Soft rough fuzzy sets and soft fuzzy rough sets |
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| Authors: | Dan Meng Xiaohong Zhang |
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| Affiliation: | a School of Economics and Information Engineering, Southwestern University of Finance and Economics, Chengdu, Sichuan 611130, Chinab Department of Mathematics, College of Arts and Sciences, Shanghai Maritime University, Shanghai, 201306, Chinac College of Mathematics, Southwest Jiaotong University, Chengdu, Sichuan 610031, China |
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| Abstract: | Fuzzy set theory, soft set theory and rough set theory are mathematical tools for dealing with uncertainties and are closely related. Feng et al. introduced the notions of rough soft set, soft rough set and soft rough fuzzy set by combining fuzzy set, rough set and soft set all together. This paper is devoted to the further discussion of the combinations of fuzzy set, rough set and soft set. A new soft rough set model is proposed and its properties are derived. Furthermore, fuzzy soft set is employed to granulate the universe of discourse and a more general model called soft fuzzy rough set is established. The lower and upper approximation operators are presented and their related properties are surveyed. |
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| Keywords: | Fuzzy set Rough set Soft set Soft rough set Soft rough fuzzy set Soft fuzzy rough set |
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