Information Technology Reference
In-Depth Information
which are indiscernible, similar, adjacent or functional. The essence of
information granulation is approximation.
Suppose
K
=(
U, R
) is an approximate space, and
R
is a partition of
U
, then the
granularity of knowledge
R
can be defined as:
R
m
|
2
) (11.10)
Granular computing is an umbrella term which covers any theories,
methodologies, techniques related with granularities. In brief, granular
computing is the superset of fuzzy granular theory, while rough set theory and
interval computing theory are the subsets of granular mathematics. When a
problem involves incomplete, uncertain or fuzzy information, the distinguishing
of objects are very difficult. Thus, granularities are needed to deal with these
cases.
The concept of granular computing was first presented by Prof. Zadeh in his
paper “Fuzzy sets and information granularity” (Zadeh, 1979). Pawlak and etc
related granular computing with rough set theory, and did many researches on
them (Peter, 2002). In Yao' work, he uses decision logic language (DL-language)
to describe the granularities of sets (that is, use the sets of objects satisfying
formula
φ
to define equivalence classes
)=(1/|U|
2
)*( |
1
|
2
+|
2
|
2
+……+|
GK(
R
R
R
(
φ
)), and then utilize the lattices
constructed by all partitions to solve consistent classification problems. Moreover,
Yao pointed out that researchers can make use of multilayer granulation to
explore the approximation of hierarchical rough sets. Lin and Yao researched on
granular computing with the help of neighbor systems.
L. Zhang and B. Zhang indicated that concepts with different granularities can
be represented by subsets, and concepts with different granularities can be
expressed by subsets with different granularities. A cluster of concepts can
constitute a partition of universe - quotient space (knowledge base). Different
concept clusters can construct different quotient spaces. Therefore, given some
knowledge bases, the research on granular computing is to find the relations and
transformations among various subsets. The model of quotient spaces can be
described by a triplet (
m
X, F, T
), where
X
denotes a universe,
F
denotes a attribute
set, and
. When choosing coarse
granularities, that is, giving an equivalence relation R (or a partition), we say that
a quotient set is related with R is generated, which is denoted by [
T
denotes the topology structure on
X
X
]. The
corresponding triplet of [
X
] is ([
X
], [
F
], [
T
]), called as the quotient space related
with
. The research on Quotient space theory is to explore the relations,
composition, synthesis, decomposition of quotient spaces and also the inference
on quotient spaces(Zhang et al, 2005).
R
