Uncertainty theory is mainly used to deal with indeterminacy problems based on belief degree. In order to solve the problem of the lack of testing process after fitting uncertain distributions in practical application

characteristic functions with uncertain distributions were studied and effectiveness-of-fit test method was proposed. Firstly

the characteristic function of uncertain distribution was defined

and its calculation formula was given based on the uncertain expectation value. On the basis of the formula

the characteristic functions of several typical uncertain distributions were derived. Secondly

the properties of the characteristic functions were analyzed

which laid foundation for subsequent demonstration of theories and calculation. Thirdly

according to the definition and properties of the characteristic functions

the definition of effectiveness of uncertainty distribution fitting and its judgment theorem were proposed based on the digital characteristics and shape of distribution function. Finally

two examples were given to verify the feasibility and effectiveness of the proposed method. Simulation results show that uncertainty theory and stochastic theory are different in product axiom

and it is difficult to extend the method of distribution fitting test in stochastic theory to the uncertainty theory. In addition

there is a one-to-one correspondence between the uncertainty characteristic function and the uncertainty distribution function

and the uncertainty characteristic function can be used as one of the approaches to study the uncertainty distribution fitting test.