Attribute reduction based on maximal rules in decision formal context

Abstract

One of the key issues in the theory of concept lattices is to extract the useful rules from the decision formal context. The maximal rules implicate the others, thus people are interested in them. This paper proposes two new kinds of attribute reduction in the decision formal context based on maximal rules. The reducts preserve all the condition extensions and the decision extensions related to the original maximal rules. The internal relationship between the original maximal rules and the maximal rules in the reduced decision formal context is derived. The reducts can make the maximal rules more concise and accurate. The mathematical property of the proposed attribute reduction is investigated and we construct the discernibility matrix and function to compute all the reducts. Finally, all the attributes are classified into three types based on the maximal rules. The characteristics of these types of attributes are also analyzed.

Concept and Attribute Reduction Based on Rectangle Theory of Formal Concept

“…The mathematical basis of concept lattice is the lattice theory, the visualization tool is the Hasse graph, and the research methods are abstract algebra, discrete mathematics, data structure and algorithm analysis, fuzzy set [28], rough set [17], granular computing [29], etc. So far, formal concept analysis has been widely used in information retrieval [4,12], knowledge discovery [13], association analysis [24], recommendation system [32] and other fields [16,18,23,25].…”

“…Second, in order to better analyze data and save storage space, it is necessary to reduce concept lattice [3,8,11,22,26,30]. Furthermore, the nodes of concept lattice can infer from each other, and based on this, one can extract rules [9][10][11][12]19].…”

“…Based on the discernibility matrix and Boolean function, a method to attribute reduction is proposed while preserving the extensions in concept lattices [30,31]. Similarly, two kinds of attribute reduction are proposed in the decision formal context based on the maximal rules [12]. Note that the attribute reduction in both [30,31] and [12] can be simplified to reducing attributes while preserving the extensions for a set of formal concepts.…”

Neighbourhood systems based attribute reduction in formal decision contexts

“…Li formulated a new framework of knowledge reduction from the perspective of rule acquisition and developed the method of corresponding reduction by using the discernibility matrix and Boolean function [5, 6], investigated the issue of reducing the object set of a formal decision context without losing the decision rule information provided by the entire set of objects [7]. Li and Mi proposed two new kinds of attribute reduction in the decision formal context based on maximal rules [8]. By combing minimal vertex covers in graph theory, Chen proposed a fast attribute reduction method for large formal decision contexts [9, 10].…”

A Novel Approach for Reducing Attributes and Its Application to Small Enterprise Financing Ability Evaluation

“…Because people are interested in the maximal rules implicated in attribute reduction, Li et al developed two new kinds of attribute reduction approaches in the decision formal context based on maximal rules [34].…”