Preprint Article Version 2 Preserved in Portico This version is not peer-reviewed

Two-stage Algorithm for Solving Arbitrary Trapezoidal Fully Fuzzy Sylvester Matrix Equations

Version 1 : Received: 8 December 2021 / Approved: 9 December 2021 / Online: 9 December 2021 (10:29:28 CET)
Version 2 : Received: 22 February 2022 / Approved: 23 February 2022 / Online: 23 February 2022 (12:17:04 CET)

A peer-reviewed article of this Preprint also exists.

Elsayed, A.A.A.; Saassouh, B.; Ahmad, N.; Malkawi, G. Two-Stage Algorithm for Solving Arbitrary Trapezoidal Fully Fuzzy Sylvester Matrix Equations. Symmetry 2022, 14, 446. Elsayed, A.A.A.; Saassouh, B.; Ahmad, N.; Malkawi, G. Two-Stage Algorithm for Solving Arbitrary Trapezoidal Fully Fuzzy Sylvester Matrix Equations. Symmetry 2022, 14, 446.

Journal reference: Symmetry 2022, 14, 446
DOI: 10.3390/sym14030446

Abstract

Many authors proposed analytical methods for solving fully fuzzy Sylvester matrix equation (FFSME) based on Vec-operator and Kronecker product. However, these methods are restricted to nonnegative fuzzy numbers and cannot be extended to FFSME with near-zero fuzzy numbers. The main intention of this paper is to develop a new numerical method for solving FFSME with near-zero trapezoidal fuzzy numbers that provides a wider scope of trapezoidal fully fuzzy Sylvester matrix equation (TrFFSME) in scientific applications. This numerical method can solve the trapezoidal fully fuzzy Sylvester matrix equation with arbitrary coefficients and find all possible finite arbitrary solutions for the system. In order to obtain all possible fuzzy solutions, the TrFFSME is transferred to a system of non-linear equations based on newly developed arithmetic fuzzy multiplication between trapezoidal fuzzy numbers. The fuzzy solutions to the TrFFSME are obtained by developing a new two-stage algorithm. To illustrate the proposed method numerical example is solved.

Keywords

Fully fuzzy Sylvester matrix equations; Fuzzy matrix equation; Numerical fuzzy solution; Trapezoidal fuzzy multiplication

Subject

MATHEMATICS & COMPUTER SCIENCE, Numerical Analysis & Optimization

Comments (1)

Comment 1
Received: 23 February 2022
Commenter: Ahmed Elsayed
Commenter's Conflict of Interests: Author
Comment: The corresponding author is now Dr Bassem Saassouh and the content has changed after reviewers' comments.
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