Approximately Groups in Proximal Relator Spaces

Abstract

The focus of this article is on de…ning descriptive approximations of sets or algebraic structures in proximal relator spaces. By way of a practical application, descriptive approximately algebraic structures such as groupoids, semigroups and groups in digital images endowed with descriptive Efremovi¼ c proximity relations are introduced.

Approximately rings in proximal relator spaces

“…Definition 2.4 [2] Let (X, R δΦ ) be a descriptive proximal relator space and let " · " be a binary operation on X . G ⊆ X is called an approximately group if the following conditions are true:…”

“…Theorem 2.6 [2] Let G be an approximately group, H be a nonempty subset of G and Φ * H be a groupoid.…”

“…Lemma 2.7 [2] Let (X, δ Φ ) be a descriptive proximity space, A, B ⊆ X and A, B, Q(A), Q(B) be groupoids.…”

“…Definition 2.3 [3] Let (X, R δΦ ) be a descriptive proximal relator space and let " • " be a binary operation on [2] Let (X, R δΦ ) be a descriptive proximal relator space and let " • " be a binary operation on X . G ⊆ X is called an approximately group if the following conditions are true:…”

“…The aim of this concept is to obtain algebraic structures in proximal relator spaces using descriptively upper approximations of the subsets of nonabstract points. In 2017 and 2018, approximately semigroups and approximately ideals, approximately groups, and approximately subgroups were introduced by İnan [2][3][4].…”