Information Technology Reference
In-Depth Information
In 1962, Zeeman proposed that cognitive activities can be viewed as some
kind tolerance spaces in a function space. The tolerance spaces, which are
constructed by distance functions based tolerance relations, is used for stability
analysis of dynamic system by Zeeman. In our work, tolerance spaces based on
distance functions are developed for the modeling and analysis of information
granulation, which is defined as tolerance relation granulation in the following
part.
The aim of describing a problem on different granularities is to enable the
computer to solve the same problem at different granule sizes hierarchically. We
can use a tolerance space to describe a problem (Zheng et al, 2005). A tolerance
granular space model
TGSM
can be formalized as a 4-tuple (
OS, TR, FG, NTC
),
where
denotes an object set system and is composed by the objects processed
and granulated in tolerance granular space, which can be viewed as the object
field;
OS
denotes a tolerance relation system and is a (parameterized) relation
structure. It is composed by a set of tolerance relations. It includes the relations
or coefficients that the granular spaces base on;
TR
FG
denotes transformation
function between tolerance granules;
denotes a nested tolerance covering
system. It is a (parameterized) granular structure, which denotes different levels
granules and the granulation process based on above object system and tolerance
relation system. It denotes a nested granular structure to express the relationships
among granules and objects.
NTC
NTC
defines a nested granular structure to represent:
Relations among granules and objects;
The composition and decomposition of granules.
11.8 Future Trends of Rough Set Theory
Rough set theory is proved to be complete and very useful in real applications. It
provides some effective methods which can be applied into many fields. Rough
set theory based rough logic seems to be a worthy topic, because the logic can
make monotone logic be nonmonotonized so that it can play a great role in the
approximation of AI or uncertainty inference. From these viewpoints, it is
obvious that the research on rough set theory based rough logic is promising.
Another important topic of rough set theory is the research on theory and
applications of rough functions, which includes various approximate operations
of rough functions, the basic properties of rough functions (such as rough
continuity, rough derivative, rough integral and rough stability, control of rough
