Axiomatics for fuzzy rough sets

✍ Scribed by Nehad N. Morsi; M.M. Yakout

• Publisher: Elsevier Science
• Year: 1998
• Tongue: English
• Weight: 580 KB
• Volume: 100
• Category: Article
• ISSN: 0165-0114
• DOI: 10.1016/s0165-0114(97)00104-8

✦ Synopsis

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 A: I x --+ IX 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 A_:lX ~ I x of (X, R). Our definition satisfies the two important identities AA = A and A/I = A, as well as a number of other interesting properties. We provide axiomatics to fully characterize those upper and lower approximations. ~