https://orcid.org/0000-0002-9255-200X
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Abstract
Many problems in systems and control theory are related to solvability of Sylvester matrix equations. In many applications, at least some of the parameters of the system should be represented by fuzzy numbers rather than crisp ones. In most of the previous literature, the solutions of fuzzy Sylvester matrix equation are only presented with triangular fuzzy numbers. In this paper, we propose two analytical methods for solving Positive Trapezoidal Fully Fuzzy Sylvester Matrix Equation (PTrFFSME). The PTrFFSME is converted to an equivalent system of crisp Sylvester Matrix Equations (SME) using the existing arithmetic fuzzy multiplication operations. The necessary and sufficient conditions for the existence and uniqueness of the positive fuzzy solutions to the PTrFFSME are investigated. In addition, the equivalency between the solution to the system of SME and the PTrFFSME are discussed. The proposed methods are illustrated by solving one example.
Acknowledgements
We would like to express our sincere thanks to Professor Mohammed Abdel Latif Ramadan for his valuable and constructive suggestions in the planning and development of this study.
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No potential conflict of interest was reported by the author(s).
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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
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.