Fuzzy Information On Discrete And Continuous Domains: Approximation Results

Measures of information based on fuzzy sets have been defined both for finite and for continuous universes. In the continuous case, the measure of information I(f) depends on the concept of non-increasing rearrangement of the function f. It has been observed that I(f) can be obtained as a limit of discrete distributions π^(N) approximating f. We consider the approximation problem in more detail, and study the convergence of I(π^(N)) to I(f) in terms of the smoothness properties of f itself (modulus of continuity and Lipschitz exponent).