A new generation method of basic probability assignment based on the normal membership function

Dempster-Shafer evidence theory is an important technique to fuse uncertain information and make decisions. As the first step of applying the evidence theory in practical applications, the generation of basic probability assignment(BPA) directly affects the subsequent fusion and decision-making. However, it is still a difficult and open issue. This paper proposed a new method to generate BPA with the normal membership function. First, we construct a normal membership function for each class with its mean value and standard deviation of a certain attribute, whose function value represents the probability of a sample belonging to it. According to the rule of the intersection of fuzzy sets, the probability of a sample belonging to the proposition with multiple classes is the minimum function value of the normal membership functions for all relevant classes. Therefore, the BPA for the attribute can be obtained with the rule. Similarly, the BPAs for other attributes can also obtained with the same method. To make decision, the BPAs for all attributes will be combined into a fused BPA with the Dempster combination rule. The final classification result is the proposition with the largest value in it. Finally, we conduct the classification experiments on nine datasets from the UCI dataset and the result shows the superiority and robustness of the proposed method.