On the Geometry of Weak Fuzzy Complex Numbers and Applications to the Classification of Some A-Curves

Abdallah Shihadeh¹, Wael Mahmoud M. Salameh^2,*, Malik Bataineh³, Hassan Al-Tarawneh⁴, Ayman Alahmade⁵, Abdallah Al-Husban⁶

¹Department of Mathematics, Faculty of Science, The Hashemite University, Zarqa 13133, PO box 330127, Jordan

²Faculty of Information Technology, Abu Dhabi University, Abu Dhabi, UAE

³Department of Mathematics and Statistics, Jordan University of Science and Technology, Irbid, Jordan,

⁴Department of Data sciences and Artificial Intelligence, Al-Ahliyya Amman University, Amman, Jordan

⁵Department of Mathematics, College of Science and Art, AlUla branch, Taibah University,Medina, Saudi Arabia

⁶Department of Mathematics, Faculty of Science and Technology, Irbid National University, P.O. Box: 2600 Irbid, Jordan

Emails: abdallaha_ka@hu.edu.jo; wael.salameh@adu.ac.ae; msbataineh@just.edu.jo; H.Altarawneh@Ammanu.edu.jo; aaahmdi@taibahu.edu.sa; dralhosban@inu.edu.jo

Abstract

The concept of A-curves is considered as a novel application of real field extensions in solving some algebraic vectorial equations defined by Euclidean norms. In this paper, we present a novel insight through the classification of A-curves by illustrating many new semi-module isomorphisms between the direct product of weak fuzzy complex numbers with itself and the direct product of classical Euclidean vector spaces multiplied by itself. These isomorphisms will give us a full classification of A-curves that are related to weak fuzzy complex ring. Also, we provide many examples to explain the contribution of our work.

Keywords: weak fuzzy complex number; weak fuzzy complex vector space; A-curve; vectorial equation.