Grouping problem with similarities between DNA sequences are studied. The similaritymeasure and the distance measure showed the complementary characteristics. Distance measure can be obtained by complementing similarity measure, and vice versa. Similarity measure is derived and proved. Usefulness of the proposed similarity measure is applied to grouping problem of 25 cockroach DNA sequences. By calculation of DNA similarity, 25 cockroaches are clustered by four groups, and the results are

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... ed with the previous neighbor-joining method. • similarity measure respectively. In the above, 1 means the sum of similarity and dissimilarity. In the previous literatures, fuzzy entropy of a fuzzy set represents a measure of fuzziness of the fuzzy set[3-10]. Furthermore, well-defined distance measure represents the fuzzy entropy. By the summing relation, we can notice that the similarity measure can be constructed through distance measure or fuzzy entropy function. Well known-Hamming distance is usually used to construct fuzzy entropy,so we compose the fuzzy entropy function through Hamming distance measure. Using the relation of distance measure and similarity measure, we construct the similarity measure with fuzzy entropy, and similarity measure is also constructed through distance measure. In the next section, the axiomatic definitions of entropy, distance measure and similarity measure of fuzzy sets are 한국융합학회논문지 제4권 제3호