BCI-algebras with Condition (S) and their Properties

BCI-algebras with Condition (S) and their Properties

The papers [5], [12], [3], [1], [6], [2], [10], [9], [4], [11], and [7] provide the notation and terminology for this paper. We introduce BCI stuctures with complements which are extensions of BCI structure with 0 and zero structure and are systems 〈 a carrier, an external complement, an internal complement, a zero 〉, where the carrier is a set, the external complement and the internal compleme...

Ideals of BCI-algebras and their Properties

For simplicity, we use the following convention: X denotes a BCI-algebra, X1 denotes a non empty subset of X, A, I denote ideals of X, x, y, z denote elements of X, and a denotes an element of A. The following four propositions are true: (1) For all elements x, y, z, u ofX such that x ≤ y holds u\(z\x) ≤ u\(z\y). (2) For all elements x, y, z, u of X holds x \ (y \ z) \ (x \ (y \ u)) ≤ z \ u. (3...

Several Classes of BCI-algebras and their Properties

We introduce BCI structures which are extensions of 1-sorted structure and are systems 〈 a carrier, an internal complement 〉, where the carrier is a set and the internal complement is a binary operation on the carrier. Let us note that there exists a BCI structure which is non empty and strict. Let A be a BCI structure and let x, y be elements of A. The functor x \ y yielding an element of A is...

Intuitionistic T-S Fuzzy Subalgebras and Ideals in BCI-algebras

Redefined fuzzy subalgebra (with thresholds) of BCK/BCI-algebras

Using the notion of anti fuzzy points and its besideness to and non-quasi-coincidence with a fuzzy set, new concepts of an anti fuzzy subalgebras in BCK/BCI-algebras are introduced and their inter-relations and related properties are investigated in [3]. The notion of the new fuzzy subalgebra with thresholds are introduced and relationship between this notion and the new fuzzy subalgebra of a B...