Fuzzy Concept Lattice Model for Three-Way Knowledge Space
ZHI Huilai1,2, WU Weizhi1,3, ZHU Daxin1,2
1. School of Mathematics and Computer Science, Quanzhou Normal University, Quanzhou 362000; 2. Fujian Provincial Key Laboratory of Data-Intensive Computing, Quanzhou Normal University, Quanzhou 362000; 3. School of Information Engineering, Zhejiang Ocean University, Zhoushan 316022
Abstract：The core challenge of knowledge space theory is to effectively construct knowledge structures from skill data to accurately reflect the cognitive abilities of learners, and this directly affects the precision of personalized learning guidance. In existing generation approaches and concept lattice models, knowledge states are characterized only by positive attributes, and negative attributes are disregarded. Diagnostic information included in negative attributes is completely ignored. Therefore, the variety of generated knowledge states is severely restricted, and actual complex learning paths are not covered. Assessment precision and learning path planning are greatly constrained. To overcome this limitation, the three-way decision is adopted. Negative attributes are incorporated into knowledge modeling. A three-way concept lattice model based on fuzzy skill formal contexts is established for the first time. At the theoretical level, knowledge spaces and knowledge states are defined from a three-way perspective. It is rigorously proved that the extents of all three-way fuzzy concepts constitute a complete knowledge space. The correctness of the lattice structure is validated through supremum operations. At the methodological level, granular description is introduced to define skill-induced atomic granules. A decision criterion based on atomic granule combinations is proposed to identify whether a problem set forms a knowledge state. Experiments indicate that the number of knowledge states yielded by the proposed model is substantially larger than that of the conventional models that omit negative attributes. Thus, stronger discriminative power of the proposed model is validated. Theoretical analysis confirms that the three-way concepts are structurally independent of any existing three-way concept types, and they degenerate into three-way object-oriented concepts under binary contexts. These results collectively indicate that the proposed model completes the information dimension by incorporating negative attributes. Not only expressive power is enhanced, but also a conceptual analysis framework is provided for knowledge space theory from the perspective of completeness.
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2026, Vol. 39 
