Granular matrix-based knowledge reductions of formal fuzzy contexts

SOLO taxonomy-based knowledge structure with subjective items

As an important mathematical theory in intelligent learning and assessment system, knowledge space theory merely cares about items are mastered or non-mastered. Thus it needs to be further explored to achieve more precise and interpretable analysis. To this end, this paper mainly focuses on knowledge structures in corporate with Solo taxonomy. Then, fuzzy knowledge structure and fuzzy learning space are gradually developed. The corresponding knowledge base and surmise relation are explored respectively as well. In such case, the induced maximal knowledge space and its properties are further studied sufficiently. And three kinds of skill models are put forward based on skill proficiency. Finally, a case study is presented to illustrate the advantage in learning description.

Matrix-based reduction approach for one-sided fuzzy three-way concept lattices

Three-way concept analysis is a mathematical model of the combination of formal concept analysis and three-way decision, and knowledge discovery plays a significant impact on formal fuzzy contexts since such datasets are frequently encountered in real life. In this paper, a novel type of one-sided fuzzy three-way concept lattices is presented in a given formal fuzzy context with its complement, in which a ternary classification is available. In such case, we comprehensively explore the connections between the proposed models and classical fuzzy concept lattices among elements, sets, and orders. Furthermore, approaches to granular matrix-based reductions are investigated, by which granular consistent sets, and granular reducts via discernibility Boolean matrices are tectonically put forward. At last, the demonstrated results are performed by several experiments which enrich the research of three-way concept analysis.

Reduction of fuzzy-crisp concept lattice based on order-class matrix

Knowledge reduction is one of critical problems in data mining and information processing. It can simplify the structure of the lattice during the construction of fuzzy-crisp concept lattice. In terms of fuzzy-crisp concept, we develop an order-class matrix to represent extents and intents of concepts, respectively. In order to improve the computing efficiency, it is necessary to reduce the size of lattices as much as possible. Therefore the judgement theorem of meet-irreducible elements is proposed. To deal with attribute reductions, we develop a discernibility Boolean matrix in formal fuzzy contexts by preserving extents of meet-irreducible elements via order-class matrix. A heuristic attribute-reduction algorithm is proposed. Then we extend the proposed model to consistent formal fuzzy decision contexts. Our methods present a new framework for knowledge reduction in formal fuzzy contexts.