On the System Algebra Foundations for Granular Computing

Granular computing studies a novel approach to computing system modeling and information processing. Although a rich set of work has advanced the understanding of granular computing in dealing with the “to be” and “to have” problems of systems, the “to do” aspect of system modeling and behavioral implementation has been relatively overlooked. On the basis of a recent development in denotational mathematics known as system algebra, this paper presents a system metaphor of granules and explores the theoretical and mathematical foundations of granular computing. An abstract system model of granules is proposed in this paper. Rigorous manipulations of granular systems in computing are modeled by system algebra. The properties of granular systems are analyzed, which helps to explain the magnitudes and complexities of granular systems. Formal representation of granular systems for computing is demonstrated by real-world case studies, where concrete granules and their algebraic operations are explained. DOI: 10.4018/978-1-4666-0261-8.ch007