Topological solution of missing attribute values problem in incomplete information tables

New Topological Approaches for Data Granulation

“…Objects of definite universe are compared by considering their descriptions. The recent generalization of rough set theory has led to the introduction of topological rough set approaches [24][25][26]35] and a consideration of the affinities (topological nearness) of objects.…”

“…To study this matter, several interesting and having an important effect generalization to equivalence relation have been proposed in the past, such as tolerance relations, similarity relations [51], topological bases and subbases [1,2,6,22,23,[27][28][29] and others [3,4,16,20,25,26,33]. Particularly, some researchers have used coverings of the universe of discourse for establishing the generalized rough sets by coverings [11,15].…”

Applications of Some Topological Near Open Sets to Knowledge Discovery

“…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.…”

Generalization of Pawlak’s rough approximation spaces by using δβ-open sets

“…It has been successfully applied such artificial intelligence fields as machine learning, pattern recognition, decision analysis, cognitive sciences, intelligent decision making and process control [6,[13][14][15]19,32,41,44]. Some of rough set applications are to approximate an arbitrary a universe by two definable subsets called lower and upper approximations, and to reduce the number of the set of attributes in data sets.…”

“…[16]). So many generalizations of Pawlak's model were proposed [1,29,[31][32][33][34]42,43,48]. Some researchers introduced approaches to relax the partition to a cover [18,19,23,40,47].…”