Ambiguity to precision: fuzzy based matrix double splitting algorithm to linear circuit equations

Abstract Fuzzy linear systems have been extensively studied in the literature to model uncertainty, particularly when the right-hand side vector exhibits imprecision. However, many real-world problems involve uncertainty in both the coefficient matrix and the right-hand side vector, which requires further study to improve the solutions of fully fuzzy linear systems (FFLS). Such type of system incorporates fuzzy constraints to provide a robust framework for circuit analysis under uncertain parameters while enabling the propagation of uncertainties throughout the circuit. The present study proposes an algorithmic approach to solve FFLS, specifically focusing on fuzzy current flow in circuit analysis. Using the parametric form, the FFLS is transformed into a crisp system with a single uncertainty-controlling parameter. The resulting parametric system is analyzed using fuzzy double splitting technique, represented as A ( ϵ ) = P ( ϵ ) − R ( ϵ ) + S ( ϵ ), where P ( ϵ ) is a non-singular fuzzy matrix. Additionally, the system is further investigated through the fuzzy double alternating scheme (fuzzy-DAS), which is constructed from two fuzzy double splittings. The resulting fuzzy iterative schemes are implemented to analog circuit theory problem involving fuzzy current flow, to demonstrate its effectiveness. Finally, a comparative analysis is presented, illustrating that the fuzzy double alternating scheme achieves faster convergence in the sense of less iterations compared to standard iterative methods with minimal error and residual norm.