Information Technology Reference
In-Depth Information
11.5.4
Integration with Other Mathematical Tools
Rough set theory and fuzzy set theory are not opposite. They are different, but
they can complement each other. Basically, rough sets show the indiscerniblity
among objects in sets, that is, the rough property caused by the granularity of
knowledge; fuzzy sets construct models for the unclear definition of subsets'
boundaries, and it shows the fuzziness of membership boundaries. They deal
with two different kinds of fuzziness and uncertainness. It is sure that
combination of them can process uncertain knowledge better. Based on the idea,
D. Dudios and H. Prade presented the concept of rough fuzzy set and fuzzy rough
set. The main idea is to define the lower approximate set and upper approximate
set of fuzzy sets when equivalence relations make the universes of fuzzy sets
rough. That is to say, the equivalence relations are transformed to fuzzy similar
relations, so that a more expressive rough model is got. D. Dudios and H. Prade
also had a detailed research on the properties of fuzzy sets' lower and upper
approximate sets, and pointed that in the case that indiscernibility and fuzzy
predications are both existent, the concept of fuzzy rough sets has potential
applications in logic inference.
D. Dudios and H. Prade also indicated that, evidence theory of Shafer and
rough set theory of Z. Pawlak are the same model under different glossaries. A.
Skowron and J. Grazymala-Buss gave more special conclusion. They pointed out
that rough set can be viewed as the basis of evidence theory. In the frame of
rough set theory, their work explained the basic concepts of evidence theory.
Especially, lower and upper approximate sets are used to explain belief and
plausibility functions, and then their complementarity is discussed.
11.6 Experimental Systems of Rough Sets
Rough set theory is proved to be very useful in practice. Plentiful applications in
our real lives also support the viewpoints. The theory is regarded as an important
one for AI and cognitive sciences. It made a lot of important applications on
decision supporting, experts systems, inductive inferences, and switch circuits.
In these years, rough set theory has a great progress in the applications on
knowledge discovery (KDD). Rough set theory based methods gradually
becomes those of main KDD methods. Knowledge discovery or data mining on
databases is a new subfield of AI, and it deals with uncommon knowledge mined
from increased information databases of enterprises. The main tasks of it are to
