Rough Set Approximation as Formal Concept | Zendy

Nozomi Ytow | Zendy; David R. Morse | Zendy; David Roberts | Zendy

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Rough Set Approximation as Formal Concept

Author(s) -

Nozomi Ytow,

David R. Morse,

David Roberts

Publication year - 2006

Publication title -

journal of advanced computational intelligence and intelligent informatics

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.172

H-Index - 20

eISSN - 1343-0130

pISSN - 1883-8014

DOI - 10.20965/jaciii.2006.p0606

Subject(s) - formal concept analysis , rough set , lattice miner , computer science , complement (music) , generalization , formal methods , equivalence (formal languages) , set (abstract data type) , dominance based rough set approach , theoretical computer science , formal description , formal specification , object (grammar) , formal system , mathematics , discrete mathematics , artificial intelligence , algorithm , programming language , complementation , gene , phenotype , mathematical analysis , biochemistry , chemistry

Formal Concept Analysis (FCA) defines a formal concept as a pair of sets: objects and attributes, called extent and intent respectively. A rough set, on the other hand, approximates a concept using sets of objects only (in terms of FCA). We show that 1) a formal concept can be composed using a set of objects and its complement, 2) such object-based formal concepts are isomorphic to formal concepts based on objects and attributes, 3) upper and lower approximations of rough sets give generalization of formal concept, and 4) the pair of positive and negative sets (sensu rough set theory) are isomorphic to complemental formal concepts when the equivalence of the rough set gives positive and negative sets unique to each of the formal concepts. Implications of this are discussed.

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