Generalized Belief Function: A new concept for uncertainty modelling and processing
This provides a new mathematical framework for uncertainty processing, potentially benefiting fields like AI and decision-making, but it appears incremental as it builds directly on existing theory.
The paper tackles the problem of uncertainty modeling by generalizing belief functions to the complex plane, introducing a complex basic belief assignment that extends traditional Dempster-Shafer theory and degenerates to it when restricted to real numbers.
In this paper, we generalize the belief function on complex plane from another point of view. We first propose a new concept of complex mass function based on the complex number, called complex basic belief assignment, which is a generalization of the traditional mass function in Dempster-Shafer evidence theory. On the basis of the de nition of complex mass function, the belief function and plausibility function are generalized. In particular, when the complex mass function is degenerated from complex numbers to real numbers, the generalized belief and plausibility functions degenerate into the traditional belief and plausibility functions in DSE theory, respectively.