Multi-level granularity in formal concept analysis

Abstract

Formal concept analysis is a tool for data analysis and knowledge processing, and granular computing is a methodology for knowledge discovery in database. Applying granular computing into some data analysis theories, such as formal concept analysis, is a new trend in recent years. The multi-level granular analysis is an essential work in formal concept analysis. In order to combine formal concept analysis and granular computing properly, some basic and specific granules in the framework of formal concept analysis are required. By collecting and organizing the existing results in the theory of lattices and formal concept analysis, we firstly extract five types of granules on the basis of concept lattices from different perspectives and levels. They include the granules induced by objects and attributes, respectively, and the granules induced by both objects and attributes simultaneously. Then, we discuss the granules' relationships and explain their semantics. The main contribution of this study is providing some specific granules, which are practical and can be used conveniently in formal concept analysis.