Granulation and granularity via conceptual structures: a perspective from the point of view of fuzzy concept lattices

Authors:
Radim Bělohlávek
Affiliations:
Institute for Research and Applications of Fuzzy Modeling, University of Ostrava, Bráfova 7, CZ-701 03 Ostrava, Czech Republic
Venue:
Data mining, rough sets and granular computing
Year:
2002

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Abstract

A fundamental way of granulation the outer world performed by humans is that by forming concepts. We present a formal model of concepts and conceptual structures called fuzzy concept lattices which is a natural formalization of the Port-Royal approach to concepts. Fuzzy concepts, i.e. the induced fuzzy granules, obey a complete hierarchy w.r.t, subconcept-superconcept relation. Attention is paid to similarity relations (similarity of objects, concepts and conceptual structures are distinguished) and to logical precision both of which represent a systematic way to control the granularity and reduce the complexity of the conceptual structure. Applications in conceptual data analysis and representation of conceptual knowledge are discussed.