## Uncertainty-based and fuzzy information

As George J. Klir and Mark J. Wierman wrote in their
book *Uncertainty-based information: elements of generalized information
theory* (Physica-Verlag, Heidelberg, 1999):

"A host of problems regarding relative measures of nonspecificity for bodies of evidence defined on infinite universal sets remains unresolved at this time".

The work described in this section was partly motivated by this. Just as in the section on Sorting and the analog median filter, the concept of rearrangement or sorting plays a central role.

*International Journal of General Systems*, vol. 33, no. 5, pp. 583-591, Oct. 2004.

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*.

*Systematic Organisation of Information in Fuzzy Systems*, P. Melo-Pinto and H.-N. Teodorescu

*(Eds.)*. IOS Press, pp. 373-392, 2002.

Part of the material in this book chapter was presented at
the *NATO Advanced Research Workshop Systematic Organisation
of Information in Fuzzy Systems*, Oct. 2001.