L-R representation of TA fuzzy arithmetic and its application to solving fuzzy equations

Fuzzy arithmetic with standard methods such as the extension principle and$alpha $-cut lead to restricted possibilities for solving fuzzy equations.The procedures to find a solution to a fuzzy equality with these methodsrequire strong assumptions and high computation costs. Among severalapproaches dealing with this restrictions this paper focuses on theTransmission Average (TA) fuzzy arithmetic. The shape preservation ofthe TA arithmetic operations on L-R fuzzy numbers is proven. Theseproperties together with some other algebraic properties investigatedin the paper are applied to solve fuzzy polynomial equations as well as systems of linear fuzzy equations in general form. Several examples in the paper present the advantages of TA arithmetic in solving fuzzy equations.  It is shown that the results in this paper support the fact that TA arithmetic is an easy to implement approach in fuzzy modeling.