Bi-Conjugate Gradient Method for Solving Positive Triangular Fully Fuzzy Linear Systems

Abstract

Fuzzy linear systems play an important and efficient role across various domains such as mathematics, engineering, physics, chemistry, economics, statistics, and so on. Dealing with these kinds of systems in the real world is still very hard. This paper suggests a new way to solve fully fuzzy linear systems quickly using the Bi-conjugate gradient method . The method builds a one-block rate matrix and lets it skip fuzzy arithmetic operations. The focus is on systems in which both the coefficients and the variables are fuzzy, aiming to produce positive results even under highly uncertain conditions. The  algorithm is efficient in solving FFLS, requiring only a few iterations and converting the system into a crisp linear system first. To test the validity of the proposed method, we ran three numerical experiments, which confirmed its effectiveness and robustness. Unlike Jacobi or Gauss-Seidel, this proposed method has more efficient and quicker convergence. It is most applicable for FFLS when there are stringent demands on precision and system parameters are uncertain.