Fixed points of covering upper and lower approximation operators
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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.
KeywordsCovering-based Rough set Causal structure Space–time Frame
The authors thank the editor and the referee for their valuable comments and suggestions for improving the paper.
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The authors declare that they have no conflict of interest.
This article does not contain any studies with human participants or animals performed by any of the authors.
- Corsini P (1999) Rough sets, fuzzy sets and join spaces, Honorary Volume Dedicated to Prof. Emeritus J. Mittas, (Aristotle, 1999) 1–12Google Scholar
- Penrose R (1987) Techniques of Differential Topology in Relativity, Society for Industrial and Applied MathematicsGoogle Scholar
- Sorkin RD (December 1990) Spacetime and causal set, in relativity and gravitation: classical and quantum. In: Proceedings of the SILARG VII conference, Cocoyoc, Mexico, pp 150–173Google Scholar