Solving Fully Fuzzy Linear System with the Necessary and Sufficient Condition to have a Positive Solution

Abstract: 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.