A Cramer Method for Solving Fully Fuzzy Linear Systems Based on Transmission Average

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.