Fuzzy Probability for System Reliability

Fuzzy fault trees provide a powerful and computationally efficient technique for developing fuzzy probabilities based on independent inputs. The probability of any event that can be described in terms of a sequence of independent unions, intersections, and complements may be calculated by a fuzzy fault tree. Unfortunately, fuzzy fault trees do not provide a complete theory: many events of substantial practical interest cannot be described only by independent operations. In this paper, we introduce a new extension of crisp probability theory. Our model is based on n independent inputs, each with a fuzzy probability. The elements of our sample space describe exactly which of the n input events did and did not occur. Our extension is complete, since a fuzzy probability is assigned to every subset of the sample space. Our extension is also consistent with all calculations that can be arranged as a fault tree