Abstract: In different fields a conception of granules is applied both as a group of elements defined by internal properties and as something inseparable whole reflecting external properties. Granular computing may be interpreted in terms of abstraction, generalization, clustering, levels of abstraction, levels of detail, and so on. We have proposed to use multialgebraic systems as a mathematical tool for synthesis and analysis of granules and granule structures. The theorem of necessary and sufficient conditions for multialgebraic systems existence has been proved.

Keywords: granular computing, multirelations, multioperations.

ACM Classification Keywords: I.2.4 Knowledge representation formalisms and methods: relation systems.

Link:

MULTIALGEBRAIC SYSTEMS IN INFORMATION GRANULATION

Alexander Kagramanyan, Vladimir Mashtalir, Vladislav Shlyakhov

http://www.foibg.com/ijita/vol15/ijita15-1-p09.pdf