Granular algebra for modeling granular systems and granular computing

Granular computing provides a new perspective on computing architectures and behaviors. 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. An abstract granule is modeled as a mathematical entity that elicits a set of basic properties of computing granules. Then, a set of algebraic operations on abstract granules is defined such as the relational, reproductive, and compositional operations. A real-world case study is presented that demonstrates how concrete granules and their algebraic operations are derived based on granular algebra. This work shows that granular algebra is not only a powerful conceptual modeling methodology for granular systems, but also a functional specification methodology for granular computing.