ORIGINAL ARTICLE
On knowledge acquisition in multi-scale decision systems
Shen-Ming Gu
•
Wei-Zhi Wu
Received: 27 December 2011 / Accepted: 11 June 2012 / Published online: 1 July 2012
Springer-Verlag 2012
Abstract The key to granular computing is to make use
of granules in problem solving. However, there are dif-
ferent 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 con-
sider elements within a granule as a whole rather than
individually. Elements in a granule may be drawn together
by indistinguishability, similarity, proximity, or function-
ality [6, 17]. Such a clustering of elements leads to infor-
mation 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.
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 pro-
posed 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 theory can fall into
the attribute-value representation model, called information
system [26]. Usually, in an information system, each object
at each attribute can only take on one value, we call such
an information system a single scale information system.
However, people can observe objects or deal with data
hierarchically structured into different scales [11, 33].
Thus, in many real-life multi-scale information systems, an
object can take on as many values as they are scales under
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: gsm@zjou.edu.cn
W.-Z. Wu
e-mail: wuwz@zjou.edu.cn
123
Int. J. Mach. Learn. & Cyber. (2013) 4:477–486
DOI 10.1007/s13042-012-0115-7