Multiview granular data analytics based on three-way concept analysis

Multiview granular data analytics reflects various aspects of the knowledge embodied in data by multiple granular structures. It has been investigated in many topics closely related to granular computing, especially those researches involving formal concept analysis. Three-way concept analysis has demonstrated its usefulness for knowledge discovery in formal contexts, since it can extract positive information and negative information between objects and attributes simultaneously. Taking advantage of it, we propose a concrete model of multiview granular data analytics based on three-way concept analysis. Firstly, two hexagons of trisections in three-way concept analysis are presented. The hexagons reveal two different trisection forms in existing three-way concept lattice models. These models are then accordingly grouped into two classes, namely, orthopair-based weak tri-partition model and weak tri-covering model. Secondly, interval-set-based weak tri-partition model of three-way concept lattices is designed by reformulating the knowledge ordering of interval sets. More specifically, sufficiency-possibility three-way concept lattices and necessity-dual three-way concept lattices are defined on the basis of different combinations of modal-style operators. Finally, the transformation methods among various types of three-way concept lattices are explored by analyzing their relationships. Further interpretations of the hidden semantics in these relationships are also given in terms of trisection.