The Concept And The Nature Of The Relationship Between Granular Computing Systems

Concept lattice, also known as formal concept analysis, was proposed by R Willein1982. Concept lattice is a data structure based on relations of objects and attributesin formal context. It embodies the relationship between concept generation and con-cept specialization. After years of development, the concept lattice theory has beenwidely applied to knowledge engineering, data mining, information retrieval, softwareengineering, and other felds.In the feld of computational intelligence, granular computing is a new way tosimulate human thinking to help solve complicated problems. Granular computing playsan important role in uncertain, inaccurate and incomplete information processing andmassive data mining. Under the theories of concept lattice and granular computing,concept granule computing system was builded in literature [1]. The paper studiedconcept recognition problems of concept granule computing system and relationships ofconcept granule computing systems, while discussing attribute recognition problems ofconcept granule computing systems.The main results and originalities of this paper are as follows:Based on fuzzy formal context and the characteristics of extension intensionoperator and intension extension operator, concept extension recognition problems ofconcept granule computing system are studied. Concept extension properties and dis-criminant theorems of two concept granule computing systems that extension is classicset, intension is fuzzy set, and the reverse are represented.According to diferent types of operators, three concept granule computing sys-tems are builded, namely modle I(#,#), modle I(◇,□)and modle I(□,◇). The relationalmodels of concept extension between I(#,#)and I(◇,□), I(#,#)and I(□,◇)are established.According to properties of concept lattice attribute feature, attribute featurerecognitions of concept granule computing systems under fuzzy formal context are re-searched. Attribute feature recognition methods of concept granule computing systemsare given.