A novel approach to fuzzy rough sets based on a fuzzy covering |
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| Affiliation: | 1. College of Science, Harbin Engineering University, Harbin 150001, PR China;2. Department of Mathematics, Harbin Institute of Technology, Harbin 150001, PR China;3. Department of Automation, Tsinghua University, Beijing 100084, PR China;1. School of Mathematical Sciences, Shandong Normal University, Jinan 250014, PR China;2. School of Mathematics and Statistics, Wuhan University, Wuhan 430072, PR China;1. State Key Laboratory of Software Development Environment, Beihang University, Beijing 100191, China;2. School of Computer Science and Engineering, Beihang University, Beijing, China;3. Department of Computer Science, New York University, New York, NY 10012, USA;4. College of Mathematics and Information Science, Hebei Normal University, Shijiazhuang, Hebei 050016, China;1. Department of Applied Mathematics, Computer Science and Statistics, Ghent University, Belgium;2. Department of Computer Science and Artificial Intelligence, Research Center on Information and Communications Technology (CITIC-UGR), University of Granada, Spain;3. Artificial Intelligence Research Institute (IIIA), Spanish National Research Council (CSIC), Bellaterra, Spain;1. School of Mathematics and Statistics, Shandong Normal University, Jinan 250014, PR China;2. School of Mathematics and Physics, Qingdao University of Science and Technology, Qingdao 266061, PR China;1. Department of Applied Mathematics, Computer Science and Statistics, Ghent University, Belgium;2. Department of Computer Science and Artificial Intelligence, Research Center on Information and Communications Technology (CITIC-UGR), University of Granada, Spain |
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| Abstract: | This paper proposes an approach to fuzzy rough sets in the framework of lattice theory. The new model for fuzzy rough sets is based on the concepts of both fuzzy covering and binary fuzzy logical operators (fuzzy conjunction and fuzzy implication). The conjunction and implication are connected by using the complete lattice-based adjunction theory. With this theory, fuzzy rough approximation operators are generalized and fundamental properties of these operators are investigated. Particularly, comparative studies of the generalized fuzzy rough sets to the classical fuzzy rough sets and Pawlak rough set are carried out. It is shown that the generalized fuzzy rough sets are an extension of the classical fuzzy rough sets as well as a fuzzification of the Pawlak rough set within the framework of complete lattices. A link between the generalized fuzzy rough approximation operators and fundamental morphological operators is presented in a translation-invariant additive group. |
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