Axiomatization of covering-based approximation operators generated by general or irreducible coverings

摘要

The axiomatization problems for generalized approximation operators are finding logical characters of these operators. Solving these problems is important not only for conceptual understanding generalized approximation operators, but also for theoretic discussing the properties of them. In recent years, many researchers explored and developed the axiomatic approach of generalized rough set theory and a lot of articles about axiomatizations of approximation operators were published. However, there are numbers of axiomatization problems for covering-based approximation operators are still open. In this article, we give axiomatic systems for several types of covering-based approximation operators. All the axiomatic systems given by us are original and one of our results answers an open problem raised by Zhu and Wang in 2007. We also discuss axiomatization problems for those covering-based approximation operators generated by irreducible coverings. We prove that for most types of operators, the axiomatic systems generated by irreducible coverings and by general coverings are the same. On the other hand, we show that for one type of operators, the axiomatic systems generated by irreducible coverings and by general coverings are different, and we give an axiomatic system for this type of operators generated by irreducible coverings. By several examples, we show that for each axiomatic system presented in this paper, conditions are independent of each other. (C) 2018 Published by Elsevier Inc.