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Ordered Nearness Semigroups

Department of Mathematics, Faculty of Arts and Sciences, Adiyaman University, 02040 Adiyaman, Türkiye

Department of Mathematics, Faculty of Science, University of Tabuk, P.O. Box 741, Tabuk 71491, Saudi Arabia

Department of Mathematics Education, Gyeongsang National University, Jinju 52828, Republic of Korea

* Corresponding Author
Annals of Communications in Mathematics 2024
, 7 (2),
Received: 16 May 2024 |
Accepted: 23 Jun 2024 |
Published: 30 Jun 2024


A semigroup is an algebraic structure that consists of a set and a binary operation that is associative, meaning that the order in which the operations are performed does not affect the outcome. For example, addition and multiplication are associative operations. The term “semigroup” was first used in its modern sense by Harold Hilton in his book on finite groups in 1908 [6]. Semigroups have since then been studied extensively in mathematics, and they have numerous applications in different fields, such as computer science, physics, and economics. Nearenness semigroup is a generalization of semigroups. Near set theory, which is a generalization of rough set theory, is based on the determination of universal sets according to the available information about the objects. Nearenness semigroups extend the concept of nearness from set theory to semigroups. ˙Inan and Öztürk applied the notion of near sets defined by J. F. Peters to the semigroups [10]. Our objective in this paper is to establish the definition of ordered semigroups on weak near approximation spaces. In addition, we investigated certain characteristics of these ordered nearness semigroups.


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Ordered Nearness Semigroups.

Annals of Communications in Mathematics,

7 (2):
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  • Copyright (c) 2023 by the Author(s). Licensee Techno Sky Publications. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (


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