Binary encoding of discernibility patterns to find minimal coverings
Rough set based methods have been applied successfully in many real world applications such as data mining, knowledge discovery, machine learning, and control. The rough set theory is used to deal with imperfect data and to eliminate dispensable, superfluous and redundant information as to obtain a simplified set of decision rules. Thus, several approaches and methods have been proposed to find minimal coverings, from which the decision rules can be induced. In many of these approaches, an improvement in the utilization of computational resources is encouraged. In this paper, a binary encoding for attribute sets and a discernibility matrix is proposed. Such a binary representation of sets and sets operations in the implementation of algorithms provides a machine-oriented approach to the utilization of computational memory and allow parallel processing among groups of attributes. The discernibility matrix is reduced to its minimal size through the identification of main patterns in order to eliminate redundancies. Bit-wise operations replace sets operations, thus the search for minimal coverings is performed in an efficient way. Resulting improvement is shown in the analysis of medium-sized data sets using two generic methods to obtain minimal coverings.
discernibility patterns minimal coverings rough set uncertainty