Generalizing Dempster-Shafer evidence theory to fuzzy sets based on the distance measure

To make D-S evidence theory manage imprecise and fuzzy information effectively in evidential reasoning, a novel generalization method of evidence theory to fuzzy sets is proposed. In the method, it discards the max and min operators in previous generalization methods based on fuzzy inclusion measure, and the distance measure of fuzzy sets is introduced to calculate the contribution of one fuzzy focal element from the others. According to the contribution, the belief function, plausibility function and Dempster´s combination rule are extended to fuzzy sets. Finally, we make the comparisons of the proposed generalization method with some existing methods. Numerical results show that proposed method can catch more changing information in response to the change of a focal element than other methods. Our generalization method extends the application of D-S evidence theory.