Granular Structure Merging Algorithm Based on Category Theory

摘要

In order to solve the problem of conversion from the finer level of granularity to the coarser level of granularity, this paper proposes a formal method for Granular structure merging based on category theory. Firstly, it takes the granular structure as the granular object and the granular structure mapping as the granular morphism, then the granular object and the granular morphism compose the granular structure category. Secondly, it uses the granular morphism and the granular pushout to achieve the granular structure merging, then gets the granular structure merging algorithm (GrSM). Finally, the author illustrates the method with the concrete examples, which solves the granular structure merging issue. This method has a solid mathematical foundation and methodology, which is worth further study.