Abstract
We demonstrate rough set based attribute reduction is a sub-problem of propositional satisfiability problem. Since satisfiability problem is classical and sophisticated, it is a smart idea to find solutions of attribute reduction by methods of satisfiability. By extension rule, a method of satisfiability, the distribution of solutions with different numbers of attributes is obtained without finding all attribute reduction. The relation between attribute reduction and missing is also analyzed from computational cost and amount of solutions.
Highlights
The size of dataset has been increasing dramatically, so it has been an important issue to reduce huge objects and large dimensionality
We demonstrate rough set based attribute reduction is a sub-problem of propositional satisfiability problem
A method of satisfiability, the distribution of solutions with different numbers of attributes is obtained without finding all attribute reduction
Summary
The size of dataset has been increasing dramatically, so it has been an important issue to reduce huge objects and large dimensionality. One is complete case analysis ignoring the samples with missing values [3]. The second approach, called imputation method, imputes the values of missing data by statistical methods or machine learning methods [4,5] This kind of approach leads to additional bias in multivariate analysis [6]. They all make assumption, so complete analysis of missing value is reduced. Rough set can hold complete analysis, since it considers missing value as “everything is possible” [8, 9].
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