Title: Granular computing I: the concept of granulation and its formal model

Authors: Tsau Young Lin

Addresses: Department of Computer Science, San Jose State University, San Jose, California 95192, USA

Abstract: The term granular computing (GrC) was coined by Lin and Zadeh (derived from Zadeh|s granular mathematics) in Fall, 1996. Since then, nine GrC models have been proposed. In GrC2008 keynote, the category theory based model (8th GrC model) was proposed to be |the (final) GrC model|; however, the announcement was not in time to be included in the proceedings. So this paper is the first printed presentation. This paper explains the concept of granulation in three ways: it is defined 1) inductively by classical example; 2) informally by Zadeh, 3) formally by the category-based GrC model. It outlines how this model can be specified into nine models by specifying the abstract category to the category of; 1) sets/type I fuzzy sets; 2) functions/generalised functions such as, random variables (measurable functions), measures/probabilities; 3) Turing machines/clusters of computers; 4) qualitative fuzzy sets. The concept of qualitative fuzzy sets is new and quite novel; we have explained it via neighbourhood systems.

Keywords: granular computing; GrC; category theory; neighbourhood systems; Heisenberg uncertainty principle; discretionary access control; social networking; cloud computing; simplicial complex; binary relation; infinitesimal; qualitative fuzzy sets; clusters.

DOI: 10.1504/IJGCRSIS.2009.026723

International Journal of Granular Computing, Rough Sets and Intelligent Systems, 2009 Vol.1 No.1, pp.21 - 42

Published online: 24 Jun 2009 *

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