Rough fuzzy approximations on two universes of discourse |
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| Authors: | Tong-Jun Li Wen-Xiu Zhang |
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| Affiliation: | a Faculty of Science, Institute for Information and System Sciences, Xi’an Jiaotong University, Xi’an, Shaanxi 710049, PR China
b Information College, Zhejiang Ocean University, Zhoushan, Zhejiang 316004, PR China |
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| Abstract: | In rough set theory, the lower and upper approximation operators can be constructed via a variety of approaches. Various fuzzy generalizations of rough approximation operators have been made over the years. This paper presents a framework for the study of rough fuzzy sets on two universes of discourse. By means of a binary relation between two universes of discourse, a covering and three relations are induced to a single universe of discourse. Based on the induced notions, four pairs of rough fuzzy approximation operators are proposed. These models guarantee that the approximating sets and the approximated sets are on the same universes of discourse. Furthermore, the relationship between the new approximation operators and the existing rough fuzzy approximation operators on two universes of discourse are scrutinized, and some interesting properties are investigated. Finally, the connections of these approximation operators are made, and conditions under which some of these approximation operators are equivalent are obtained. |
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| Keywords: | Binary relations Coverings Fuzzy sets Rough fuzzy approximation operators Two universes |
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