Knowledge reduction in formal decision contexts based on an order-preserving mapping

Abstract

Knowledge reduction is one of the basic issues in knowledge presentation and data mining. In this study, an order-preserving mapping between the set of all the extensions of the conditional concept lattice and that of the decision concept lattice is defined to classify formal decision contexts into consistent and inconsistent categories. Then, methods of knowledge reduction for both the consistent and the inconsistent formal decision contexts are formulated by constructing proper discernibility matrices and their associated Boolean functions. For the consistent formal decision contexts, the proposed reduction method can avoid redundancy subject to maintaining consistency, while for the inconsistent formal decision contexts, the reduction method can make the set of all the compact non-redundant decision rules complete in the initial formal decision context.

Attribute reduction based on maximal rules in decision formal context

“…Recently, the relation among attribute reductions in formal, object-oriented and property-oriented concept lattices is studied and the equivalence among them has also been proved 16 . Besides, much attention has been paid to attribute reduction of the decision formal context 11,12,28,29,34 . A decision formal context consists of a universe of discourse U, a conditional attributes set A, a decision attribute set C, and binary relations I from U to A and J from U to C. Based on the discernibility matrix and Boolean function, attribute reduction of the strongly consistent decision formal context and the weakly consistent decision formal context was discussed 29 .…”

“…Then their corresponding knowledge reduction methods are given by constructing the suitable discernibility matrices and Boolean functions 12 .…”

Tacit Knowledge Mining of Formula Based on Double Decision Attribute Concept Lattices

“…As we can see, rule acquisition has been one of the main purposes in the analysis of decision formal context [2,3,[13][14][15][16][17][18][19][20]. Several types of rules have been obtained, such as decision implications [13], granular rules [14] and decision rules [15][16][17]. An important aspect of knowledge discovery is knowledge reduction.…”

“…Wei et al [12] put forward the concept lattice attribute reduction theory of decision formal context and defined the strong coordination and weak coordination of the decision formal context. As we can see, rule acquisition has been one of the main purposes in the analysis of decision formal context [2,3,[13][14][15][16][17][18][19][20]. Several types of rules have been obtained, such as decision implications [13], granular rules [14] and decision rules [15][16][17].…”

“…Similarly, the object set of low cost:{5,10,11,12,13}, the object set of medium cost:{1, 4,6,8,9,15,16,17,18,20,22,24,25} and the object set of high cost:{2,3,7,14,19,21,23} can be obtained (Figure 2 in Appendix). Correspondingly, the formulas were divided into three categories: low cost (W1), medium cost (W2) and high cost (W3).…”