Fatemeh Babakordi; Tofigh Allahviranloo
Abstract
Solving fuzzy linear systems has been widely studied during the last decades. However, there are still many challenges to solving fuzzy linear equations, as most of the studies have used the principle of extension, which suffers from shortcomings such as the lack ...
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Solving fuzzy linear systems has been widely studied during the last decades. However, there are still many challenges to solving fuzzy linear equations, as most of the studies have used the principle of extension, which suffers from shortcomings such as the lack of solution, achieving solutions under very strong conditions, large support of the obtained solutions, inaccurate or even incorrect solutions due to not utilizing all the available information, complicated process and high computational load. These problems motivated us to present a fuzzy Cramer method for solving fuzzy linear equations, which uses arithmetic operations based on the Transmission Average (TA). In this study, fully fuzzy linear systems in the form of $ \tilde{A}\tilde{X}=\tilde{B} $, and dual fuzzy linear systems in the form of $ \tilde{A}\tilde{X}+\tilde{B}=\tilde{C}\tilde{X}+\tilde{D} $ are solved using the proposed fuzzy Cramer method, and numerical examples are provided to confirm the effectiveness and applicability of the proposed method.
