Gröbner Basis Approach for Solving Fuzzy Complex System of Linear Equations

Abstract

The foundation of Gröbner’s work is a potent approach for separating polynomial systems of equations. In this study, we solve complex fuzzy systems of linear equations utilizing Gröbner’s basic technique. First, a system of explicit polynomial equations is generated by applying fuzzy computations and fuzzy complex computations to the fundamental system. Taking into account the lexicographical order, Gröbner’s basis is then determined for the ideal given by a definite equivalent polynomial system. The Gröbnerbase that was obtained has a high triangular structure. Thus, the system solution may be readily implemented by proceeding. Hence, all of the system’s answers are readily attainable. Next, a criterion is established to identify whether or not a solution exists for the primary system. The advantage of the proposed approach is that it acquires all of the problem’s solutions simultaneously. Using this technique, a mathematical example and an application issue based on an electrical circuit are resolved. Comparing the generated findings to the known outcomes reveals a high level of congruence.