ech T Press Science Computer Modeling in Engineering & Sciences DOI: 10.32604/cmes.2022.018615 ARTICLE Neutrosophic κ-Structures in Ordered Semigroups G. Muhiuddin 1,* , K. Porselvi 2 , B. Elavarasan 2 and D. Al-Kadi 3 1 Department of Mathematics, Faculty of Science, University of Tabuk, Tabuk, 71491, Saudi Arabia 2 Department of Mathematics, Karunya Institute of Technology and Sciences, Coimbatore, 641114, India 3 Department of Mathematics and Statistic, College of Science, Taif University, Taif, 21944, Saudi Arabia * Corresponding Author: G. Muhiuddin. Email: chishtygm@gmail.com Received: 06 August 2021 Accepted: 03 November 2021 ABSTRACT In general, ordered algebraic structures, particularly ordered semigroups, play an important role in fuzzifcation in many applied areas, such as computer science, formal languages, coding theory, error correction, etc. Nowadays, the concept of ambiguity is important in dealing with a variety of issues related to engineering modeling problems, network theory, decision-making problems in real-life situations, and so on. Several theories have been developed by various researchers to overcome the difculties that arise from uncertainty, including fuzzy sets, intuitionistic fuzzy sets, probability, sof sets, neutrosophic sets, and many more. In this paper, we focus solely on neutrosophic set theory. In ordered semigroups, we defne and investigate the properties of neutrosophic κ-ideals and neutrosophic κ-interior ideals. We also use neutrosophic κ-ideals and neutrosophic κ-interior ideals to characterize ordered semigroups. KEYWORDS Ordered semigroup; ideals; neutrosophic κ-structures; neutrosophic κ-ideals; neutrosophic κ-interior ideals 1 Introduction In [1], Zadeh proposed the theory of fuzzy sets to model vague notions in the universe. In [2], Atanassov generalized the fuzzy set theory concepts and renamed as Intuitionistic fuzzy set theory. According to his view, there are the two kinds of degrees of freedom in a globe such as membership to a vague subset and non-membership to that given subset. In [3], Rosenfeld introduced the concepts of fuzziness in groups and obtained several results. Recently, many researchers pursue their research in this area and these concepts have been applied to different algebraic structures such as semigroups, ordered semigroups, rings (see [4–10]). Smarandache proposed the notions of neutrosophic sets to handle uncertainty that arises everywhere. It is the generalization of fuzzy sets and intuitionistic fuzzy sets. Using these three attributes such as a truth (T ), an indeterminacy (I ) and a falsity (F ) membership functions, neutrosophic sets are characterized. These sets have numerous applications in various disciplines to deal with the complexities that arise primarily from ambiguity data. A neutrosophic set This work is licensed under a Creative Commons Attribution 4.0 International License, whichpermits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Published Online: 05 January 2022