On the solution of fully fuzzy Sylvester matrix equation with trapezoidal fuzzy numbers

Sylvester matrix equations play a prominent role in various areas such as control theory, medical imaging acquisition systems, model reduction, and stochastic control. Considering any uncertainty problems such as conflicting requirements during system process, instability of environmental conditions, distraction of any elements and noise, all for which the classical matrix equation is sometimes ill-equipped, fuzzy numbers represent the most effective tool that can be used to model matrix equations in the form of fuzzy equations. In most of the previous literature, the solutions of fuzzy systems are only presented with triangular fuzzy numbers. In this paper, we discuss fully fuzzy Sylvester matrix equation with positive and negative trapezoidal fuzzy numbers. An analytical approach for solving a fully fuzzy Sylvester matrix equation is proposed by transforming the fully fuzzy matrix equation into a system of four crisp Sylvester linear matrix equation. In obtaining the solution the Kronecker product and Vec-operator are used. Numerical examples are solved to illustrate the proposed method.