Ranking invariance between fuzzy similarity measures applied to image retrieval

We first introduce the fuzzy similarity measures in the context of a CBIR system. This leads to the observation of an invariance in the ranking for different similarity measures. We then propose an explanation to this phenomenon, and a larger theory about order invariance for fuzzy similarity measures. We introduce a definition for equivalence classes based on order conservation between these measures. We then study the consequences of this theory on the evaluation of document retrieval by fuzzy similarity.