A Generalized Dempster--Shafer Evidence Theory

Dempster-Shafer evidence theory has been widely used in various fields of applications. Besides, it has been proven that the quantum theory has powerful capabilities of solving the decision making problems. However, due to the inconsistency of the expression, the classical Dempster-Shafer evidence theory modelled by real numbers can not be integrated directly with the quantum theory modelled by complex numbers. The main contribution in this study is that, unlike the existing evidence theory, a mass function in the generalized Dempster-Shafer evidence theory is modelled by a complex number, called as a complex mass function. When the complex mass function is degenerated from complex numbers to real numbers, the generalized Dempster's combination rule degenerates to the classical evidence theory. This generalized Dempster-Shafer evidence theory provides a promising way to model and handle more uncertain information. Numerical examples are illustrated to show the efficiency of the generalized Dempster-Shafer evidence theory.