Generalization of Dempster-Shafer theory: A complex belief function
  Dempster-Shafer evidence theory has been widely used in various fields of
applications, because of the flexibility and effectiveness in modeling
uncertainties without prior information. However, the existing evidence theory
is insufficient to consider the situations where it has no capability to
express the fluctuations of data at a given phase of time during their
execution, and the uncertainty and imprecision which are inevitably involved in
the data occur concurrently with changes to the phase or periodicity of the
data. In this paper, therefore, a generalized Dempster-Shafer evidence theory
is proposed. To be specific, a mass function in the generalized Dempster-Shafer
evidence theory is modeled by a complex number, called as a complex basic
belief assignment, which has more powerful ability to express uncertain
information. Based on that, a generalized Dempster's combination rule is
exploited. In contrast to the classical Dempster's combination rule, the
condition in terms of the conflict coefficient between the evidences K<1 is
released in the generalized Dempster's combination rule. Hence, it is more
general and applicable than the classical Dempster's combination rule. 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 under the condition that the conflict coefficient between the evidences
K is less than 1. In a word, this generalized Dempster-Shafer evidence theory
provides a promising way to model and handle more uncertain information.
