The Association between Non-Stationary and Interval Type-2 Fuzzy Sets: A Case Study

In this paper a notion termed nonstationary fuzzy sets is introduced and the concept of random perturbations that can be used for generating these nonstationary fuzzy sets is also presented. A case study was carried out to investigate the relationship between the performance of nonstationary fuzzy logic systems and interval type-2 fuzzy logic systems. It can be observed that in case of centre variation, the lower-upper boundaries of outputs predicted by nonstationary systems are slightly narrower than those from the corresponding interval type-2 systems. On the other hand, in case of width variation, the lower-upper boundaries of outputs predicted by nonstationary systems are slightly wider than those from the type-2 systems. Moreover, an interesting observation is that the secondary membership function of the type-2 sets corresponding to nonstationary fuzzy sets generated using normally distributed perturbations are nonuniform. In contrast to noninterval type-2 sets, this does not affect the inference process of the nonstationary sets. In this sense, the use of nonstationary fuzzy sets may enable approximations to be made of general type-2 fuzzy inferencing