Yue-jin Lv

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 real 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.

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.

Application of Quantum Genetic Algorithm on Finding Minimal Reduct

Quantum Genetic Algorithm (QGA) is a promising area in the field of computational intelligence nowadays. Although some genetic algorithms to find minimal reduct of attributes have been proposed, most of them have some defects. On the other hand, quantum genetic algorithm has some advantages, such as strong parallelism, rapid good search capability, and small population size. In this paper, we propose a QGA to find minimal reduct based on distinction table. The algorithm can obtain the best solution with one chromosome in a short time. It is testified by two experiments that our algorithm improves the GA from four points of view: population size, parallelism, computing time and search capability.

A Heuristic Knowledge Reduction Algorithm for Real Decision Formal Contexts

Knowledge reduction is one of the key issues in real formal concept analysis. This study investigates the issue of developing efficient knowledge reduction methods for real decision formal contexts. A corresponding heuristic algorithm is proposed and some numerical experiments are conducted to assess its efficiency.

A multiple attribute decision making method with interval rough numbers based on the possibility degree

Aiming at the interval rough numbers of multiple attribute decision making (MADM) problems, a method of ranking interval rough numbers based on possibility degree is proposed. First, the deviation degree for interval rough numbers is given, and then an optimal model with maximum deviation to solve the attribute weights is set up. Second, a possibility degree formula of interval rough numbers is proposed and then we do some research on it to find out the desirable properties. Simultaneously, an algorithm to rank the interval rough numbers based on possibility degree matrix is presented. Finally, an example is provided to illustrate the application of the proposed models.

Attribute Reduction of Formal Context Based on Concept Lattice

The concept lattice is useful in knowledge processing and analyzing. And it has been used with a high intensity to knowledge reduction and data mining. This paper, from the viewpoint of concept extents, studies new and relatively reasonable formulas measuring attribute significance and proposes a theory for justifying whether an attribute set is a reduction on concept lattice, and then uses those formulas as heuristic information to design a novel and heuristic algorithm for attribute reduction on concept lattice. Finally, a real example is used to demonstrate both its feasibility and effectiveness.

A Different Quantity of Partition-Based Efficient Algorithm for Reduction of Attribute in Information Systems

Reduction of attribute is one of the key problems in rough set theory. In this paper, first, the notion of different quantity of partition is defined in information systems; from the viewpoint of which two new and relatively reasonable formulas measuring attribute significance are designed for reducing searching space. Then the two formulas are used as heuristic information to develop an efficient attribute reduction algorithm, which can avoid repeatedly calculating important value of unimportant attributes; the theoretical analysis shows that this algorithm is much less time complexity than those existed algorithms. Finally, an example and experimental results demonstrate its feasibility and effectiveness, respectively.

A New Attribute Reduction Algorithm in Continuous Information Systems

This paper puts forward a new method of discretizing continuous attributes. Compared with the traditional approach, the method, proposed in this paper, can make the number of the obtained classes be more moderate, as well as the lost information be fewer. And then a simple attribute reduction algorithm is developed in continuous information systems. Finally, a real example is used to illustrate its feasibility and effectiveness, respectively.