The Geometrical Characterization for The Solutions of a Vectorial Equation By Using Weak Fuzzy Complex Numbers and Other Generalizations Of Real Numbers

Yaser Ahmad Alhasan^1,*, Lee Xu², Raja Abdullah Abdulfatah³, Abuobida M. Ahmed Alfahal⁴

¹Deanship of the Preparatory Year, Prince Sattam bin Abdulaziz University, Alkharj, Saudi Arabia  

² University of Chinese Academy of Sciences, CAS, Mathematics Department, Beijing, China

³Deanship the Preparatory Year, Prince Sattam bin Abdulaziz University, Alkharj, Saudi Arabia

⁴Deanship of the Preparatory Year, Prince Sattam bin Abdulaziz University, Alkharj, Saudi Arabia

Emails: y.alhasan@psau.edu.sa; Leexu1244@yahoo.com; r.abdulfatah@psau.edu.sa; a.alfahal@psau.edu.sa.

Abstract

The main goal of this paper is to study the geometrical characterization of the solutions for a vectorial equation defined in the two/three dimensional Euclidean spaces. The geometrical characterization of the solutions for the desired vectorial equation is obtained for many different values of t based on the circles and spheres in some generalizations of the real field, especially dual numbers, weak fuzzy complex numbers split-complex numbers, and complex numbers.

Keywords: A-curve; dual numbers; weak fuzzy complex numbers; split-complex numbers