Stability of three-way concepts and its application to natural language generation

Three-way concept analysis (3WCA) has been an emerging and important methodology for knowledge discovery and data analysis. Particularly, 3WCA can efficiently characterize the information of “jointly possessed” and “jointly not possessed” compared to the classical formal concept only can describe common attributes owned by objects. This property, typical of 3WCA has a huge potential in the field of Natural Language Generation (NLG). However, the construction of a three-way concept lattice is proved as an NP-complete problem and even harder than the construction of conventional concept lattice. This could negatively affect the use of 3WCA for NLG in real contexts. Hence, it is necessary to prune the three-way concept lattice and extract more interesting three-way concepts for knowledge acquisition. To this end, this paper defines the stability of a three-way concept and analyzes the relevant properties. An efficient computational algorithm for calculating the stability of three-way concepts is developed and evaluated by an experiment. In addition, a case study on NLG is conducted for demonstrating the applicability of the proposed technique.