A Normalization Method of Interval-valued Belief Structures

Within the framework of Dempster-Shafer (D-S) theory of evidence, interval-valued belief structures (interval basic probability assignments, IBPAs for short), which can be used for combination, must be valid and normalized. In this paper, such IBPA is referred to as "standard IBPA". Because of the uncertainties of information collected by sensors and knowledge provided by experts, generally, the obtained original IBPAs are merely valid, but most of them are not normalized. The existing normalization approaches shorten width of probability mass interval so that the generated standard IBPA meets the requirements of interval evidence combination rule. However, the shortening process often leads to the loss of available information contained in original IBPA, so combination results may be irrational or suboptimal. This paper presents a new approach to realize global normalization and defines a similarity measure between original IBPA and its standard IBPA to measure information loss. Compared with the standard IBPA given by the existing classical approach, the standard IBPA obtained by the proposed approach is more similar to the corresponding original IBPA, so has more information for combination. Numerical examples are provided to prove the effectiveness of the proposed method.