A Comparative Study of Compatibility and Transformation between Probability and Possibility

In this paper, an annotated survey of approaches to the transformation from a probability measure to a possibility measure or conversely is provided and noticeable properties of the transformations are described. The close relationship of possibility theory and probability theory on quantifying uncertainty is an interesting question which needs further theoretical research. Moreover, the transformations between them are vital for practical applications and attract more attention. The already- existing approaches considered less on discussions of the basis for such transformation. Hence, the compatibility of possibility and probability theory based on evidence theory is investigated first, and then detailed transformations are presented and their characteristics are proved to be a foundation of the transformations. From the systematic point of view, this paper also points out that information semantics inherent in possibility and probability measures may be an elementary factor worth considering. At last, application areas, technical difficulties and future work are stated.