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functions) and the construction of discrete dynamic systems controlled by rough
real functions. These topics need to be formalized under the model of rough
function theory. The research on these topics will make contributions to the
exploration on qualitative inference methods. The essence of these researches is
to discrete continuous mathematics. Thus, continuous mathematics can also be
processed by modern computers.
Control based on rough set theory seems to be another promising application
field. Besides, the development of new neural network algorithms and genetic
algorithms with the help of rough set theory is also very important. How to
construct a uniform logic model to explain uncertainty theories, such as rough set
theory, fuzzy set theory, evidence theory, probability theory and etc, is also worth
to be researched. At present, there are still a few noticeable fields not mentioned.
They are introduced in brief as follows.
(1) Based on the inheritance of original rough set models' basic mathematical
properties, research on how to extend the models so that they can be applied
to data compression and information system analysis better;
(2) In the distributed environments, research on the expression of incomplete or
uncertain knowledge and the knowledge transformation among multi-agents;
(3) Research on how to introduce the concepts of upper and lower approximate
sets, and their mathematical properties to some special algebraic structures.
For example, research on the definition and relations of rough set operations
defined on concept lattices;
(4) Research on the relations between rough set theory and formalized languages.
From the viewpoints of knowledge discovery, we list some possible research
topics and application fields as follows.
Efficient reduction algorithms
Efficient reduction algorithms are the basis of
rough set theory applied to knowledge discovery. At present, there is not a very
efficient method. Therefore, develop a fast reduction algorithm and its
incremental version is still one of the main topics.
Huge data problems
In practice, the sizes in databases are increased. For rough
set theory, how to deal with the challenge is still a problem. Although exists a lot
of helpful explorations, there are not satisfactory methods. Possible solving
methods can be sampling, parallelizing, and etc.
Integration of various methods
There are a lot of data mining methods.
Experiments showed that, there is not a method that exceeds all of others.
