Relation granulation and algebraic structure based on concept lattice in complex information systems
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ORIGINAL ARTICLE
Relation granulation and algebraic structure based on concept lattice in complex information systems Xiangping Kang1,2 · Duoqian Miao1 · Guoping Lin3 · Yong Liu4
Received: 19 November 2015 / Accepted: 29 May 2017 © Springer-Verlag Berlin Heidelberg 2017
Abstract Normally, there may exist some kind of relationship among different attribute values such as order relationship, similarity relationship or other more complicated relationship hidden in complex information systems. In the case, the binary relation on the universe is probably a kind of more general binary relation rather than equivalence relation, tolerance relation, order relation, etc. For the case, the paper tries to take concept lattice as theoretical foundation, which is appropriate very well for analyzing and processing binary relations, and finally proposes a new rough set model from the perspective of sub-relations. In the model, one general binary relation can be decomposed into several sub-relations, which can be viewed as granules to study algebraic structure and offer solutions to problems such as reduction, core. The algebraic structure mentioned above can organized all of relation granulation results in the * Xiangping Kang [email protected] Duoqian Miao [email protected] Guoping Lin [email protected] Yong Liu [email protected] 1
Key Laboratory of Embedded System and Service Computing, Ministry of Education, Tongji University, Shanghai 201804, China
2
China National Tobacco Corporation, Shanxi Branch, Taiyuan 030000, Shanxi, China
3
School of Mathematics and Statistics, Minnan Normal University, Zhangzhou 363000, Fujian, China
4
School of Computer Science and Technology, Shandong University, Jinan 250101, China
form of lattice structure. In addition, the computing process based on concept lattice is often accompanied by high time complexity, aiming at the problem, the paper attempts to overcome it by introducing granular computing, and further converts complex information systems into relatively simple ones. In general, the paper is a new attempt and exploring to the fusion of rough set and concept lattice, and also offers a new idea for the expansion of rough set from the perspective of relation granulation. Keywords Rough set · Concept lattice · General binary relations · Granular computing · Relation granulation.
1 Introduction In the age of information globalization, how to process massive data for knowledge acquisition has already become one of the research hotspots. In 1982, Pawlak proposed rough set [31], which is a mathematical theory developed on the basis of predecessors’ research theories like Zadeh’s fuzzy set theory [54] and Shafer’s evidence theory [40] for processing uncertainty information. Although rough set has similarities with theories mentioned above for processing uncertain problems, there are still some differences. The most remarkable distinction is that rough set does not require offering any priori knowledge, such as fuzzy membership function in fuzzy set, belief function in
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