On some bridges to complex evidence theory

Abstract

Complex evidence theory, an extension of Dempster–Shafer evidence theory, is a generalized evidence theory based on complex values, which has been widely used to solve decision making of uncertainty information. In order to make a step development based on previous researches, we set out to make a connection between CET and other uncertainty theories like possibility theory, modal logic, fuzzy set theory and probability theory. With a restricted condition of a special generalized consonant belief function, it is found that possibility and necessity measure can be regarded as generalized plausibility measure and belief measure in possibility theory, and the standard interpretation of fuzzy sets in complex evidence theory is obtained by summing up the experience of predecessors and modifying the upper bound of fuzzy sets in this paper. In addition, we established the relationship between generalized plausibility, belief function and modal logic, and elaborate how to explain the complex basic belief distribution with the general semantics of modern modal logic. Finally, the transformation algorithm between complex basic belief assignment and probability distribution is proposed by using the transformation of uncertainty invariance principle, and some properties of them are derived.