In this contribution there are considered interval-valued methods of improving the quality of classification by the k- N N binary classifiers in the case of large number of attributes in data sets. One of the possible applications of the introduced method are the microarray data so the presented results may be applied in medical diagnosis support, for example, in identification of marker genes. The proposed algorithm involving reduction methods of time complexity and interval modeling of data using interval-valued aggregation functions has a significantly higher classification quality than the other considered algorithm with the aggregation method involving the numerical arithmetic mean. The former algorithm is based on the interval-valued aggregation of uncertainty intervals determined on the basis of certainty coefficients of individual k- N N classifiers while the latter is based on the aggregation of certainty coefficients of individual k- N N classifiers with the use of the numerical arithmetic mean. Moreover, the performance of the new algorithm based on interval-valued methods was compared with the known from the literature classifiers in cancer diagnosis based on gene expression microarrays. The obtained results prove that in practical applications the newly proposed algorithm can be successfully used.

A new concept of equivalence between intervals and the induced indistinguishability between interval-valued (IV) fuzzy sets are proposed and considered. A new notion of the degree of IV equivalence is presented where partial or linear orders and the width of intervals are involved reflecting uncertainty. Furthermore, construction methods of the considered equivalences are provided and the relation between them and other notions of IV equivalences are studied. Finally, a methodology to apply the proposed equivalences in the field of image processing is shown, along with an illustrative example.