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This paper proposes new matrix methods for solving positive solutions for a positive Fully Fuzzy Linear System (FFLS). All coefficients on the right hand side are collected in one block matrix, while the entries on the left hand side are collected in one vector. Therefore, the solution can be gained with a non-fuzzy common step. The necessary theorems are derived to obtain a necessary and sufficient condition in order to obtain the solution.The solution for FFLS is obtained where the entries of coefficients are unknown. The methods and results are also capable of solving Left-Right Fuzzy Linear System (LR-FLS). To best illustrate the proposed methods, numerical examples are solved and compared to the existing methods to show the efficiency of the proposed method. New numerical examples are presented to demonstrate the contributions in this paper.

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.

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