Ordering of functions according to multiple fuzzy criteria: application to denoising electroencephalography

We introduce a new relation of order over functions according to multiple fuzzy criteria. Proof of the complied properties for relations of partial orders is given. Convergent and divergent validity of the new membership functions is established. Tolerance to noise of the relation of order is evaluated by corrupting synthetic prototypes and observing changes in the retrieved ordering. The effect of weighting strategies is evaluated in terms of Jaccard and XOR indices. The performance of the ordering algorithm is quantified in terms of richness of the resulting Hasse diagram. Applicability is demonstrated in the context of de-noising electroencephalographic (EEG) signals exemplified over two datasets and evaluated by classification wrapping.