Fuzzy Information On Discrete And Continuous Domains: Approximation Results

Authors: Paulo J.S.G. Ferreira; Manuel J.C.S. Reis

Source: International Journal of General Systems, Volume 33, Number 5, October, 2004 , pp. 583-591(9)

Publisher: Taylor and Francis Ltd

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).

Keywords: Approximation; fuzzy information; measures of information; non-increasing rearrangement; sorting; uncertainty-based information

Document Type: Research article

DOI: http://dx.doi.org/10.1080/03081070410001685763

Publication date: 2004-10-01

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