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Article

Title Fuzzy information on discrete and continuous domains: approximation results
Author Paulo J S G Ferreira, Manuel J. C. S. Reis
Journal International Journal of General Systems
Volume 33
Number 5
Pages 583-591
Month October
Year 2004
DOI [1]
Group
Group (before 2015) Signal Processing Laboratory
Indexed by ISI Yes

Abstract

Measures of information based on fuzzy sets have been defined for finite and for continuous universes. In the continuous case, the measure of information I(f) depends on the concept of sorting or nonincreasing rearrangement of f.

The paper studies the extent to which this measure of information can be approximated as a limit of discrete distributions with N distinct values, as N tends to infinity. It gives conditions under which there is convergence, and the order of approximation in terms of N and the Lipschitz exponent of the possibility function f.