Textures and dynamic relational systems

Dynamic relational systems have different forms in literature of rough set theory. They are divided into two parts by Pagliani as synchronic and diachronic dynamics. Synchronic dynamic case is related to the presence of a multi-sources. In the case of diachronic dynamics, it is supposed that changes occur in time. These changes are related to new objects, attributes or attribute values entered into the system. Here, we consider the dynamic systems which are related to the both of these types of dynamics. In a recent paper, the author studied on the results about reduct, definability and quasi-uniformity in dynamic relational systems. Here, the natural generalizations of these results are given. In particular, it is proved that weak and strong definabilities are preserved under pre-images with respect to direlation preserving difunctions between textural dynamic relational systems. Further, the connections between definable sets and the ditopology are determined by ditopologies of reflexive direlations. Then it is given some basic results on ditopologies induced by direlations and direlational quasi-uniformities. Morover, it is discussed on the connections between textural approximation spaces and direlational-quasi uniformities.