TY  - CHAP
A1  - Abu Abed, Wassim
A1  - Milbradt, Peter
ED  - Gürlebeck, Klaus
ED  - Könke, Carsten
T1  - UNDERSTANDING THE ASPECT OF FUZZINESS IN INTERPOLATION METHODS
N2  - Fuzzy functions are suitable to deal with uncertainties and fuzziness in a closed form maintaining the informational content. This paper tries to understand, elaborate, and explain the problem of interpolating crisp and fuzzy data using continuous fuzzy valued functions. Two main issues are addressed here. The first covers how the fuzziness, induced by the reduction and deficit of information i.e. the discontinuity of the interpolated points, can be evaluated considering the used interpolation method and the density of the data. The second issue deals with the need to differentiate between impreciseness and hence fuzziness only in the interpolated quantity, impreciseness only in the location of the interpolated points and impreciseness in both the quantity and the location. In this paper, a brief background of the concept of fuzzy numbers and of fuzzy functions is presented. The numerical side of computing with fuzzy numbers is concisely demonstrated. The problem of fuzzy polynomial interpolation, the interpolation on meshes and mesh free fuzzy interpolation is investigated. The integration of the previously noted uncertainty into a coherent fuzzy valued function is discussed. Several sets of artificial and original measured data are used to examine the mentioned fuzzy interpolations.
KW  - Angewandte Informatik
KW  - Angewandte Mathematik
KW  - Architektur <Informatik>
KW  - Computerunterstütztes Verfahren
KW  - Computer Science Models in Engineering; Multiscale and Multiphysical Models; Scientific Computing
Y1  - 2010
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:gbv:wim2-20170314-28726
UR  - http://euklid.bauing.uni-weimar.de/ikm2009/paper.html
SN  - 1611-4086
ER  -