On knowledge acquisition in multi-scale decision systems
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ORIGINAL ARTICLE
On knowledge acquisition in multi-scale decision systems Shen-Ming Gu • Wei-Zhi Wu
Received: 27 December 2011 / Accepted: 11 June 2012 Springer-Verlag 2012
Abstract The key to granular computing is to make use of granules in problem solving. However, there are different granules at different levels of scale in data sets having hierarchical scale structures. Therefore, the concept of multi-scale decision systems is introduced in this paper, and a formal approach to knowledge acquisition measured at different levels of granulations is also proposed, and some algorithms for knowledge acquisition in consistent and inconsistent multi-scale decision systems are proposed with illustrative examples. Keywords Decision systems Granular computing Granules Knowledge acquisition Multi-scale Rough sets
1 Introduction In many situations, it is impossible to distinguish individual objects in a universe of discourse. This forces us to consider elements within a granule as a whole rather than individually. Elements in a granule may be drawn together by indistinguishability, similarity, proximity, or functionality [6, 17]. Such a clustering of elements leads to information or knowledge granulation, which form a basis of granular computing (GrC) [29]. Basic ingredients of GrC are subsets, classes, and clusters of a universe of discourse.
S.-M. Gu (&) W.-Z. Wu School of Mathematics, Physics and Information Science, Zhejiang Ocean University, Zhoushan 316000, Zhejiang, People’s Republic of China e-mail: [email protected] W.-Z. Wu e-mail: [email protected]
GrC is a basic approach for knowledge representation and data mining. The purpose of GrC is to seek for an approximation scheme which can effectively solve a complex problem, albeit not in the most precise way [27]. The topic of fuzzy information granulation was first proposed and discussed by Zadeh [34]. A general framework of GrC was presented by Zadeh [35] in the context of fuzzy set theory. Since its conception, ‘‘granular computing‘‘ has become a fast growing field of research [1–4, 19, 28–32]. Various methods of GrC concentrating on concrete models in specific contexts have been proposed over the years. Rough set theory is perhaps one of the most advanced areas that popularize GrC [5, 8, 14, 29–32]. It was originally proposed by Pawlak [16] as a formal tool for modelling and processing incomplete information. Rough set models enable us to precisely define and analyze many notions of GrC. For example, Yao [31] proposed a partition model of GrC. The model is constructed by granulating a finite universe of discourse through a family of pairwise disjoint subsets under an equivalence relation. The partition model is actually important and is based on the Pawlak approximation space [15, 18, 25]. Qian et al. [20, 21] proposed the concept of multi-granulation rough sets. It is different from Pawlak’s rough sets since the former is constructed on the basis of a family of the binary relations instead of a single one. Most applications based on rough set th
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