Rule Acquisition in Formal Decision Contexts Based on Formal, Object-Oriented and Property-Oriented Concept Lattices

Abstract

Rule acquisition is one of the main purposes in the analysis of formal decision contexts. Up to now, there have been several types of rules in formal decision contexts such as decision rules, decision implications, and granular rules, which can be viewed as ∧-rules since all of them have the following form: “if conditions 1,2,…, and m hold, then decisions hold.” In order to enrich the existing rule acquisition theory in formal decision contexts, this study puts forward two new types of rules which are called ∨-rules and ∨-∧ mixed rules based on formal, object-oriented, and property-oriented concept lattices. Moreover, a comparison of ∨-rules, ∨-∧ mixed rules, and ∧-rules is made from the perspectives of inclusion and inference relationships. Finally, some real examples and numerical experiments are conducted to compare the proposed rule acquisition algorithms with the existing one in terms of the running efficiency.

Attribute Reduction and Rule Acquisition of Formal Decision Context Based on Dual Concept Lattice

“…Assume that L(C N ) is computed by using the algorithms presented in [37] given by Table 1. It follows that Ren et al [33] proposed an algorithm to acquire necessary I-decision rules. The time complexity of the algorithm is…”

“…Clearly, Algorithm 1 and Algorithm 2 presented in this subsection have lower time complexity than the algorithm presented in [33]. If necessary I-decision rules are computed by using Algorithm 1, we just need to compute (O…”

“…In this part, we further research the rule acquisition and attribute reduction methods for this kind of decision rules. We propose new rule acquisition methods and make some comparative study on the rule acquisition algorithms presented in [33] and the rule acquisition algorithms presented in this paper. Furthermore, we present related attribute reduction methods.…”

“…In Section 2, the basic definitions of FCA such as formal concept, property-oriented concept and object-oriented concept are concisely recalled. In Section 3, we propose algorithms for I-decision rule acquisition and make some comparative analysis with the existing algorithms presented in [33]. In addition, we present attribute reduction method for Fdc to preserve I-decision rules.…”

“…A decision rule is an implication in which the premise and conclusion are concepts of conditional context and decision context respectively. The criteria of attribute reduction for formal decision contexts can be roughly categorized into two groups: to preserve a kind of consistency [15,27,28,29], and to preserve a specific kind of decision rules [30,31,32,33,34] of Fdcs. Qin et al [35] made a comparative research on attribute reduction of formal context and Fdc under the framework of local reduction.…”