Learning multi-granularity decision implication in correlative data from a logical perspective

Formal Concept Analysis (FCA) is a method rooted in order theory, with the aim of analyzing and visually representing concepts. Decision implication serves as a fundamental means of knowledge representation in FCA in the case of decision-making. This paper extends the scope of knowledge discovery within FCA in single domains to the realm of multi-domains, with introducing a framework for knowledge representation and reasoning within correlative data from the perspectives of cross-domain and multi-granularity. Firstly, we delve into the acquisition and modeling of decision knowledge within correlative data, and introduce the concept of multi-granularity decision implication. We then establish multi-granularity decision implication logic to study the completeness, non-redundancy and optimality of multi-granularity decision implications and introduce inference rules with semantical compatibility. Furthermore, we define lattice fusion decision context to seamlessly integrate information within correlative data and construct a multi-granularity decision implication basis (MGDIB) based on lattice fusion decision context. Finally, we conduct an experiment of generating MGDIB based on GroupLens_MovieLens dataset.