On relationship between modified sets, topological spaces and rough sets

Applications of Some Topological Near Open Sets to Knowledge Discovery

“…We have proved that there exist similar properties and there exist different properties among the approximations raised from this paper and that studied from many authors [5,6,7,11,13,14,15,16,25,27,30]. We will investigate new applications of these tools using topological generalizations in a future paper.…”

“…An important field of this technology is the information discovery via available information. Rough set theory and their topological generalizations using some topological near open sets [1,2,4,5,7,12,13,15,17,18,19,20] are a recent, an accurate and applicable approach for reasoning about data. Many researchers generalized rough sets, but the concept of a topological rough set given by Wiweger [16] in 1989 is the basic starting point.…”

The Functorial Relations Between Alexandrov Fuzzy Topologies and Upper Approximation Operators

“…The relationship between rough set theory and topological spaces was investigated in sets [8]. Hájek [2] introduced a complete residuated lattice which is an algebraic structure for many valued logic.…”

Some Properties of Approximation Operators

“…Pawlak [9,10] introduced rough set theory as a formal tool to deal with imprecision and uncertainty in data analysis. By using the concepts of rough approximation operators, information systems and decision rules are investigated in complete residuated lattices [1,[3][4][5][6][7][8]11]. Zhang [12,13] introduced the fuzzy complete lattice which is defined by join and meet on fuzzy partially ordered sets.…”