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.
Highlights
The concept of granulation plays an essential role in human cognition, especially in the realm of everyday reasoning (Pedrycz 2013).Originally, the notion of granulation can be rooted in the concept of a linguistic variable, which was introduced by Zadeh (1973). Zadeh (1979) contributed the first paper on information granularity
Pedrycz (2014) suggested that granular computing has emerged as a unified and coherent platform of constructing, describing, and processing information granules, which can be treated as a definition of GrC from the perspective of description
Since a concept lattice is a lattice, we introduce an important notion in theory of lattices, it will be one of the granules in our research
Summary
The concept of granulation plays an essential role in human cognition, especially in the realm of everyday reasoning (Pedrycz 2013). Pedrycz (2014) suggested that granular computing has emerged as a unified and coherent platform of constructing, describing, and processing information granules, which can be treated as a definition of GrC from the perspective of description. Besides these contribution, Bargiela and Pedrycz have a deep research about GrC (Bargiela and Pedrycz 2003, 2005a, b; Pedrycz 2005; Bargiela and Pedrycz 2008).
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