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Keywords = fully fuzzy sylvester matrix equations

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24 pages, 2056 KB  
Article
Two-Stage Algorithm for Solving Arbitrary Trapezoidal Fully Fuzzy Sylvester Matrix Equations
by Ahmed Abdel Aziz Elsayed, Bassem Saassouh, Nazihah Ahmad and Ghassan Malkawi
Symmetry 2022, 14(3), 446; https://doi.org/10.3390/sym14030446 - 23 Feb 2022
Cited by 7 | Viewed by 2137
Abstract
Sylvester Matrix Equations (SME) play a central role in applied mathematics, particularly in systems and control theory. A fuzzy theory is normally applied to represent the uncertainty of real problems where the classical SME is extended to Fully Fuzzy Sylvester Matrix Equation (FFSME). [...] Read more.
Sylvester Matrix Equations (SME) play a central role in applied mathematics, particularly in systems and control theory. A fuzzy theory is normally applied to represent the uncertainty of real problems where the classical SME is extended to Fully Fuzzy Sylvester Matrix Equation (FFSME). The existing analytical methods for solving FFSME are based on Vec-operator and Kronecker product. Nevertheless, these methods are only applicable for nonnegative fuzzy numbers, which limits the applications of the existing methods. Thus, this paper proposes a new numerical method for solving arbitrary Trapezoidal FFSME (TrFFSME), which includes near-zero trapezoidal fuzzy numbers to overcome this limitation. The TrFFSME is converted to a system of non-linear equations based on newly developed arithmetic fuzzy multiplication operations. Then the non-linear system is solved using a newly developed two-stage algorithm. In the first stage algorithm, initial values are determined. Subsequently, the second stage algorithm obtains all possible finite fuzzy solutions. A numerical example is solved to illustrate the proposed method. Besides, this proposed method can solve other forms of fuzzy matrix equations and produces finite fuzzy and non-fuzzy solutions compared to the existing methods. Full article
(This article belongs to the Special Issue Fuzzy Set Theory and Uncertainty Theory)
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