Approximately Semigroups and Ideals: An Algebraic View of Digital Images

Abstract

ÖzetBu makalede proksimal relator uzaylarında yaklaşımlı yarıgruplar ve ideallere giriş yapılmıştır. Tanımsal proksimiti bağıntısı ile birlikte dikkate alınan dijital görüntülerde yaklaşımlı yarıgrup ve ideal örnekleri verilmiştir. Bundan başka, nesne tanımlaması homomorfizması kullanılarak tanımsal yaklaşımların bazı özellikleri incelenmiştir. Yaklaşımlı Yarıgruplar ve İdealler: Dijital Görüntülerin Cebirsel İncelenmesi AbstractIn this article, approximately semigroups and ideals in proximal relator spaces have beenintroduced. In addition to, some examples of approximately semigroups and ideals in digital images endowed with descriptive proximity relation have been given. Furthermore, some properties of descriptively approximations using object descriptive homomorphism have been obtained.

Approximately rings in proximal relator spaces

“…for all x, y ∈ A. Definition 2.1 [3] Let (X, R δΦ ) be a descriptive proximal relator space and A ⊆ X . A descriptively upper approximation of A is defined with…”

“…Definition 2.3 [3] Let (X, R δΦ ) be a descriptive proximal relator space and let " · " be a binary operation on…”

“…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].…”

Approximately Groups in Proximal Relator Spaces

“…Lemma 2 [5] Let , be descriptive proximity space and , ⊂ . If : → ℝ is an object descriptive homomorphism, then .…”

“…Example 1 [5] Let be a digital image endowed with descriptive proximity relation and consists of 25 pixels as in Figure 1. A pixel is an element at position , (row and column) in digital image .…”