A Note on the New Similarity Measure for Fuzzy sets

Abstract

In this article, we intend to draw attention on the new Similarity measure for Fuzzy sets based on the extended definition of complementation. The old existing measures are based on traditional Zadehian Theory of Fuzzy sets where it is believed that there is no difference between Fuzzy membership function and Fuzzy membership value for the complement of a Fuzzy set which is already proved to be wrong. As a result, the previous Similarity measures have been proved illogical from the standpoints of new defi nition of complementation of Fuzzy set based on the fact that Fuzzy membership function and Fuzzy membership value for the complement of a Fuzzy set are two different things. Accordingly, we have already established a new Similarity measure with the help of exte nded definition of complementation using reference function. In this paper, an effort has been put forward to show the validity of the results obtained from our proposed measure with the help of traditional Hamming distance and Euclidean distance measures.