Comparative study of alternative types of knowledge reduction in inconsistent systems

Abstract

Many types of attribute reduction and decision rules have been proposed in the area of rough sets. It is required to provide their consistent classification. The task is not easy because new proposals address different issues such as: noise in data, compact representation, prediction capability. Usually, when introducing a new knowledge reduction method the authors relate it only to one basic type of knowledge reduction. The main objective of the paper was to find and prove static relationships among classical types of knowledge reduction in inconsistent decision tables in order to provide an underlying classification of knowledge reduction types. Hence, if a newly devised reduction type is a specialization of some known type then all its properties inherited from generalized types will be also known. © 2001 John Wiley & Sons, Inc.

A Rough Set Approach for the Discovery of Classification Rules in Interval-Valued Information Systems

“…The extensions of Pawlak's rough set model may be used in reasoning and knowledge acquisition in incomplete decision tables [5,8,11,[18][19][20][21][22].…”

Analysis of alternative objective functions for attribute reduction in complete decision tables

“…Therein, possible reduct preserves the upper approximation of each decision class. Some types of knowledge reduction for a single object and an entire decision table were, respectively, compared by Kryszkiewicz (2001). For the latter, approximate reduct which preserves the decision values for each object and possible reduct which distinguishes each object from objects that do not belong to the relevant upper approximation are both presented.…”

“…A sort of formulation description cannot represent all the properties. Many objective functions for attribute reduction have been proposed by means of some special facets in a complete decision table (Kryszkiewicz 2001;Li and Zhang 2004;Miao and Wang 1997;Miao et al 2009;Pawlak and Skowron 2007;Slezak 2000;Wang et al 2002Wang et al , 2005Zhang et al 2003). Classical objective function for attribute reduction proposed by Pawlak (1982) focuses on the remaining positive region or the quality of classification.…”

Dependence-space-based attribute reduction in consistent decision tables

“…Knowledge reduction is thus an outstanding contribution made by rough set research to data analysis. Extensive research from various points of view has been made in recent years (Beynon 2001;Jensen and Shen 2004;Kryszkiewicz 2001;Lashin and Medhat 2005;Leung et al 2006Leung et al , 2008Leung and Li 2003;Li et al 2006;Maji and Pal 2007;Mi et al 2004;Pawlak 1991;Slowinski et al 2000;Wu et al 2005;Wu 2008;Zhang et al 2003;Zhu and Wang 2003). By using the notion of discernibility matrix and Boolean reasoning techniques (Skowron and Rauszer 1992;Skowron 1993), various approaches have also been proposed to perform knowledge reduction and to optimally obtain true, certain, and possible decision rules from decision tables.…”