6 . A subset S of a BCI-algebra X is called subalgebra of X if x ∗ y ∈ S whenever x, y ∈ S. For a BCI-algebra X, we denote x ∧ y y ∗ y ∗ x for all x, y ∈ X 6 . For more details we refer to 3, 5, 6 . 3. t-Derivations in a BCI-Algebra/p-Semisimple BCI-Algebra The following definitions introduce the notion of t-derivation for a BCI-algebra. Definition 3.1....

In this paper, a new notion, called TM-algebra, which is a generalization of the idea of Q/BCH/BCI/BCK/BCC-algebra, is introduced. Some theorems discussed in Q-and BCK algebras are generalized. Definition of TM-algebra along with various propositions are stipulated and presented with their respective proofs. The relation between TM-algebra and other algebra has been investigated and detailed in...