δ-granular reduction in formal fuzzy contexts: Boolean reasoning, graph represent and their algorithms

The fuzzy concept lattice is one of the effective tools for data mining, and granular reduction is one of its significant research contents. However, little research has been done on granular reduction at different granularities in formal fuzzy contexts (FFCs). Furthermore, the complexity of the composition of the fuzzy concept lattice limits the interest in its research. Therefore, how to simplify the concept lattice structure and how to construct granular reduction methods with granularity have become urgent issues that need to be investigated. To this end, firstly, the concept of an object granule with granularity is defined. Secondly, two reduction algorithms, one based on Boolean reasoning and the other on a graph-theoretic heuristic, are formulated while keeping the structure of this object granule unchanged. Further, to simplify the structure of the fuzzy concept lattice, a partial order relation with parameters is proposed. Finally, the feasibility and effectiveness of our proposed reduction approaches are verified by data experiments.