Picture Fuzzy Concept Lattice Models for Knowledge Structure Analysis

Knowledge space theory is a theory that uses mathematical language to evaluate learners’ knowledge and guide future learning, belonging to the research field of mathematical psychology. Existing research results mainly focus on classical knowledge spaces, while insufficient attention has been paid to the uncertainty of data in practical problems. Therefore, this paper introduces picture fuzzy sets into knowledge space theory and combines them with formal concept analysis. The relationship between formal contexts and picture fuzzy skill mappings is discussed, and two models, namely the knowledge space picture fuzzy concept lattice and the closure space picture fuzzy concept lattice, are constructed. Based on skill atomic granules and problem atomic granules, corresponding concept construction algorithms are developed respectively, and the relationships between different fuzzy concept lattices are deeply explored. Compared with traditional fuzzy and intuitionistic models, the picture fuzzy concept lattice models proposed in this paper have significant advantages in describing uncertain information. For example, in multi-attribute decision-making scenarios, traditional models may not be able to accurately distinguish between neutral and hesitant attitudes, while the picture fuzzy concept lattice models can effectively distinguish them through the degree of neutral membership, thus enabling more precise analysis and decision-making in complex situations.