Fuzzy Set Extensions of the Dominance-Based Rough Set Approach
Salvatore Greco, Benedetto Matarazzo, Roman Słowiński · 2013
Abstract Rough set theory has been proposed by Pawlak in the early 80s to deal with inconsistency problems following from information granulation. It operates on an information table composed of a set U of objects described by a set Q of condition and decision attributes. Decision attributes make a partition of U into decision classes. Basic concepts of rough set theory are: indiscernibility relation on U, lower and upper (rough) approximations of decision classes, dependence and reduction of attributes from Q, and decision rules induced from rough approximations of decision classes. The original rough set idea was failing, however, to handle preferential ordering of domains of attributes (scales of criteria), as well as preferential ordering of decision classes. In order to deal with multiple criteria decision problems a number of methodological changes to the original rough set theory were necessary. The main change is the substitution of the indiscernibility relation by a dominance relation, which permits approximation of ordered sets. In multiple criteria decision context, the information table is composed of decision examples given by a decision maker. The Dominance-based Rough Set Approach