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A class of new fuzzy inference systems New-FISs is presented. Compared with the standard fuzzy system,New-FIS is still a universal approximator and has no fuzzy rule base and linearly parameter growth. Thus, it effectively overcomes the second curse of dimensionality: there is an exponential growth in the number of parameters of a fuzzy system as the number of input variables, resulting in surprisingly reduced computational complexity and being especially suitable for applications, where the complexity is of the first importance with respect to the approximation accuracy.