Statistical results to show the superiority of type two fuzzy logic systems over type one counterparts under noisy conditions

In this paper, some statistical quantities of the distortion caused by noise in the rule base of type-2 fuzzy logic systems are calculated. In many papers, the justification of better performance of type-2 fuzzy logic systems over type-1 counterparts in noisy conditions are studied only for some specific cases. In this paper, a simple type-2 fuzzy logic system with the ellipsoidal membership function is considered. Using this fuzzy system, it is possible to statistically study the effect of noise in the rule base of fuzzy systems. Using this statistical analysis, it is shown that the type-2 fuzzy logic systems with ellipsoidal membership function is less influenced in the presence of high level of noise when compared to its type-1 counterparts.