Fixed points of covering upper and lower approximation operators

Abstract

Pawlak’s rough set and its extension, covering-based rough set, are important techniques for reasoning in incomplete information systems. In this paper, by studying some results about the Feynman paths, we show that the family of all fixed points of covering upper and lower approximation operators is an atomic frame and a complete lattice, respectively. Then, we find a relation between some major causal operators of relativity theory and covering approximation operators. As a result of this connection, we introduce a Feynman index to classify space–times.