On Granular Algebra: A Denotational Mathematics for Modeling Granular Systems in Granular Computing
Yingxu Wang · Journal of Advanced Mathematics and Applications · 2014
Granular computing is an emerging technology for modeling and implementing complex computing architectures, behaviors, and big data manipulations. This paper presents a recent development in denotational mathematics known as granular algebra, which enables a rigorous treatment of computing granules as a generic abstract mathematical structure and granular behaviors as a set of algebraic operations. A formal granule is introduced as a mathematical model that elicits a set of basic properties of computing granules. A set of algebraic operations on formal granules is rigorously defined for the relational, reproductive, and compositional operations. A real-world case study is presented that demonstrates how concrete granules and their algebraic operations are manipulated by granular algebra. This work demonstrates that granular algebra is not only a powerful conceptual modeling methodology for granular systems, but also a practical functional specification methodology for granular computing.