Maximum entropy principle for uncertain sets with expectation and variance constraints

Up to now, the entropy of uncertain sets has found many applications in areas including uncertain finance, uncertain inference, and learning curves. Providing a maximum entropy principle for uncertain sets is helpful for selecting appropriate membership functions in these areas. This paper proposes the maximum entropy principle for uncertain sets and obtains the membership function which achieves the maximum entropy by using the Euler equation in the calculus of variations. Additionally, the entropy of some commonly used uncertain sets is computed in the manuscript.