Extended rough set model based on improved complete tolerance relation

Variable Threshold Valued Tolerance Relation in Incomplete Information System

“…Therefore, in recent years, many scholars and experts focus on how to manage incomplete information. To find out the solution, they have presented several extended rough set model [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15]. However, they all have merits and faults.…”

“…(1) The classical tolerance relation has its own limitations [2] . By an example, the object are divided into the tolerance class, but actually there are no equal certain attribute value between the two objects.…”

“…The definition of non-symmetric similarity relation is defined as [3] ))} ( ) ( (2) According to the definition of non-symmetric similarity relation, the object X= (0, *, 1, 6, 9, 8, 12, 3) and the object Y= (*, 0, 1, 6, 9, 8, 12, 3) can be distinguished, so they are not satisfied with the similar relation. In fact, object X has six attributes equaled with object Y among its all eight attributes.…”

“…MA Xi-ao also analyses some limitations of completeness tolerance relation [2] . For example, two objects which are satisfied with the completeness tolerance relation's definition with the condition:…”