The study of symmetry is one the most important and beautiful themes uniting various areas contemporary arithmetic. Algebraic structures are useful in pure mathematics for learning a geometrical object’s symmetries. In this paper, we introduce new concepts an algebraic structure called BCI-algebra, where present bipolar fuzzy (closed) BCI-positive implicative ideals BCI-commutative BCI-algebras...

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).

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.

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...

In this paper we consider pseudo-BCK/BCI-algebras. In particular, we consider properties of minimal elements (x ≤ a implies x = a) in terms of the binary relation ≤ which is reflexive and antisymmetric along with several more complicated conditions. Some of the properties of minimal elements obtained bear resemblance to properties of B-algebras in case the algebraic operations ∗ and ◦ are ident...

Abstract The class of pseudo-M algebras contains pseudo-BCK, pseudo-BCI, pseudo-BCH, pseudo-BE, pseudo-CI and many other logic. In this paper, the notion deductive system in a algebra is introduced its elementary properties are investigated. Closed systems defined studied. homomorphic (closed) provided. concepts translation R-congruences It shown that there bijection between closed R-congruence...

Based on the theory of a falling shadow which was first formulated by Wang [15], a theoretical approach of the pseudo ideal structure in pseudo d-algebras is established. Several properties are investigated, and relations among a falling pseudo d-subalgebra, a falling pseudo BCK-ideal and a falling pseudo d-ideal are discussed. A characterization of a falling pseudo d-ideal is provided. Conditi...