Recognition Dilemma for Similarity Measure Based on the Radius of Gyration

We use an analytical algorithm to show that the similarity measure based on the radius of gyration, still suffers from unresolved pattern recognition dilemmas. We improve the results of the radius of gyration with the y axis to prove that it is independent of the height of the trapezoidal fuzzy number, which is the key factor to constructing our counterexample. We also show that a previously developed counterexample contained questionable results. Our findings demonstrate that relying on only a few similarity measures is not sufficient to fully resolve pattern recognition dilemmas. Hence, we suggest that researchers who refer to those papers that constructed iterative algorithms with several similarity measures and repeatedly applied those measures to look for a complete solution algorithm.