Construction of fuzzy indices from fuzzy DI-subsethood measures: Application to the global comparison of images

Two measures are presented for comparing fuzzy sets. The method for constructing these measures is studied, starting from fuzzy DI-subsethood measures (see [H. Bustince, V. Mohedano, E. Barrenechea, M. Pagola, Definition and construction of fuzzy DI-subsethood measures, Information Sciences 176 (2006) 3190–3231]). We then analyze and compare the properties satisfied by the measures and those satisfied by other classical indices used in the literature on fuzzy sets. The minimal set of conditions are studied that, from our point of view, must be met by any given measure for comparing images. We also prove that only one of the measures identified fulfills such conditions. Finally, all the measures studied are applied to different images and the results are analyzed, indicating that measures constructed from fuzzy DI-subsethood measures provide the best results.