Textural unit operations in rough set theory

Abstract

In this study, we introduce a textural counterpart of the unit operation of Wybraniec-Skardowska. A unit di-operation has two parts which are called a unit co-operation and a unit operation, respectively. In this respect, we have two types of symmetry. We show that the symmetricity of direlations is equivalent to the Galois connectivity of unit di-operations. For discrete textures, we determine the image co-operation of a unit co-operation. We prove that the symmetricity and duality are equivalent concepts for unit di-operations if one of the compounds is symmetric. We consider definability in terms of unit operations and unit co-operations. Further, we present a categorical discussion defining a category UN whose structures of objects are unit operations. We show that the category Rel whose objects are approximation spaces and morphisms are relation preserving functions can be embedded into UN.