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Smarandache refined fuzzy sets to handle an object's sub-membership degrees. Applications for fuzzy convexity are numerous and include pattern recognition, optimization, and related issues. By taking into account a more precise definition of fuzzy sets, these applications can be handled more effectively. This paper uses theoretical and analytical techniques to construct the novel idea of convexity cum concavity on refined fuzzy sets. The convex (concave) fuzzy sets proposed by Zadeh [1], [2] and Chaudhuri [3], [4] are extended in this work. Some of its significant findings are also generalizable.
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