Jinhai Li

Concepts reduction in formal concept analysis with fuzzy setting using Shannon entropy

In this paper we propose a method for reducing the number of formal concepts in formal concept analysis of data with fuzzy attributes. We compute the weight of fuzzy formal concepts based on Shannon entropy. Further, the number of fuzzy formal concepts is reduced at chosen granulation of their computed weight. We show that the results obtained from the proposed method are in good agreement with Levenshtein distance method and interval–valued fuzzy formal concepts method but with less computational complexity.

Cognitive concept learning from incomplete information

Cognitive concept learning is to learn concepts from a given clue by simulating human thought processes including perception, attention and thinking. In recent years, it has attracted much attention from the communities of formal concept analysis, cognitive computing and granular computing. However, the classical cognitive concept learning approaches are not suitable for incomplete information. Motivated by this problem, this study mainly focuses on cognitive concept learning from incomplete information. Specifically, we put forward a pair of approximate cognitive operators to derive concepts from incomplete information. Then, we propose an approximate cognitive computing system to perform the transformation between granular concepts as incomplete information is updated periodically. Moreover, cognitive processes are simulated based on three types of similarities. Finally, numerical experiments are conducted to evaluate the proposed cognitive concept learning methods.

Optimal scale selection in dynamic multi-scale decision tables based on sequential three-way decisions

Abstract It has been recognized that optimal scale selection in rough set theory is one of the most important problems in the study of multi-scale decision tables. Recently, much attention has been paid to this issue and quite a few appealing results have been obtained. However, the existing results are not applicable to the situation where the objects or attributes in a multi-scale decision table are sequentially updated, although this situation is frequently encountered in many real-world problems. Motivated by the fact that sequential three-way decisions are an effective mathematical tool in dealing with the data with information sequentially updated, we therefore use this methodology to investigate the optimal scale selection problem in a dynamic multi-scale decision table. Specifically, a sequential three-way decision model is first developed in multi-scale information tables, which can be viewed as multi-granularity of the universe of discourse. Then, this model is employed to present an optimal scale selection approach for such multi-scale decision tables that the number of objects is increasing. Finally, numerical experiments are conducted to evaluate the performance of the proposed optimal scale selection approach. Compared to the existing methods, the current approach does not need to consider the consistent and the inconsistent multi-scale decision tables separately and is especially suitable for updating the optimal scales of the multi-scale decision tables with new objects added.

Concept lattice compression in incomplete contexts based on K -medoids clustering

Incomplete contexts are a kind of formal contexts in which information about the relationship between some objects and attributes is not available or is lost. Knowledge discovery in incomplete contexts is of interest because such databases are frequently encountered in the real world. The existing work has proposed an approach to construct the approximate concept lattice of an incomplete context. Generally speaking, however, the huge nodes in the approximate concept lattice make the obtained conceptual knowledge difficult to be understood and weaken the efficiency of the related decision-making analysis as well. Motivated by this problem, this paper puts forward a method to compress the approximate concept lattice using K-medoids clustering. To be more concrete, firstly we discuss the accuracy measure of approximate concepts in incomplete contexts. Secondly, the similarity measure between approximate concepts is presented via the importance degrees of an object and an attribute. And then the approximate concepts of an incomplete context are clustered by means of K-medoids clustering. Moreover, we define the so-called K-deletion transformation to achieve the task of compressing the approximate concept lattice. Finally, we conduct some experiments to perform a robustness analysis of the proposed clustering method with respect to the parameters

Parallel computing techniques for concept-cognitive learning based on granular computing

\varepsilon

Influence of dynamical changes on concept lattice and implication rules

ε and K, and show the average rate of compression of approximate concept lattice.

Neighborhood attribute reduction: a multi-criterion approach

In this paper, the notion of a projected context is proposed to explore a novel algorithm of computing triadic concepts of a triadic context, and a triadic decision context is defined by combining triadic contexts. Then a rule acquisition method is presented for triadic decision contexts. It can be considered as an information fusion technology for decision-making analysis of multi-source data if the data under each condition is viewed as a single-source data. Moreover, a knowledge reduction framework is established to simplify knowledge discovery. Finally, discernibility matrix and Boolean function are constructed to compute all reducts, which is beneficial to the acquisition of compact rules from a triadic decision context.

A quantitative approach to reasoning about incomplete knowledge

Concept-cognitive learning, as an interdisciplinary study of concept lattice and cognitive learning, has become a hot research direction among the communities of rough set, formal concept analysis and granular computing in recent years. The main objective of concept-cognitive learning is to learn concepts from a give clue with the help of cognitive learning methods. Note that this kind of studies can provide concept lattice insight to cognitive learning. In order to deal with more complex data and improve learning efficiency, this paper investigates parallel computing techniques for concept-cognitive learning in terms of large data and multi-source data based on granular computing and information fusion. Specifically, for large data, a parallel computing framework is designed to extract global granular concepts by combining local granular concepts. For multi-source data, an effective information fusion strategy is adopted to obtain final concepts by integrating the concepts from all single-source data. Finally, we conduct some numerical experiments to evaluate the effectiveness of the proposed parallel computing algorithms.