A New Approach to the Rule-Base Evidential Reasoning with Application

In this paper, a new approach to the rule-base evidential reasoning (RBER) based on a new formulation of fuzzy rules is presented. We have shown that the traditional fuzzy logic rules lose an important information when dealing with the intersecting fuzzy classes, e.g., such as Low and Medium, and this property may lead to the controversial results. In the framework of our approach, an information of the values of all membership functions representing the intersecting (competing) fuzzy classes is preserved and used in the fuzzy logic rules. As RBER methods are based on the synthesis of fuzzy logic and the Dempster-Shafer theory of evidence (DST), the problem of the combination of basic probability assignments (bpas) from different sources of evidence arises. The classical Dempster’s rule of combination is usually used for this purpose. The classical Dempster’s rule may provide controversial results in the case of great conflict and is not idempotent one. We show that the Dempster’s rule may provide unreasonable results not only in the case of large conflict, but in the case of complete absence of conflict, too. At the end, we show that in the cases of small and large conflict, the use of simple averaging rule for combination of bpas seems to be a best choice. The developed approach is illustrated by the solution of simple, but real-world problem of diagnostics of type 2 diabetes.