Parallelotope-formed evidence theory model for quantifying uncertainties with correlation

Abstract Due to the flexibility of evidence framework, evidence theory is recognized as a more general uncertainty quantification tool. However, the traditional evidence theory model only can deal with the uncorrelated evidence variables, which restricted its applicability in practical engineering problems. In this paper, a concept of evidence correlation coefficient is firstly defined to characterize the correlation between evidence variables. In view of that, a new parallelotope-formed evidence theory model which consists of the parallelotope-formed frame of discernment and the parallelotope-formed joint focal elements with basic probability assignments is proposed for effectively quantifying the correlated and uncorrelated evidence variables. Because of the consistency of frame of discernment and joint focal elements, the parallelotope-formed evidence theory model can freely realize affine transformation from correlated evidence variables to uncorrelated evidence variables, and can deal with the correlated and uncorrelated evidence variables in unified framework. Therefore, for the structural uncertainty quantification based on the proposed parallelotope-formed evidence theory model, the calculation process can be implemented in the transformed uncorrelated evidence space, and then the belief and plausibility measures can be conveniently obtained. Finally, two numerical examples and one engineering application are utilized to demonstrate the validity of the proposed parallelotope-formed evidence theory model.