An Efficient Method to Reduce the Size of Consistent Decision Tables

Abstract

Finding reductions from decision tables is one of the main objectives in information processing. Many studies focus on attribute reduct that reduces the number of columns in the decision table. The problem of finding all attribute reducts of consistent decision table is exponential in the number of attributes. In this paper, we aim at finding solutions for the problem of decision table reduction in polynomial time. More specifically, we deal with both the object reduct problem and the attribute reduct problem in consistent decision tables. We proved theoretically that our proposed methods for the two problems run in polynomial time. The proposed methods can be combined to significantly reduce the size of a consistent decision table both horizontally and vertically.

Some NP-Complete Problems for Attribute Reduction in Consistent Decision Tables

“…As proved in [5], the number of steps computing E r is bounded from above by |U | 2 . The number of steps computing…”

“…In [5], we propose an algorithm for nding a reduct from a consistent decision table. The statement of algorithm is given in Algorithm 2.…”

“…Algorithm 2: Finding a reduct over consistent decision table [5] Input: DS = U, C ∪ {d}, V, f , where…”

On the Problem Related to Reductive Attributes in the Incomplete Decision Tables

“…In consistent complete decision tables, many scientist proposed new methods related to the properties of reduct and inferring knowledge by relational database theory approach in recent years [2][3][4][5][6][7][8][9]. In paper [2], authors proved that the time complexly of calculating all reducts is exponentials in the number of conditional attributes.…”

“…A polynomial algorithm was introduced in order to construct a novel reduction decision table from an already build decision table and also presented another new method to extract entire the functional dependencies from the consistent decision table. Authors in paper [7] proposed some algorithms to decrease the quantity of objects in consistent complete decision tables by discovering some features of reduct and reductive attributes in regard to relational database theory approach. The proposed algorithms can be effectively applied in the data preprocessing phase to improve data mining efficient and machine learning models.…”