TELKOMNIKA Telecommunication, Computing, Electronics and Control
A modification of fuzzy arithmetic operators for solving near-zero fully fuzzy matrix equation

TELKOMNIKA Telecommunication, Computing, Electronics and Control
A modification of fuzzy arithmetic operators for solving near-zero fully fuzzy matrix equation

Control system engineering
Fully fuzzy matrix equation
Fully fuzzy linear system
Fuzzy arithmetic operators
Near-zero fuzzy numbers

Matrix equations have its own important in the field of control system engineering
particularly in the stability analysis of linear control systems and the reduction of
nonlinear control system models. There are certain conditions where the classical
matrix equation are not well equipped to handle the uncertainty problems such as
during the process of stability analysis and reduction in control system engineering.
In this study, an algorithm is developed for solving fully fuzzy matrix equation
particularly for A ̃X ̃B ̃−X ̃ = C ̃, where the coefficients of the equation are in near-zero
fuzzy numbers. By modifying the existing fuzzy multiplication arithmetic operators,
the proposed algorithm exceeds the positive restriction to allow the near-zero fuzzy
numbers as the coefficients. Besides that, a new fuzzy subtraction arithmetic operator
has also been proposed as the existing operator failed to satisfy the both sides of
the near-zero fully fuzzy matrix equation. Subsequently, Kronecker product and
V ec-operator are adapted with the modified fuzzy arithmetic operator in order to
transform the fully fuzzy matrix equation to a fully fuzzy linear system. On top of that,
a new associated linear system is developed to obtain the final solution. A numerical
example and the verification of the solution are presented to demonstrate the proposed
algorithm.

W. S. W. Daud, N. Ahmad, G. Malkawi

http://journal.uad.ac.id/index.php/TELKOMNIKA

Sep 16, 2020

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