Fuzzy modelling using wavelet transforms
A new approach to fuzzy modelling using wavelet transforms is proposed. A fuzzy inference system with some minor restrictions and modifications can function as a discrete wavelet transform. The feasibility of the proposed fuzzy model is proved by modelling a highly nonlinear function and comparing it with previous research.
A weightedL2 norm is introduced in which Markov operators, e.g., associated with noisy maps, are contracting provided the kernel (i.e., the transitional distribution) is smooth enough. This results in strong relaxational properties of noisy maps. Similar to this norm, integral functionals appear useful when studying spatiotemporal chaos and random fields.