A generalized topological view of motion in discrete space

New Approach to Covering Rough Sets via Relations

“…The present section is divided to subsections; the first section is devoted to introduce a new definition for the closure and interior operators using general binary relation depending on Galton definition, see [6]. Moreover, we are study the topological structures and the properties of the operators.…”

“…Definition 2.6. (see [6]) For an operator cl : P (U ) −→ P (U ), if it satisfies the following rules, then we call it a closure operator on U . For X, Y ⊆ U :…”

“…In this paper, we introduce new definition for the approximations based on general binary relation. In addition, we introduce a new closure operator based on Galton definition (see [6]), and give some topological properties of them. New closure operators derived from relation using relation coverings concepts are introduced and its properties are studied.…”

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.…”

Spatio-temporal reasoning by combined topological and directional relations information

“…In this paper only translation is considered and it is supposed that the entities (objects) don't change the topological configuration, i. e., object is not splits into multiple objects. Under these conditions, translated object is considered as the moving object and a discrete motion is considered [9]. Most of the reasoning process is based on the composition tables, entities in these tables are interrelated and abide by a certain mathematical formula.…”