An incremental approach to attribute reduction of dynamic set-valued information systems
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ORIGINAL ARTICLE
An incremental approach to attribute reduction of dynamic set-valued information systems Guangming Lang • Qingguo Li • Tian Yang
Received: 3 July 2013 / Accepted: 15 December 2013 Springer-Verlag Berlin Heidelberg 2013
Abstract Set-valued information systems are important generalizations of single-valued information systems. In this paper, three relations are proposed for attribute reduction of set-valued information systems. Then, we convert a large-scale set-valued information system into a smaller relation information system. An incremental algorithm is designed to compress dynamic set-valued information systems. Concretely, we mainly address the compression updating from three aspects: variations of attribute set, immigration and emigration of objects and alterations of attribute values. Finally, several illustrative examples are employed to demonstrate that attribute reduction of dynamic set-valued information systems are simplified significantly by our proposed approaches. Keywords Rough sets Attribute reduction Homomorphism Set-valued information system Dynamic set-valued information system
G. Lang Q. Li (&) College of Mathematics and Econometrics, Hunan University Changsha, 410082 Hunan, People’s Republic of China e-mail: [email protected] G. Lang e-mail: [email protected] T. Yang College of Science, Central South University of Forestry and Technology, Changsha 410082, Hunan, People’s Republic of China e-mail: [email protected]
1 Introduction Rough set theory proposed by Pawlak [40] is a powerful mathematical tool to deal with vagueness and uncertainty of information. But the condition of equivalence relation is so restrictive that limits applications of rough sets in practice. By combining with fuzzy sets [1–6, 17, 23, 24, 36, 37, 39, 48, 49], probability theory [32, 33, 44, 45, 53–55, 62], topology [16, 18, 42. 43, 50, 52, 56, 59], matroid theory [47] and other theories [29, 38], rough set theory has been successfully applied to various areas such as knowledge discovery, data mining and pattern recognition. Set-valued information systems as generalized models of single-valued information systems and a representation of incomplete information have attracted a great deal of attention [8–15, 20, 22, 25, 31, 41, 51, 52, 57]. For example, Guan et al. [22] initially introduced set-valued information systems and investigated their basic properties. Chen et al. [8, 9] studied attribute reduction of set-valued information systems based on tolerance relations and variable tolerance relations. Liu et al. [31] discussed attribute reduction of set-valued information systems on the basis of maximal variable precision tolerance classes. Zhang et al. [57] introduced matrix approaches for approximations of concepts in set-valued information systems with dynamic attribute variation. In practice, the tolerance relation discerns objects on the basis of whether there are common attribute values or not, and it neglects some differences between objects. For instance, there are
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