Rough fuzzy approximations on two universes of discourse
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- 作者：Tong-Jun Li ; Wen-Xiu Zhang
- 关键词：Binary relations ; Coverings ; Fuzzy sets ; Rough fuzzy approximation operators ; Two universes
- 刊名：Information Sciences
- 出版年：2008
- 出版时间：1 February 2008
- 年：2008
- 卷：178
- 期：3
- 页码：892-906
- 全文大小：227 K
文摘
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.