Fully Fuzzy Linear System in Circuit Analysis with the Study of Weak Solution

Abstract

In this paper, a simpler method to solve a fully fuzzy linear system (FFLS) with unrestricted coefficient matrix is discussed. FFLS is applied in circuit analysis instead of crisp linear system to reflect the real life situation much better. Arithmetic operations of triangular fuzzy number (TFN) are justified by forming FFLS in an electrical circuit with fuzzy sources and fuzzy resistors and then the system was solved by the simpler method. Finally, the case of weak solution is overcome by proposing a new definition of TFN.

Keywords: Fuzzy number, Triangular fuzzy number, Fully fuzzy linear system, Circuit analysis, Weak solution