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International Journal of Fuzzy Logic and Intelligent Systems 2021; 21(1): 86-92

Published online March 25, 2021

https://doi.org/10.5391/IJFIS.2021.21.1.86

© The Korean Institute of Intelligent Systems

On the Left and Right Almost Hyperideals of LA-Semihypergroups

Shah Nawaz1, Muhammad Gulistan1 , Nasreen Kausar2 , Salahuddin3 , and Mohammad Munir4

1Department of Mathematics and Statistics, Hazara University, Mansehra, Pakistan
2Department of Mathematics and Statistics, University of Agriculture, Faisalabad, Pakistan
3Department of Mathematics, Jazan University, Jazan, Kingdom of Saudi Arabia
4Department of Mathematics, Government Postgraduate College, Abbottabad, Pakistan

Correspondence to :
Nasreen Kausar (kausar.nasreen57@gmail.com)

Received: December 17, 2020; Revised: January 29, 2021; Accepted: February 22, 2021

This is an Open Access article distributed under the terms of the Creative Commons Attribution Non-Commercial License (http://creativecommons.org/licenses/by-nc/3.0/) which permits unrestricted noncommercial use, distribution, and reproduction in any medium, provided the original work is properly cited.

In this paper, we define left almost hyperideals, right almost hyperideals, almost hyperideals, and minimal almost hyperideals. We demonstrate that the intersection of almost hyperideals is not required to be an almost hyperideal, but the union of almost hyperideals is an almost hyperideal, which is completely different from the classical algebraic concept of the ideal theory.

Keywords: LA-semihypergroups, Left almost hyperideals, Right almost hyperideals, Almost hyperideals, Minimal almost hyperideals

No potential conflict of interest relevant to this article was reported.

Shah Nawaz is a Ph.D. student of Dr. Muhammad Gulistan and has submitted his Ph.D. thesis in the field of non-associative hyperstructures. He has authored some papers on the introduction of new non-associative hyperstructures such as LA-polygroups and LA-hypergroups.

E-mail: shahnawazawan82@gmail.com


Muhammad Gulistan received his M.Phil. degree from Quaid-i- Azam University, Islamabad, in 2011, and his Ph.D. degree from Hazara University, in 2016, where he is currently working as an Assistant Professor in the Department of Mathematics and Statistics. He has supervised many M.Phil. and Ph.D. research students. He has published more than 80 research papers in different well reputed journals. His area of research interests includes cubic sets and their generalizations, non-associative hyperstructures, neutrosophic cubic sets, neutrosophic cubic graphs, and decision making.

E-mail: gulistanmath@hu.edu.pk

ORCID: https://orcid.org/0000-0002-6438-1047


Nasreen Kausar received her Ph.D. degree in Mathematics from the Quaid-i-Azam University in Islamabad, Pakistan. She is currently an assistant Professor of Mathematics at the University of Agriculture Faisalabad, Pakistan. Her research interests include the numerical analysis and numerical solutions of ordinary differential equations (ODEs), partial differential equations (PDEs), and Volterra integral equations. She also has research interests in associative and commutative, non-associative and non-commutative fuzzy algebraic structures and their applications. Department of Mathematics and Statistics University of Agriculture, Faisalabad, Pakistan.

E-mail: kausar.nasreen57@gmail.com

ORCID: https://orcid.org/0000-0002-8659-0747


Salahuddin received his Ph.D. degree for his research work in Mathematics in 2001. He is a faculty member of the Department of Mathematics, Jazan University, Jazan, Saudi Arabia. He is working on a fuzzy set, fuzzy group theory, fuzzy ring and fuzzy ideal theory, variational inequality, and optimization theory.

E-mail: drsalah12@hotmail.com

ORCID: https://orcid.org/0000-0002-0496-3379


Mohammad Munir received his Ph.D. degree in Applied Mathematics from the University of Graz, Graz, Austria, in 2010. He completed his Ph.D. thesis on a project titled “Generalized Sensitivity Functions in Physiological Modelling”. His research interests are in the mathematical modelling of biological systems in the fields of the glucose-insulin dynamics, solute kinetics and hemodialysis using ordinary differential equations (ODEs). Parameter identification, sensitivity analysis and generalized sensitivity analysis are more concentrated areas of his research. His other interests include the applications of the fuzzy sets theory to multi-criteria decision-making (MCDM) problems.

Email: dr.mohammadmunir@gpgc-atd.edu.pk

ORCID: https://orcid.org/0000-0002-4891-2995


Article

Original Article

International Journal of Fuzzy Logic and Intelligent Systems 2021; 21(1): 86-92

Published online March 25, 2021 https://doi.org/10.5391/IJFIS.2021.21.1.86

Copyright © The Korean Institute of Intelligent Systems.

On the Left and Right Almost Hyperideals of LA-Semihypergroups

Shah Nawaz1, Muhammad Gulistan1 , Nasreen Kausar2 , Salahuddin3 , and Mohammad Munir4

1Department of Mathematics and Statistics, Hazara University, Mansehra, Pakistan
2Department of Mathematics and Statistics, University of Agriculture, Faisalabad, Pakistan
3Department of Mathematics, Jazan University, Jazan, Kingdom of Saudi Arabia
4Department of Mathematics, Government Postgraduate College, Abbottabad, Pakistan

Correspondence to:Nasreen Kausar (kausar.nasreen57@gmail.com)

Received: December 17, 2020; Revised: January 29, 2021; Accepted: February 22, 2021

This is an Open Access article distributed under the terms of the Creative Commons Attribution Non-Commercial License (http://creativecommons.org/licenses/by-nc/3.0/) which permits unrestricted noncommercial use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

In this paper, we define left almost hyperideals, right almost hyperideals, almost hyperideals, and minimal almost hyperideals. We demonstrate that the intersection of almost hyperideals is not required to be an almost hyperideal, but the union of almost hyperideals is an almost hyperideal, which is completely different from the classical algebraic concept of the ideal theory.

Keywords: LA-semihypergroups, Left almost hyperideals, Right almost hyperideals, Almost hyperideals, Minimal almost hyperideals

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