The Study Of Preclusivity Rough Approximation Operators

The core of rough set theory is a pair of lower and upper approximation operators induced from an approximation space. Using the concepts of lower and upper approximations in rough set theory, the uncertainly concepts may be unraveled and expressed through two precise concepts. Therefore, the study of approximate operator has important theoretical significance and practical value. The indiscernibility relation in classical Pawlak rough set model is an equivalence relation, it seems to be a very stringent condition that may limit the applications domain of the rough set model. In order to extend the range of applications of rough set theory, generalizations of Pawlak rough set model were considered by people, such as rough set model based on general binary relations, the variable precision rough set model, covering rough set model, fuzzy rough set model. In this paper, the constructive approaches and related properties of a new approximation operator are studied, mainly containing following two parts:1. Basic properties of preclusivity rough approximation operators.In this paper, the preclusive relation#is constructed based on general binary relation R, the preclusivity rough upper and lower approximations are defined using complement operator C and preclusive relation#. The properties such as contraction, extension, multiplication, addition, idempotency, monotone of preclusivity rough approximation operators are discussed. For general binary relation, reflexive relation, symmetric relation, reflexive and symmetric relation, the relationships between preclusivity approximation operators and the neighborhood based approximation operators are investigated.2. The topological properties of preclusivity rough approximation operators.The topological space based on the preclusivity approximation operators is constructed, in which the open sets are all lower approximation sets. The relationship among interior operator, closure operator and preclusivity rough approximation operators of this topological space are analyzed. Also, the topological space constructed by rough set based on the preclusivity relation is constructed. Furthermore, the interior operator and closure operator of this topological space have been given.