A Weighted Similarity Measure Between <i>Z</i>-Numbers and Bow-Tie Quantification

Abstract

In this article, we propose a new weighted Z-similarity measure between two Z-numbers, which is able to retain the original information provided by experts in linguistic terms. This measure takes care of the directional aspect of reliability of information by leveraging the Hausdorff distance. Probabilistic-approach-based statistical distance measure is used to characterize the internal relationship between two parts of a Z-number. Some properties of the Z-similarity measure are proved. The measure is capable of quantifying the probability of basic events in bow-tie analysis. It is experimentally shown that the Z-similarity measure is able to overcome the lacuna of the available techniques. Sensitivity analysis is done to verify its feasibility and applicability. We further propose another measure, called Z-similarity-based basic event contribution (Z-BEC), to quantify the contribution of basic events to the occurrence of different accidents. The performance of the Z-BEC measure is compared with that of Fussell-Vesely index and Birnbaum's structural index.