Reasoning of fuzzy Causality Diagram with interval probability

Causality diagram is a probabilistic reasoning method. Fuzzy set theory was introduced to develop causality diagram methodology after discussing the development and the restriction of conventional causality diagram. The application of causality diagram is extended to fuzzy field by introducing fuzzy set theory. Fuzzy causality diagram can overcome the shortcomings that it is difficult to gain the accurate probability of the event in conventional causality diagram. Interval numbers can express all kinds of fuzzy number. So it is necessary to dicuss the reasoning of fuzzy causality diagram with interval probability. Based on the interval number, operator, fuzzy conditional probability and the normalization method were discussed in this paper. Then two reasoning algorithm of single-value fuzzy causality diagram is proposed, some remarks about these algorithms are given. The result of numerical simulating of a subsystem in nuclear plant is coincident with the fact, and it shows the normalizing method is effective. The research shows that Interval Fuzzy causality diagram is so effective in fault analysis, and it is more flexible and adaptive than conventional method.