A Novel Approach to Compute Lower and Upper Approximations of Dominance Based Rough Set Theory

Abstract

In the age of technology, terabytes of data are generated each day. Such huge flow of data can bring many benefits to the business organizations, but it also poses various challenges due to large volume, velocity, variety, variability, and complexity. These properties of large datasets making it difficult to perform effective analysis using the traditional techniques. For effective decision making and accurate results, it is important to analyze data deeply. Rough set theory (RST) is one of the prominent mathematical-based techniques that analyses huge datasets. It is the best technique to deal with uncertain, vague, and incomplete data. Moreover, RST does not require any additional information to analyze data like probability distribution require for Bayesian Decision Theory. However, in a case where values of attributes maintain preference order over each other, RST does not consider it. Dominance-based Rough Set Approach (DRSA), a generalization of RST, studies the dominance aspect of attributes and define the dominance relation. DRSA is an excellent data analysis tool for multicriteria decision-making, considering preference order of attributes. To efficiently handle large volume datasets, data mining tools need to be computational efficient. In DRSA, data analysis mainly depends on the calculations of lower and upper approximations and computation of these two measures are utilizing many resources i.e., time and memory, due to the consideration of preference order. In this research, it is proposed a new concept of heuristic rules, to compute lower and upper approximations without calculating dominance positive/negative relations. By using the properties and logical structure of approximations, our mathematical implications select an object for all relevant approximation sets instantaneously and similarly select remaining objects without even considering the intersection and subset relations. By avoiding the heavy and redundant computations, the proposed rules can be an efficient replacement for the conventional method of measuring approximations, especially for large datasets. An experimental framework was devised to measure the performance of proposed method in comparison with other techniques in terms of efficiency and accuracy, using benchmark datasets from UCI. The performance of proposed algorithm and other similar approaches are measured, against execution time, memory requirements and structural complexity. The algorithms have been implemented using visual basics platform and conducted experiments on windows 10 operating system with i-7 generation, x64-based processor and 16GB memory. The results show that the proposed rules significantly reduce the execution time by avoiding the redundant and lengthy computations with 100% accuracy, which ultimately reducesthe structural complexity and runtime memory requirements. By applying proposed rules in parallel threads, a further reduction in computation time while computing DRSA approximations has been achieved. However, these two approaches designed for static dataset. To enhance the scope of application, two methods to accommodate dynamic datasets has been proposed, which can efficiently and accurately handle single and multi-dimensional variations. In comparison with other similar approaches, proposed methods successfully update approximation sets using less computational resources.