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A generalized Borgonovo's importance measure for fuzzy input uncertainty

机译：模糊输入不确定性的广义Borgonovo重要性度量

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摘要

In this work, the way in which fuzzy uncertainty in a model's output is apportioned to fuzzy uncertainty in model inputs is studied through a sensitivity analysis. Here, an optimization technique is employed to obtain the membership functions of the fuzzy structural response, for which a global sensitivity indicator is introduced to measure the influence of fuzzy input uncertainty on fuzzy output uncertainty. The global sensitivity indicator is the important measure of the fuzzy input uncertainty, which extends Borgonovo's measure. In this study, the mathematical properties of the important measure of the fuzzy input uncertainty are discussed and proved. The results of numerical examples and engineering examples show that the proposed importance measure can effectively describe the effect of fuzzy input uncertainty on fuzzy structural response. When the sensitivity indicator is larger, the basic fuzzy-valued variable becomes more important. The sensitivity indicators of the fuzzy structural response can give an essential importance sequence of all the basic fuzzy-valued variables and identify key contributing fuzzy-valued variables. The sensitivity indicators can provide the availability guidance to reduce the number of basic variables and optimize the fuzzy response model.
机译：在这项工作中，通过敏感性分析研究了将模型输出中的模糊不确定性分配给模型输入中的模糊不确定性的方法。在这里，采用一种优化技术来获得模糊结构响应的隶属函数，为此引入了一个全局灵敏度指标来测量模糊输入不确定性对模糊输出不确定性的影响。全局灵敏度指标是模糊输入不确定性的重要度量，它扩展了Borgonovo的度量。在这项研究中，讨论并证明了模糊输入不确定性的重要度量的数学性质。数值算例和工程算例的结果表明，所提出的重要性测度可以有效地描述模糊输入不确定性对模糊结构响应的影响。当灵敏度指标较大时，基本模糊值变量将变得更加重要。模糊结构响应的灵敏度指标可以给出所有基本模糊值变量的重要重要性序列，并确定关键的贡献模糊值变量。灵敏度指标可以提供可用性指导，以减少基本变量的数量并优化模糊响应模型。

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