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**1 - 4**of**4**### Fuzzy Information on Discrete and Continuous Domains: Approximation Results

, 2004

"... 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 nonincreasing rearrangement of the function f . It has been observed that I(f) can be obtained as a limit ..."

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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 nonincreasing rearrangement of the function f . It has been observed that I(f) can be obtained as a limit of discrete distributions # approximating f .

### RESEARCH Open Access

"... A general solution to the continuous-time estimation problem under widely linear processing ..."

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A general solution to the continuous-time estimation problem under widely linear processing

### FUZZY INFORMATION ON DISCRETE AND CONTINUOUS DOMAINS: APPROXIMATION RESULTS

, 2004

"... 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 ..."

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

### Impulsive Noise, Fuzzy Uncertainty, and the Analog Median Filter

, 2002

"... Additive fuzzy systems combined with supervised or unsupervised learning have been proposed to deal with impulsive noise in discrete-time signals, but suffer from the curse of dimensionality. Faster methods, possibly based on new paradigms, would be welcome. Order statistics filters and their fuz ..."

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Additive fuzzy systems combined with supervised or unsupervised learning have been proposed to deal with impulsive noise in discrete-time signals, but suffer from the curse of dimensionality. Faster methods, possibly based on new paradigms, would be welcome. Order statistics filters and their fuzzy counterparts provide alternative and robust ways of dealing with discrete-time data, but the idea of ranking (or fuzzy ranking) does not appear at first sight to be meaningful in the continuous-time case. This chapter investigates to which extent the concept of "sorting" is meaningful for continuous-time signals. It presents a tutorial on the basic concepts behind sorting, and applies the results to the study of the single-input single-output analog median filter. Interestingly, the concept of sorting or rearrangement, which plays a fundamental role in the development, appears naturally when trying to define the uncertainty associated with a general set membership function.