On the combination and normalization of interval-valued belief structures

This paper investigates the issues of combination and normalization of interval-valued belief structures within the framework of Dempster–Shafer theory (DST) of evidence. Existing approaches are reviewed, examined and critically analysed. They either ignore the normalization or separate it from the combination process, leading to irrational or suboptimal interval-valued belief structures. A new logically correct optimality approach is developed, where the combination and the normalization are optimised together rather than separately. Numerical examples are provided throughout the paper.