Bibliographic Details
| Title: |
Granular Structure of Type-2 Fuzzy Rough Sets over Two Universes. |
| Authors: |
Juan Lu1,2 nancylu0312@163.com, De-Yu Li1 lidy@sxu.edu.cn, Yan-Hui Zhai1 chai_yanhui@163.com, He-Xiang Bai1 baihx@sxu.edu.cn |
| Source: |
Symmetry (20738994). Nov2017, Vol. 9 Issue 11, p284. 29p. |
| Subject Terms: |
*GRANULAR materials, *FUZZY systems, *SET theory, *MATHEMATICAL logic, *ANALYTIC sets |
| Abstract: |
Granular structure plays a very important role in the model construction, theoretical analysis and algorithmdesign of a granular computingmethod. The granular structures of classical rough sets and fuzzy rough sets have been proven to be clear. In classical rough set theory, equivalence classes are basic granules, and the lower and upper approximations of a set can be computed by those basic granules. In the theory of fuzzy rough set, granular fuzzy sets can be used to describe the lower and upper approximations of a fuzzy set. This paper discusses the granular structure of type-2 fuzzy rough sets over two universes. Definitions of type-2 fuzzy rough sets over two universes are given based on a wavy-slice representation of type-2 fuzzy sets. Two granular type-2 fuzzy sets are deduced and then proven to be basic granules of type-2 fuzzy rough sets over two universes. Then, the properties of lower and upper approximation operators and these two granular type-2 fuzzy sets are investigated. At last, several examples are given to show the applications of type-2 fuzzy rough sets over two universes. [ABSTRACT FROM AUTHOR] |
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| Database: |
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