New PDF release: 10th GAMM - IMACS International Symposium on Scientific

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By Alt R., Vignes J.

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Peters, J. : Rough Sets and Current Trends in Computing, LNAI 2475, Springer Verlag, Berlin (2002). 2. : Extensions and Intensions in the Rough Set Theory. Information Sciences 107 (1998) 149–167 Generalizations of Rough Sets: From Crisp to Fuzzy Cases 37 3. : Rough Fuzzy Sets and Fuzzy Rough Sets. Int. J. General Syst. 17 (1990) 191–209. 4. : Putting Rough Sets and Fuzzy Sets Together. in: R. ) Intelligent Decision Support, Kluwer, Dordrecht (1992) 203– 232. 5. : Rough Sets and Gradual Decision Rules.

G1< = g4< = g5< = g6< = U , 2. g2< = g3< = g7< = U \ {x6 }, 3. g8< = {x1 , x2 , x3 , x7 , x8 }, providing a nested sequence of three distinct granules. 2 Extending Rough Inclusions to Granules We now extend µ over pairs of the form x, g, where x ∈ UIN D , g a granule. We define µ in this case as follows, µ(x, g, r)if and only if for some y ∈ UIN D , yelπ g and µ(x, y, r). , we admit that, xelπg if and only if for each element z of x, there exist elements w, t such that welπ z, welπ q, and g(q). By g(q) true, we mean that q has the property defining g.

G2< = g3< = g7< = U \ {x6 }, 3. g8< = {x1 , x2 , x3 , x7 , x8 }, providing a nested sequence of three distinct granules. 2 Extending Rough Inclusions to Granules We now extend µ over pairs of the form x, g, where x ∈ UIN D , g a granule. We define µ in this case as follows, µ(x, g, r)if and only if for some y ∈ UIN D , yelπ g and µ(x, y, r). , we admit that, xelπg if and only if for each element z of x, there exist elements w, t such that welπ z, welπ q, and g(q). By g(q) true, we mean that q has the property defining g.

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10th GAMM - IMACS International Symposium on Scientific Computing, Computer Arithmetic, and Validated Numerics by Alt R., Vignes J.


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