Complex-Valued Migrativity of Complex Fuzzy Operations
Complex fuzzy sets (CFSs), as an important extension of fuzzy sets, have been investigated in the literature. Operators of CFSs are of high importance. In addition, α−migrativity for various fuzzy operations on [0, 1] has been well discussed, where α is a real number and α∈0,1. Thus, this paper stud...
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| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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Wiley
2022-01-01
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| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2022/1813717 |
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| author | Yingying Xu Haifeng Song Lei Du Songsong Dai |
| author_facet | Yingying Xu Haifeng Song Lei Du Songsong Dai |
| author_sort | Yingying Xu |
| collection | DOAJ |
| description | Complex fuzzy sets (CFSs), as an important extension of fuzzy sets, have been investigated in the literature. Operators of CFSs are of high importance. In addition, α−migrativity for various fuzzy operations on [0, 1] has been well discussed, where α is a real number and α∈0,1. Thus, this paper studies α−migrativity for binary functions on the unit circle of the complex plane O, where α is a complex number and α∈O. In particular, we show that a binary function is α−migrativity for all α∈O if and only if it is α−migrativity for all α∈0,1∪O¯, where O¯ is the boundary point subset of O. Finally, we discuss the relationship between migrativity and rotational invariance of binary operators on O. |
| format | Article |
| id | doaj-art-cb3e700ca9a24c1da8b5aaeaabbc7e22 |
| institution | Kabale University |
| issn | 2314-4785 |
| language | English |
| publishDate | 2022-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj-art-cb3e700ca9a24c1da8b5aaeaabbc7e222025-02-03T07:26:17ZengWileyJournal of Mathematics2314-47852022-01-01202210.1155/2022/1813717Complex-Valued Migrativity of Complex Fuzzy OperationsYingying Xu0Haifeng Song1Lei Du2Songsong Dai3School of Electronics and Information EngineeringSchool of Electronics and Information EngineeringSchool of Electronics and Information EngineeringSchool of Electronics and Information EngineeringComplex fuzzy sets (CFSs), as an important extension of fuzzy sets, have been investigated in the literature. Operators of CFSs are of high importance. In addition, α−migrativity for various fuzzy operations on [0, 1] has been well discussed, where α is a real number and α∈0,1. Thus, this paper studies α−migrativity for binary functions on the unit circle of the complex plane O, where α is a complex number and α∈O. In particular, we show that a binary function is α−migrativity for all α∈O if and only if it is α−migrativity for all α∈0,1∪O¯, where O¯ is the boundary point subset of O. Finally, we discuss the relationship between migrativity and rotational invariance of binary operators on O.http://dx.doi.org/10.1155/2022/1813717 |
| spellingShingle | Yingying Xu Haifeng Song Lei Du Songsong Dai Complex-Valued Migrativity of Complex Fuzzy Operations Journal of Mathematics |
| title | Complex-Valued Migrativity of Complex Fuzzy Operations |
| title_full | Complex-Valued Migrativity of Complex Fuzzy Operations |
| title_fullStr | Complex-Valued Migrativity of Complex Fuzzy Operations |
| title_full_unstemmed | Complex-Valued Migrativity of Complex Fuzzy Operations |
| title_short | Complex-Valued Migrativity of Complex Fuzzy Operations |
| title_sort | complex valued migrativity of complex fuzzy operations |
| url | http://dx.doi.org/10.1155/2022/1813717 |
| work_keys_str_mv | AT yingyingxu complexvaluedmigrativityofcomplexfuzzyoperations AT haifengsong complexvaluedmigrativityofcomplexfuzzyoperations AT leidu complexvaluedmigrativityofcomplexfuzzyoperations AT songsongdai complexvaluedmigrativityofcomplexfuzzyoperations |