Fatemeh Babakordi - Department of Mathematics and Statistics‎, ‎Gonbad Kavous University‎, ‎Gonbad Kavous‎, ‎Iran.
Tofigh Allahviranloo - Faculty of Humanities and Social Sciences‎, ‎Istinye University‎, ‎Istanbul‎, ‎Turkey‎.

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.

Transmission average‎, ‎Fuzzy arithmetic‎, ‎Fuzzy approximation‎, ‎Fuzzy Cramer method