Title: Granular computing I: the concept of granulation and its formal model
Author: Tsau Young Lin
Address: 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.
Int. J. of Granular Computing, Rough Sets and Intelligent Systems, 2009 Vol.1, No.1, pp.21 - 42
Available online: 24 Jun 2009