The introduction and utilization of ( l , u )‐graphs in the extended variable precision rough sets model

The extended variable precision rough sets model (VPRS l , u ) is a development of the rough set theory methodology first introduced in the seminal work by Zdzislaw Pawlak. As a technique for data analysis it is based on a set theoretical approach for the possible classification of groups of objects (condition classes) in a decision table to categorical decision attribute values (decision classes). Two measures are considered in this paper which utilize the l and u values necessary within VPRS l , u , the degree of dependency ( l , u )‐ DoD of a decision class and the quality of classification ( l , u )‐ QoC of objects in the model. This article introduces the notion of the ( l , u )‐graph, which elucidates the effect of the choice of the l and u values on the associated levels of ( l , u )‐ DoD and ( l , u )‐ QoC . A number of descriptive measures including specific lines are defined that utilize the information contained in the ( l , u )‐graphs. These measures and lines are used to intelligently identify and select subsets of condition attributes described ( l , u )‐reducts and a choice of the l and u values, based on retaining the underlying ( l , u )‐ DoD or ( l , u )‐ QoC within the associated ( l , u )‐graph. © 2003 Wiley Periodicals, Inc.