A rule-extraction framework under multigranulation rough sets
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ORIGINAL ARTICLE
A rule-extraction framework under multigranulation rough sets Xin Liu • Yuhua Qian • Jiye Liang
Received: 25 January 2013 / Accepted: 10 August 2013 / Published online: 24 August 2013 Springer-Verlag Berlin Heidelberg 2013
Abstract The multigranulation rough set (MGRS) is becoming a rising theory in rough set area, which offers a desirable theoretical method for problem solving under multigranulation environment. However, it is worth noticing that how to effectively extract decision rules in terms of multigranulation rough sets has not been more concerned. In order to address this issue, we firstly give a general ruleextraction framework through including granulation selection and granule selection in the context of MGRS. Then, two methods in the framework (i.e. a granulation selection method that employs a heuristic strategy for searching a minimal set of granular structures and a granule selection method constructed by an optimistic strategy for getting a set of granules with maximal covering property) are both presented. Finally, an experimental analysis shows the validity of the proposed rule-extraction framework in this paper. keywords Multigranulation rough set Rule extraction Granulation selection Granule selection
1 Introduction Along with the development of information era, mass data have been collected and accumulated at a rapid pace. The X. Liu (&) Y. Qian J. Liang School of Computer and Information Technology, Shanxi University, Taiyuan 030006, Shanxi, China e-mail: [email protected] Y. Qian e-mail: [email protected] J. Liang e-mail: [email protected]
useful information and knowledge hidden in large amounts of data are so much that we have an urgent need to mine potential rules and knowledge from rapidly growing data. For purpose of extracting implicit knowledge from the data, a great many of theories have been proposed and developed in recent years, which are fuzzy set theory [12], rough set theory [1, 2], computing with words [3, 13], granular computing [14, 16], computational theory for linguistic dynamic systems [4], and so on. Rough set theory, introduced by Pawlak [1, 2], is a wellestablished mechanism for vagueness and uncertainty in data analysis. So for, it has been widely applied in knowledge discovery, decision analysis, pattern recognition and so on. In rough set theory, a target concept is always approximated by the so-called lower and upper approximations that are defined by an equivalence (indiscernibility) relation. According to various requirements, a great many of extensions of Pawlak’s rough set have been developed, such as variable precision rough set [5], rough set based on tolerance relation [6, 7], Bayesian rough set [8], fuzzy rough set [9–11] and rough fuzzy set [9–11]. However, it can be seen that the above extensional rough sets are constructed on the basis of a single binary relation, which limits some applications of rough set theory. Granular computing, proposed by Lin [14, 16], is an umbrella term that covers all theories, methodologies, tech
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