Gröbner Basis Approach for Solving Fuzzy Complex System of Linear Equations
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Published:2023-07-29
Issue:
Volume:
Page:1-18
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ISSN:1793-0057
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Container-title:New Mathematics and Natural Computation
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language:en
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Short-container-title:New Math. and Nat. Computation
Author:
Farahmand Nejad Maryam1,
Farahani Hamed2,
Nuraei Rahele1,
Gilani Alireza1
Affiliation:
1. Department of Mathematics, South Tehran Branch, Islamic Azad University, Tehran, Iran
2. Department of Mathematics, Chabahar Maritime University, Chabahar, Iran
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.
Publisher
World Scientific Pub Co Pte Ltd
Subject
Applied Mathematics,Computational Theory and Mathematics,Computational Mathematics,Computer Science Applications,Human-Computer Interaction