Fuzzy Information On Discrete And Continuous Domains: Approximation Results

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Abstract:

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  ( N ) approximating f . We consider the approximation problem in more detail, and study the convergence of I ( ( N ) ) to I ( f ) in terms of the smoothness properties of f itself (modulus of continuity and Lipschitz exponent).
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