Spectral FUllY Sets and Sof( Thresholding
Sankar Kumar Pal, Arish Dasgupta · 1992
A new concept of spectral fuzzy sets ha~ been introduce<.l for dealing with the uncertainty in ~ubjective assignment of membership value to the clements of a fuzzy ~et. The concept is characterized by a ~el of membership functions reflecting an individual's (or several individuals') opinion. The uncertainty due to spcclralness has becn explaine<.l. To <.Iemon stratc [he necessity and effectiveness of this concept, Lhe problem of image scgmcnlation is comidcrcd as an example. Here the uncertainty may arise from differences in opinion in sdcCI ig a threshol<.l from an ambiguous flat-valleyed histogram and in ~clecting i II-<.Ie uned \� regIon boundaries. It has been shown that the new concept can be considere<.l as a useful tool for the managcmel1l of such uncertainty since it allows the irnplcrnent<Jtion of soft deci~ions on the basis of various opinions on membership functions resulting in a ban<.l of thresholds with their respective uncertainties. A hard (crisp) decision obviously correspon<.ls to one with minimum uncertainty. Besides the intro<.luction of a new concept of specl ral fua.y set, the work abo shows a natural and appropriate way that the incertitude arising from settling a deunite <.Iegree of fuzziness (or from <.Ieuning a precise membership function) may still lead 10 son decisions when the image regions are ill-<.Ieuned.