Probability measures compatible with the fuzzy Dempster-Shafer belief structure

In this paper, we show that the belief and plausibility measures defined on finite level fuzzy subset space are the lower and upper probabilities, respectively, of probability measures compatible with the fuzzy Dempster-Shafer (D-S) belief structure. We first introduce a probability measure which is additive on finite-level fuzzy sets space and show that the belief and plausibility measures determined by the fuzzy D-S belief structure are upper-additive and sub-additive, respectively. And then we discuss an objective function whose solutions correspond to a class of probability measures compatible with the fuzzy D-S belief structure. Lastly, a specific probability measure compatible with the fuzzy D-S belief structure is presented.