Restricted Similarity Functions, Distances and Entropies with Intervals Using Total Orders

The paper deals with theoretical investigation targeting in practical utilization in image processing. First the interval valued restricted equivalence functions together with interval valued dissimilarity functions with respect to total order are introduced. The novelty of the approach lays in the using of total orders of intervals and the fact that the outputs of the functions are intervals and not numbers as in previous works. Then both interval valued restricted equivalence functions and interval valued dissimilarity functions are aggregated and similarity measures, distance measures and entropies for interval-valued fuzzy sets are yielded, with respect to total order as well. The investigation is a continuation of previous works of the authors aiming in improvement of existing tools in image processing.