Similarity measure design and similarity computation for discrete fuzzy data

The similarity computations for fuzzy membership function pairs were carried out. Fuzzy number related knowledge was introduced, and conventional similarity was compared with distance based similarity measure. The usefulness of the proposed similarity measure was verified. The results show that the proposed similarity measure could be applied to ordinary fuzzy membership functions, though it was not easy to design. Through conventional results on the calculation of similarity for fuzzy membership pair, fuzzy membership-crisp pair and crisp-crisp pair were carried out. The proposed distance based similarity measure represented rational performance with the heuristic point of view. Furthermore, troublesome in fuzzy number based similarity measure for abnormal universe of discourse case was discussed. Finally, the similarity measure computation for various membership function pairs was discussed with other conventional results.