Abstract

The problem of quantifying uncertainty has not been well solved. To measure the uncertainty of uncertain variables, we first propose the concept of arc entropy via uncertainty distributions and introduce a new effective method in this paper. Some properties of arc entropy are derived, and some practical examples of uncertain variables are given. A formula for arc entropy is derived via inverse uncertainty distributions, and several basic theorems are proposed. Moreover, two general arc entropies are defined, and their properties are investigated. An application to uncertain learning curves is introduced, and an uncertain learning curve model is proposed. Another application to portfolio selection is presented, and its mathematical model is established.