Adapted a novel similarity and its application in fuzzy risk analysis

Generalized trapezoidal fuzzy numbers (GTFNs) and their similarity measures have been widely applied in fuzzy risk analysis. However, some existing similarity measures of GTFNs cannot identify the similarity of some special GTFNs properly. In this study, we introduce the exponential distance of center of gravity (COG) and an amending value to adapted a novel similarity measure between GTFNs. Then, seven properties of this new method are investigated and proved. In addition, in order to verify the superiority of the new method, fifteen special testing sets are given to compare the performance of seven existing similarity measures with the new method. Moreover, the presented new similarity measure is used to solve a case study about the failure risk analysis of six major subsystems of the reciprocating pump system (RPS) in which different parameters are expressed by generalized trapezoidal fuzzy linguistic term.

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