A New Similarity Measure for Fuzzy Sets with the Extended Definition of Complementation
Pranamika Kakati, Department of Computer Application, Girijananda Chowdhury Institute of Management &Technology, Guwahati, Assam, India.
Manuscript received on August 06, 2013. | Revised Manuscript received on August 27, 2013. | Manuscript published on September 05, 2013. | PP: 203-207 | Volume-3, Issue-4, September 2013. | Retrieval Number: D1829093413/2013©BEIESP
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© The Authors. Published By: Blue Eyes Intelligence Engineering and Sciences Publication (BEIESP). This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/)
Abstract: Similarity measure for Fuzzy sets is one of the researched topics of Fuzzy set theory. Till now there have been several methods to measure similarity between two Fuzzy sets. The existing methods 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. In this article, effort has been made to put forward a new similarity measure with the help of extended definition of complementation of Fuzzy sets using reference function. Our proposed method is based on the fact that Fuzzy membership function and Fuzzy membership value for the complement of a Fuzzy set are two different things. With this new approach an attempt has been made to design a new Similarity measure for Fuzzy sets so that it becomes free from any further controversy.
Keywords: Complement of a Fuzzy set, Fuzzy membership function, Fuzzy membership value, Fuzzy reference function, Fuzzy set, Similarity measure.