This paper proposes the p-factor index for the comparison of the robustness of the fuzzy systems constructed by the different fuzzy t-norms and contrasts the robust performance of the so-called smooth t-norms with the standard product t-norm in the fuzzy systems. It is the author's conjecture that the improved robustness of the fuzzy systems with the smooth compositions rather than the standard product t-norm is something inherently different about the way that the smooth compositions handle the uncertainties. The comparison of the value of p-factor for the different compositions explains and justifies the previously published results and evidence on the robust performance of the smooth compositions in the theoretical and industrial applications. Hence, upon the p-factor analysis, we conclude that the smooth fuzzy systems are structurally robust to the uncertainties. We have clarified the proposed theories through the different simulations on two academic examples. More evidence and justifications on the robust performance of the smooth compositions are available in the literature.

本文提出了 p 因子指标来比较不同模糊 t 范数构建的模糊系统的鲁棒性，并将所谓平滑 t 范数与标准乘积 t 范数在模糊系统中的鲁棒性进行对比。系统。作者推测，平滑组合的模糊系统的鲁棒性比标准乘积 t 范数的改进鲁棒性与平滑组合处理不确定性的方式有本质的不同。不同组合物的 p 因子值的比较解释并证明了先前公布的结果和关于光滑组合物在理论和工业应用中的稳健性能的证据。因此，根据 p 因子分析，我们得出结论，平滑模糊系统在结构上对不确定性具有鲁棒性。我们通过对两个学术实例的不同模拟阐明了所提出的理论。文献中提供了关于光滑组合物的稳健性能的更多证据和理由。