A Note on Granular Sets and Their Relation to Rough Sets

Authors:
Antoni Ligęza;Marcin Szpyrka
Affiliations:
Institute of Automatics, AGH University of Science and Technology, Al. Mickiewicza 30, 30-059 Kraków, Poland;Institute of Automatics, AGH University of Science and Technology, Al. Mickiewicza 30, 30-059 Kraków, Poland
Venue:
RSEISP '07 Proceedings of the international conference on Rough Sets and Intelligent Systems Paradigms
Year:
2007

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Abstract

The paper discusses mathematical concept of granular model for data and knowledge manipulation. In order to overcome the difficulties caused by extensive data representation a new model based on granular setsand granular relationsis put forward. The key idea is that the notion of set may consist of basic elements grouped into bigger granules. A granular set is formed from a universe set and a semi-partition defining granules of its elements. Formal definition of granular sets and some basic algebraic operations on granular sets are introduced in the paper. Further, the concept of granular relation is also defined and some possibilities of application of granular sets and relations to knowledge representation are put forward.