Rough Mereotopology

Rough set theory and Mereotopology are two theories for knowledge representation and knowledge reasoning. Rough set theory is a method to study how to represent, learn inductively and deduce the imprecise, uncertain or imcomplete knowledge. Mereotopology is based on mereology, and uses topological means to study the boundaries and interiors of wholes, relation of connectedness, and so on. By combining mereotopology with rough set theory, we can study the topological relations of uncertain knowledge. So we discuss the theory of "Rough Mereotopology" to represent the uncertain knowledge in knowledge reasoning.The paper shows how the basic definitions in mereotopology are redefined with the method of rough set theory, such as the rough inclusion function, and shows how the rough relations between sets change when the partition changes. The theory can be used in the knowledge representation, knowledge analysis and qualitative spatial reasoning, etc.