https://orcid.org/0000-0002-9255-200X
![Sample our Information Science journals, sign in here to start your FREE access for 14 days]({"type":"image" , "src" : "/sda/5940/TOC-Subject-Sample-2021-Communication-Studies.jpg"})
Abstract
A couple of Sylvester matrix equations (CSME) are required to be solved simultaneously in many applications, especially in analysing the stability of control systems. However, there are some situations in which the crisp CSME are not well equipped to deal with the uncertainty problem during the stability analysis of control systems. Thus, this paper proposes a new method for solving Arbitrary Coupled Trapezoidal Fully Fuzzy Sylvester Matrix Equation (ACTrFFSME). New arithmetic fuzzy multiplication operations are developed and applied to convert the ACTrFFSME to a reduced system of non-linear equations. Then it is converted to a system of absolute equations where the arbitrary fuzzy solution is obtained by solving that system. The proposed method can solve many arbitrary fuzzy equations, such as fully fuzzy matrix equations, Sylvester and Lyapunov fully fuzzy matrix equations with triangular and trapezoidal fuzzy numbers without any restrictions. We illustrate the proposed method by solving two numerical examples.
Disclosure statement
No potential conflict of interest was reported by the author(s).
Funding
This research received no external funding.
Additional information
Notes on contributors
Ahmed Abdel Aziz Elsayed
Dr. Ahmed Abdel Aziz Elsayed works at the Institute of Applied Technology, Abu Dhabi campus, United Arab Emirates (UAE). He obtained his bachelor's degree in Mathematics and Education in 2007, a Master's in Mathematics in 2018 from the American University in Sharjah, UAE, and a PhD in Mathematics in 2022 from the School of Quantitative Sciences, Universiti Utara Malaysia (UUM). His current research interests include Fuzzy Logic, Numerical Analysis and Linear Algebra.
Nazihah Ahmad
Dr. Nazihah Ahmad works at the School of Quantitative Sciences, Universiti Utara Malaysia (UUM). She obtained her bachelor's degree in Mathematics with honours in 2001, a Master's in Mathematics in 2002, and a PhD in Mathematics in 2009. Her current research interests include fuzzy mathematics, topology, and mathematical modelling in medicine, healthcare, finance, and psychology. She has been awarded several research grants by the Ministry of Education Malaysia and UUM as a principal and co-investigator. The quality of her work has been published in international journals (indexed by SCOPUS or Web of Science), conference proceedings, books and book chapter. She has been teaching mathematics for more than 20 years at the undergraduate and master's level. She has also supervised master and PhD students. Her expertise was acknowledged by her academic peers when she was appointed as an external/internal examiner, article reviewer and external assessor. At national level, she has involved in revising the mathematics syllabus based on the Secondary School Standard Curriculum and in organizing STEM service-learning activities to inspire and strengthen STEM education among young people.
Ghassan Malkawi
Ghassan Malkawi Assistant Professor. Dr. Ghassan Malkawi has been on the mathematics faculty since 2003 at the Higher College of Technology (HCT) in the United Arab Emirates. Where he holds the position of Assistant Professor in the Division of Engineering. Malkawi completed his doctorate from the Universiti Utara Malaysia. His master's degree in applied mathematics from the University of Jordan. Fuzzy linear systems are the primary area of interest for Dr. Malkawi's research.