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Axiomatics for fuzzy rough sets
Authors:Nehad N Morsi and M M Yakout
Institution:

a Department of Mathematics, Military Technical College, Cairo, Egypt

b Department of Mathematics, Faculty of Education, Ain Shams University, Roxy, Cairo, Egypt

Abstract:A fuzzy T-rough set consists of a set X and a T-similarity relation R on X, where T is a lower semi-continuous triangular norm. We generalize the Farinas-Prade definition for the upper approximation operator Image of a fuzzy T-rough set (X, R); given originally for the special case T = Min, to the case of arbitrary T. We propose a new definition for the lower approximation operator Image of (X,R). Our definition satisfies the two important identities Image and Image , as well as a number of other interesting properties. We provide axiomatics to fully characterize those upper and lower approximations.
Keywords:Triangular norm  Similarity relation  Upper and lower approximations in fuzzy rough sets
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