Rough Sets Modeling - Probabilistic Composition of Preferences, Theory and Applications - page 100

Chapter 10
Rough Sets Modeling

Abstract The transformation in probabilities of being the best can reduce the
number of possible values of the attributes. By this property, it may be used to
amplify the roughness of decision attributes in Rough Sets Theory applications.
This can be explored to increase the index of quality of approximation and simplify
the classi

cation rules.

Keywords Rough sets Reducts Index of quality of approximation

Dominance Probabilistic transformation

10.1 Roughness Modeling

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Rough Sets Theory RST (Pawlak 1982 ) is based on identifying approximately

classes determined by a set of attributes, named decision attributes, according to
another set of attributes, named condition attributes.
An important stage in the characterization of rough sets is the identification of
reducts, subsets of the set of condition attributes able to offer the same quality of
approximation as the whole set. The possibility of approximation and, conse-
quently, the number of reducts depend on the roughness of the sets, a concept
whose characterization has been centered, in previous developments, on properties
of the vector of values of the different attributes, but may consider also the precision
in the measurement of each attribute.
The approach here employed to simplify the approximation applies to the sit-
uation in which the attributes are ordered variables. For this situation was developed
the extension of RST called by Greco et al. ( 2001 , 2002 ) Dominance-based Rough
Sets Approach DRSA.

A form of easing the approximation on DRSA employing relaxation of the rules
for the entry of alternatives in the approximation by ignoring some contradictions is
Dominance-based Rough Sets with Variable Consistency VC

—

— DRSA, developed

by Greco et al. ( 2005 ).