Set-theoretic Approaches to Granular Computing

Authors:
Yiyu Yao;Nan Zhang;Duoqian Miao;Feifei Xu
Affiliations:
Department of Computer Science, University of Regina, Regina, Saskatchewan, Canada S4S 0A2, Canada. yyao@cs.uregina.ca;(Correspd.) Department of Computer Science and Technology, Tongji University, Shanghai, China 201804, China. zhangnan0851@163.com;Department of Computer Science and Technology, Tongji University, Shanghai, China 201804, China. miaoduoqian@163.com;Department of Computer Science and Technology, Tongji University, Shanghai, China 201804, China. xufeifei1983@hotmail.com
Venue:
Fundamenta Informaticae - Rough Sets and Knowledge Technology (RSKT 2010)
Year:
2012

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Abstract

A framework is proposed for studying a particular class of set-theoretic approaches to granular computing. A granule is a subset of a universal set, a granular structure is a family of subsets of the universal set, and relationship between granules is given by the standard set-inclusion relation. By imposing different conditions on the family of subsets, we can define several types of granular structures. A number of studies, including rough set analysis, formal concept analysis and knowledge spaces, adopt specific models of granular structures. The proposed framework therefore provides a common ground for unifying these studies. The notion of approximations is examined based on granular structures.