Sensitivity analysis through random and fuzzy sets

Abstract

Sensitivity analysis has become a major tool in the assessment of the reliability of engineering structures. Given an input-output system, the question is which input variables have the most decisive influence on the output. Random and/or fuzzy sets offer a framework for modelling the data variability. Propagating random set data or fuzzy set data through a deterministic system provides a valuable impression of the output variability. The sensitivity can be assessed by pinching individual variables, changing their correlations or by varying their degree of interactivity. An important ingredient in the quantification of the changes derives from generalized information theory, namely, measures of nonspecificity, in particular, Hartley-like measures. The purpose of this contribution is to present an investigation of various methods of modelling correlations and interactivity, quantifying the results by Hartley-like measures and exhibiting a number of concrete applications in engineering.