A new method for solving an arbitrary fully fuzzy linear system

Abstract

In this paper, We propose a simple and practical method (that works only for triangular fuzzy numbers) to solve an arbitrary fully fuzzy linear system (FFLS) in the form $$\widetilde{A}\otimes \widetilde{x}=\widetilde{b},$$ where $$\widetilde{A}_{n \times n}$$ is a fuzzy matrix, $$\widetilde{x}$$ and $$\widetilde{b}$$ are n × 1 fuzzy vectors. The idea of the presented method is constructed based on the extending 0-cut and 1-cut solution of original fully fuzzy linear systems (FFLS). We also define a fuzzy solution of FFLS and establish the necessary and sufficient conditions for the uniqueness of a fuzzy solution.