Formal Decision Contexts Research Articles

On rule acquisition in decision formal contexts

Rule acquisition is one of the main purposes in the analysis of decision formal contexts. Up to now, there have existed several types of rules (e.g., the decision rules and the granular rules) in decision formal contexts. This study firstly proposes a new algorithm with less time complexity for deriving the non-redundant decision rules from a decision formal context. Then, we invesigate decision rules and the granular rules in the consistent decision formal contexts and make a contrast between the decision rule oriented knowledge reduction and the granular rule oriented knowledge reduction. Finally, some experiments are conducted to assess the efficiency of the proposed rule acquisition algorithm.

Incomplete decision contexts: Approximate concept construction, rule acquisition and knowledge reduction

Incomplete decision contexts are a kind of decision formal contexts in which information about the relationship between some objects and attributes is not available or is lost. Knowledge discovery in incomplete decision contexts is of interest because such databases are frequently encountered in the real world. This paper mainly focuses on the issues of approximate concept construction, rule acquisition and knowledge reduction in incomplete decision contexts. We propose a novel method for building the approximate concept lattice of an incomplete context. Then, we present the notion of an approximate decision rule and an approach for extracting non-redundant approximate decision rules from an incomplete decision context. Furthermore, in order to make the rule acquisition easier and the extracted approximate decision rules more compact, a knowledge reduction framework with a reduction procedure for incomplete decision contexts is formulated by constructing a discernibility matrix and its associated Boolean function. Finally, some numerical experiments are conducted to assess the efficiency of the proposed method.

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

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.

Knowledge reduction in real decision formal contexts

Rule acquisition is one of the main purposes in the analysis of real decision formal contexts. In general, the decision rules derived directly from a real decision formal context are not concise or compact. In order to derive more compact decision rules, this study proposes a rule acquisition oriented framework of knowledge reduction for real decision formal contexts and formulates a corresponding reduction method by constructing a discernibility matrix and its associated Boolean function. The proposed reduction method is applicable to any real decision formal contexts and with the reduced real decision formal contexts, we can obtain more compact decision rules that can imply all the decision rules derived from the initial real decision formal context. Some numerical experiments are conducted to assess the efficiency of the proposed method.

Attribute reduction in decision formal context based on homomorphism

Attribute reduction in concept lattices is one of the key problems in the study of concept lattice theory. This paper defines a homomorphism consistent set and provides an approach to attribute reduction of a consistent decision formal context based on concept lattices. We also examine the relationship between homomorphism consistent set and attribute consistent set. The method for judging a homomorphism consistent set is simpler than the existing ones.

Using Formal Concept Analysis and Rough Set Constructing the System of Semantic Web

Formal concept analysis (FCA) is based on a formalization of the philosophical understanding of a concept as a unit of thought constituted by its extent and intent. The rough set philosophy is founded on the assumption that with every object of the universe of discourse we associate some information. This paper deals with approaches to knowledge reduction in generalized consistent decision formal context. Finally, a new system model of semantic web based on FCA and rough set is proposed, which preserve more structural and featural information of concept lattice. In order to obtain the concept lattices with relatively less attributes and objects, we study the reduction of the concept lattices based on FCA and rough set theory. The experimental results indicate that this method has great promise.

Knowledge reduction in decision formal contexts

This study deals with the problem of knowledge reduction in decision formal contexts. From the perspective of rule acquisition, a new framework of knowledge reduction for decision formal contexts is formulated and a corresponding reduction method is also developed by using the discernibility matrix and Boolean function. The presented framework of knowledge reduction is for general decision formal contexts, and based on the proposed reduction method, knowledge hidden in a decision formal context can compactly be unravelled in the form of implication rules.

A heuristic knowledge-reduction method for decision formal contexts

Computing a minimal reduct of a decision formal context by Boolean reasoning is an NP-hard problem. Thus, it is essential to develop some heuristic methods to deal with the issue of knowledge reduction especially for large decision formal contexts. In this study, we first investigate the relationship between the concept lattice of a formal context and those of its subcontexts in preparation for deriving a heuristic knowledge-reduction method. Then, we construct a new framework of knowledge reduction in which the capacity of one concept lattice implying another is defined to measure the significance of the attributes in a consistent decision formal context. Based on this reduction framework, we formulate an algorithm of searching for a minimal reduct of a consistent decision formal context. It is proved that this algorithm is complete and its time complexity is polynomial. Some numerical experiments demonstrate that the algorithm can generally obtain a minimal reduct and is much more efficient than some Boolean reasoning-based methods.

Rule acquisition and attribute reduction in real decision formal contexts

Formal Concept Analysis of real set formal contexts is a generalization of classical formal contexts. By dividing the attributes into condition attributes and decision attributes, the notion of real decision formal contexts is introduced. Based on an implication mapping, problems of rule acquisition and attribute reduction of real decision formal contexts are examined. The extraction of “if–then” rules from the real decision formal contexts, and the approach to attribute reduction of the real decision formal contexts are discussed. By the proposed approach, attributes which are non-essential to the maximal s rules or l rules (to be defined later in the text) can be removed. Furthermore, discernibility matrices and discernibility functions for computing the attribute reducts of the real decision formal contexts are constructed to determine all attribute reducts of the real set formal contexts without affecting the results of the acquired maximal s rules or l rules.

Granular Computing and Knowledge Reduction in Formal Contexts

Granular computing and knowledge reduction are two basic issues in knowledge representation and data mining. Granular structure of concept lattices with application in knowledge reduction in formal concept analysis is examined in this paper. Information granules and their properties in a formal context are first discussed. Concepts of a granular consistent set and a granular reduct in the formal context are then introduced. Discernibility matrices and Boolean functions are, respectively, employed to determine granular consistent sets and calculate granular reducts in formal contexts. Methods of knowledge reduction in a consistent formal decision context are also explored. Finally, knowledge hidden in such a context is unraveled in the form of compact implication rules.

Approaches to knowledge reduction in generalized consistent decision formal context

This paper deals with approaches to knowledge reduction in generalized consistent decision formal context. The concept of generalized consistent decision formal context is introduced and its equivalent definitions are examined. We suggest a theory of knowledge reduction for generalized consistent decision formal context and give the judgement theorems and discernibility matrix. Based on discernibility matrix, we provide the approaches to knowledge reduction in generalized consistent decision formal context of concept lattice.

Attribute reduction theory of concept lattice based on decision formal contexts

The theory of concept lattices is an efficient tool for knowledge representation and knowledge discovery, and is applied to many fields successfully. One focus of knowledge discovery is knowledge reduction. Based on the reduction theory of classical formal context, this paper proposes the definition of decision formal context and its reduction theory, which extends the reduction theory of concept lattices. In this paper, strong consistence and weak consistence of decision formal context are defined respectively. For strongly consistent decision formal context, the judgment theorems of consistent sets are examined, and approaches to reduction are given. For weakly consistent decision formal context, implication mapping is defined, and its reduction is studied. Finally, the relation between reducts of weakly consistent decision formal context and reducts of implication mapping is discussed.