A Generalized Algebraic Approach To Finding
Rough Set Approximations And Generating
Logic Rules
Author(s)
D. Sitnikov, O. Ryabov, O. Titova & O. Romanenko
Abstract
The rough set concept is a relatively new mathematical approach to vagueness
and uncertainty in data. The rough set theory is a well-understood formal
framework for building data mining models in the form of logic rules, on the
basis of which it is possible to issue predictions that allow the classification of
new cases. The indiscernibility relation and approximations based on this
relation form the mathematical basis of the rough set theory. The classical
topological definitions of rough approximations are based on this relation.
Unlike the classical approaches it is possible to define rough approximations in
an algebraic way. This paper represents a generalization of the algebraic
approach suggested by the authors earlier. We use a set of discrete characteristic
functions taking on values from finite sets (not necessarily Boolean values) and
operations on them including comparison and Boolean operations, which we call
the approximation language. We use the terms \“exact upper approximation” and
\“exact lower approximation” to stress the fact that there can exist a variety of
approximations but it is always possible to select the approximations that cannot
be improved in the terms of the approximation language. We consider the
process of generating logic rules based on the exact approximations in the case
of arbitrary discrete characteristic functions taking on values from finite sets.
Logic rules are naturally obtained from predicate formulae for the exact
approximations. The introduced approach allows the generation of logic rules
quickly and efficiently since only comparison operations with discrete values
and Boolean operations with binary values are used to produce logic formulae.
Keywords
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