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

Abstract

Attribute reduction and reducts are important notions in rough set theory that can preserve discriminatory properties to the highest possible extent similar to the entire set of attributes. In this paper, the relationships among 13 types of alternative objective functions for attribute reduction are systematically analyzed in complete decision tables. For inconsistent and consistent decision tables, it is demonstrated that there are only six and two intrinsically different objective functions for attribute reduction, respectively. Some algorithms have been put forward for minimal attribute reduction according to different objective functions. Through a counterexample, it is shown that heuristic methods cannot always guarantee to produce a minimal reduct. Based on the general definition of discernibility function, a complete algorithm for finding a minimal reduct is proposed. Since it only depends on reasoning mechanisms, it can be applied under any objective function for attribute reduction as long as the corresponding discernibility matrix has been well established.

Quick general reduction algorithms for inconsistent decision tables

“…In inconsistent decision tables, for different user requirements in different applications, we can obtain different types of attribute reducts. Zhou et al [50] studied the relationships among 12 types of the relative reduct (where absolute reduct is not a relative reduct) for inconsistent decision tables, where there are only five intrinsically different relative reducts, namely relative relation reduct (Hu's discernibility matrix reduct, denoted as H-reduct), positive-region reduct, distribution reduction, maximum distribution reduct, and assignment reduct. In the following, we provide five representative relative reduct definitions:…”

Bidirectional heuristic attribute reduction based on conflict region

“…It has been widely applied in many fields such as machine learning (Swiniarski and Skowron 2003), data mining (Liu and Motoda 1998), intelligent data analyzing (Pawlak 2002) and control algorithm acquiring (Fayyad et al 1996), and so on. In rough set theory, attribute reduction can be considered a kind of specific feature selection method to find minimum subset of attributes that retain some special properties of information system or decision table (Kryszkiewicz 2001(Kryszkiewicz , 2007Miao et al 2009;Zhang et al 2003a,b,c;Zhou et al 2011). In the last three decades, based on rough set theory, many techniques of attribute reduction have been developed (Hu and Cercone 1995;Korze and Jaroszewicz 2005;Nguyen and Nguyen 1996;Qian et al 2010;Slezak 2002;Skowron and Rauszer 1992;Wang et al 1998;Yao and Zhao 2009).…”

Heuristic Approaches to Attribute Reduction for Generalized Decision Preservation

“…Mutual information preservation reduction [14] can leave mutual information, with respect to the decision attributes, unchanged. In the last twenty years, many methods for attribute reduction have been studied, such as discernibility matrix-based attribute reduction methods [15][16][17][18][19][20], heuristic attribute reduction methods [10,[21][22][23], metaheuristic attribute reduction methods [24][25][26][27][28][29][30], and so on.…”