Soft Mathematical Aggregation in Safety Assessment and Decision Analysis

摘要

This paper improves on some of the limitations of conventional safety assessment and decision analysis methods. It develops a top-down mathematical method for expressing imprecise individual metrics as possibilistic or fuzzy numbers and shows how they may be combined (aggregated) into an overall metric, also portraying the inherent uncertainty. Both positively contributing and negatively contributing factors are included. Metrics are weighted according to significance of the attribute and evaluated as to contribution toward the attribute. Aggregation is performed using exponential combination of the metrics, since the accumulating effect of such factors responds less and less to additional factors. This is termed "soft" mathematical aggregation. Dependence among the contributing factors is accounted for by incorporating subjective metrics on "overlap" of the factors and by correspondingly reducing the overall contribution of these combinations to the overall aggregation. Decisions corresponding to the meaningfulness of the results are facilitated in several ways. First, the results are compared to a soft threshold provided by a sigmoid function. Second, information is provided on input "Importance" and "Sensitivity," in order to know where to place emphasis on controls that may be necessary. Third, trends in inputs and outputs are tracked in order to add important information to the decision process. The methodology has been implemented in software.