Generalization of Dempster-Shafer theory: A complex belief function
This provides a more flexible framework for modeling uncertainties in fields like data fusion, but it is incremental as it builds directly on existing evidence theory.
The paper tackles the limitation of Dempster-Shafer theory in expressing data fluctuations and concurrent uncertainties by proposing a generalized version using complex numbers for belief assignments, which releases the conflict coefficient condition and generalizes the combination rule.
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.