The Development of the Generalization Algorithm Based on the Rough Set Theory

This paper considers the problem of concept generalization in decision-making systems where such features of real-world databases as large size, incompleteness and inconsistence of the stored information are taken into account. The methods of the rough set theory (like lower and upper approximations, positive regions and reducts) are used for the solving of this problem. The new discretization algorithm of the continuous attributes is proposed. It essentially increases an overall performance of generalization algorithms and can be applied to processing of real value attributes in large data tables. Also the search algorithm of the significant attributes combined with a stage of discretization is developed. It allows avoiding splitting of continuous domains of insignificant attributes into intervals.

A Distance-Based Method for Attribute Reduction in Incomplete Decision Systems

There are limitations in recent research undertaken on attribute reduction in incomplete decision systems. In this paper, we propose a distance-based method for attribute reduction in an incomplete decision system. In addition, we prove theoretically that our method is more effective than some other methods.

Generalized Discernibility Function Based Attribute Reduction in Incomplete Decision Systems

A rough set approach for attribute reduction is an important research subject in data mining and machine learning. However, most attribute reduction methods are performed on a complete decision system table. In this paper, we propose methods for attribute reduction in static incomplete decision systems and dynamic incomplete decision systems with dynamically-increasing and decreasing conditional attributes. Our methods use generalized discernibility matrix and function in tolerance-based rough sets.

On the Time Complexity of the Problem Related to Reducts of Consistent Decision Tables

In recent years, rough set approach computing issues concerning reducts of decision tables have attracted the attention of many researchers. In this paper, we present the time complexity of an algorithm computing reducts of decision tables by relational database approach. Let DS = (U, C ∪ {d}) be a consistent decision table, we say that A ⊆ C is a relative reduct of DS if A contains a reduct of DS. Let s = be a relation schema on the attribute set C ∪ {d}, we say that A ⊆ C is a relative minimal set of the attribute d if A contains a minimal set of d. Let Qd be the family of all relative reducts of DS, and Pd be the family of all relative minimal sets of the attribute d on s. We prove that the problem whether Qd ⊆ Pd is co-NP-complete. However, the problem whether Pd ⊆ Qd is in P .