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Attribute-oriented concept lattice and object-oriented concept lattice theory of particle reduction

Author: ZhangXiaoHua
Tutor: WeiLing
School: Northwestern University
Course: Applied Mathematics
Keywords: property oriented concept lattice object oriented concept lattice granule granular consistent set granular reduct set
CLC: O153.1
Type: Master's thesis
Year: 2011
Downloads: 59
Quote: 0
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Abstract


Fomal concept analysis, also called concept lattice theory, proposed by Wille. R in 1982, is a method for data analysis used in finding, ordering and displaying of concepts. Concept lattice is a model of knowledge representation, and an effective tool for data analysis and rule extraction. Y. Y. Yao, Duntch and Gediga introduced approximation operator of Rough Sets into concept lattices, and presented object oriented concept lattices and property oriented concept lattices respectively.Granular reduction of property oriented concept lattices and object oriented concept lattices are studied based on granulation concept. The main results of this thesis are summarized as follows:1. Granular reduction of property oriented concept lattices is studied. For a property oriented concept lattice, the granular consistent set and the granular reduct set are developed, and the granular discernibility attribute matrix and the granular discernibility attribute function are respectively employed to determine granular core attribute characteristics and calculate granular reducts. Furthermore, the ralation between a granular consistent set and a lattice consistent set of a property oriented concept lattice is discussed.2. Granular reduction of object oriented concept lattices is studied. For a object oriented concept lattice, the granular consistent set and the granular reduct set are developed, and the granular discernibility object matrix and the granular discernibility object function are respectively employed to determine granular core object characteristics and calculate granular reducts. Furthermore, the ralation between a granular consistent set and a lattice consistent set of a object oriented concept lattice is discussed.

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CLC: > Mathematical sciences and chemical > Mathematics > Algebra,number theory, portfolio theory > Abstract algebra ( Algebra ) > Collection of partial order and lattice theory
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