Interval-Valued Restricted Equivalence Functions Applied on Clustering Techniques

In this work we use interval-valued fuzzy sets in the Fuzzy C-Means algorithm for image segmentation. We introduce interval-valued restricted equivalence functions as a way of measuring the equivalence between the intervals associated to different pixels. We propose two construction methods for those new functions. We also prove experimentally that with these new concepts, the algorithm provides better results in ultrasound image segmentation that than those not using intervals. Keywords— Decomposability, Fuzzy C-Means, Interval-Valued Fuzzy Sets, Restricted Equivalence Functions, Ultrasound image.