Formal concept analysis based on fuzzy granularity base for different granulations

This paper introduces granular computing (GrC) into formal concept analysis (FCA). It provides a unified model for concept lattice building and rule extraction on a fuzzy granularity base for different granulations. One of the strengths of GrC is that larger granulations help to hide some specific details, whereas FCA in a GrC context can prevent losses due to concept lattice complexity. However, the number of superfluous rules increases exponentially with the scale of the decision context. To overcome this we present some inference rules and maximal rules and prove that the set of all these maximal rules is complete and nonredundant. Thus, users who want to obtain decision rules should generate maximal rules. Examples demonstrate that application of the method is valid and practicable. In summary, this approach utilizes FCA in a GrC context and provides a practical basis for data analysis and processing. © 2012 Elsevier B.V. All rights reserved.