On the combination and normalization of conflicting interval-valued belief structures

Dempster-Shafer theory (DST) or evidence theory has significant advantages in the fields of information aggregation and decision analysis. In this paper, in order to overcome the counter-intuitive behavior or specificity changes caused by evidence theory, the evidential reasoning (ER) rule which handles the weight and reliability of evidence in an appropriate way, is generalized to deal with the combination of conflicting interval-valued belief structures (IBSs). Specifically, an optimization model of pignistic probability distance is established from the global perspective to provide the relative weights for interval evidence so that the modified interval evidence can be reasonably combined, and then a modified interval evidence combination approach is proposed which is based on ER rule. The method can lead to a rational combination of conflicting interval evidence, which is also a development of Yang's ER rule. Numerical examples are provided to indicate that the proposed method is not only suitable for combining conflict-free interval evidence, but can also suitably combine conflicting interval evidence. At last, a case study is conducted on the actual pattern recognition problem to illustrate the applicability of the proposed method and the potential in dealing with the combination of conflicting interval evidence.