Information Granule Based Uncertainty Measure of Fuzzy Evidential Distribution

Quantifying the uncertainty of information distributions containing randomness, imprecision, and fuzziness is the premise of processing them. A useful information representation in the field of intelligent computing are information granules, which optimize data from the perspective of specificity and coverage. We introduce information granularity into evidential information and model the basic probability assignment (BPA) as a weighted information granules model. Based on the proposed model, a new uncertainty measure of BPA is derived from the quality evaluation of granules. In addition, the proposed measure is extended to fuzzy evidential information distributions. When the Fuzzy BPA (FBPA) degenerates into the Probability Mass Function (ProbMF) and Possibility Mass Function (PossMF), the proposed method degenerates to Gini entropy and Yager's specificity measure, respectively. We use a refined belief structure to interpret the meaning of FBPA in the transfer belief model, and verify the validity of the proposed method by analyzing its properties and presenting numerical examples. The concept of information granule is used for the first time to model focal set and beliefs. Compared with Shannon entropy based information measures, the proposed method provides a novel perspective on the relationship between randomness, imprecision, and fuzziness in FBPA.