Panel Discussion on Granular Computing at RSCTC2004

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Title: Panel Discussion on Granular Computing at RSCTC2004

1
Panel Discussion on Granular Computing at
RSCTC2004

2
What is Granular Computing?

There are three basic concepts that underline
human cognition granulation, organization and
causation.
Informally, granulation involves decomposition of
whole into parts
Organization involves integration of parts into
whole
Causation involves association of causes with
effects.
Granulation of an object A leads to a collection
of granules of A, with a granule being a clump of
points (objects) drawn together by
indistinguishability, similarity, proximity or
functionality (Zadeh 1997)

3
What is Granular Computing

An umbrella term to cover any theories,
methodologies, techniques, and tools that make
use of granules in problem solving.
A subset of the universe is called a granule in
granular computing.
Basic ingredients of granular computing are
subsets, classes, and clusters of a universe.

4
Granule Computing and Data Mining

A concept is understood as a unit of thoughts
that consists of two parts, the intension and
extension of the concept.
The intension of a concept consists of all
properties or attributes that are valid for all
those objects to which the concept applies.
The extension of a concept is the set of objects
or entities which are instances of the concept.
A rule can be expressed in the form, fgt?
where f and ? are intensions of two concepts.
Rules are interpreted using extensions of the two
concepts.

5
How do Rough Sets Contribute to Granular
Computing?

Zadeh define Granular Computing in BISC/SIG on
GrC as a superset of the theory of fuzzy
information granulation, rough set theory and
interval computations, and is a subset of
granular mathematics.

6
Zadehs Fuzzy GrC Model

Granules are constructed and defined based on the
concept of generalized constraints. Relationships
between granules are represented in terms of
fuzzy graphs or fuzzy if then rules.
A granule is defined by a fuzzy set G X X
isr R

7
Pawlaks Rough Set Model

8
Information Tables

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Concept Formation

10
Classification Problems

Assume that each object is associated with a
unique class label.
Objects are divided into disjoint classes which
form a partition of the universe.
The set of attributes is expressed as At F ?
class, where F is the set of attributes used to
describe the objects.
To find classification rules of the form, f ?
class ci, where f is a formula over F and ci is
a class label.

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Solution to Classification Problems

The partition solution to a consistent
classification problem is a conjunctively
definable partition p such that p ? pclass.
The covering solution to a consistent
classification problem is a conjunctively
definable covering ? such that ? ? pclass.

12
A construction algorithm

Construct the family of basic concept with
respect to atomic formulas
BC(U) (av, m (a v)) a ? F, v ? Va
Set the unused basic concepts to the set of basic
concepts
UBC(U) BC(U).
Set the granule network to GN (U,?), which is
a graph consists of only one node and no arc.
While the set of smallest granules in GN is not a
covering solution of the classification problem
do the following
Compute the fitness of each unused basic concept.
Select the basic concept C(av, m(av)) with
maximum value of fitness.
Set UBC(U) UBC(U) - C.
Modify the granule network GN by adding new nodes
which are the intersection of m(av) and the
original nodes of GN connect the new nodes by
arcs labelled by a v.

13
References

Pawlak, Z., Granularity of knowledge,
indiscernibility and rough sets, IEEE
International Conference on Fuzzy Systems,
106-110, 1998.
Yao, J.T., Yao, Y.Y. A granular computing
approach to machine learning, FSKD'02, 732-736,
2002.
Yao, Y.Y. Granular computing basic issues and
possible solutions, JCIS (I), 86-189, 2000.
Zadeh, L.A. Towards a theory of fuzzy information
granulation and its centrality in human reasoning
and fuzzy logic, Fuzzy Sets and Systems, 19,
111-127, 1997.