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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.

Comparison and data analysis with the similarity measures and entropy for fuzzy sets were carried out. The distance proportional value between the fuzzy set and the corresponding crisp set was considered by the fuzzy entropy. The relation between the similarity measure and the entropy for fuzzy set was also analyzed. The fuzzy entropy was reformulated as the dissimilarity measure. Furthermore, crisp set having the minimum uncertainty with respect to the corresponding fuzzy set was also proposed. Finally, derivation of a similarity measure from entropy with the help of total information property was derived. A simple example shows the relation between similarity measure and fuzzy entropy, in which the summation of similarity measure and fuzzy entropy represents a constant value.

An advanced fuzzy C-mean (FCM) algorithm was proposed for the efficient regional clustering of multi-nodes interconnected systems. Due to various locational prices and regional coherencies for each node and point, modified similarity measure was considered to gather nodes having similar characteristics. The similarity measure was needed to contain locational prices as well as regional coherency. In order to consider the two properties simultaneously, distance measure of fuzzy C-mean algorithm had to be modified. Regional clustering algorithm for interconnected power systems was designed based on the modified fuzzy C-mean algorithm. The proposed algorithm produces proper classification for the interconnected power system and the results are demonstrated in the example of IEEE 39-bus interconnected electricity system.