Smooth compositions are candidates for robust fuzzy systems

Abstract

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.