A new approach for the optimal fuzzy linear time invariant controlled system with fuzzy coefficients

•The fuzzy control system and the optimal control system with fuzzy coefficients are solved.•Using α-cuts and presentation of numbers in a more compact form, those systems are solved.•This approach is very simple.

In this article, a new technique for solving the linear time invariant dynamical system with fuzzy parameters is proposed. This approach is used to solve a fuzzy controlled system by using α-cuts and presentation of numbers in a more compact form by moving to the field of complex numbers. By considering a new feature of the Hamiltonian function and using the Pontryagin maximum principle, the solution of the fuzzy optimal controlled system is considered.