On Cohesive Fuzzy Sets, Operations and Properties with Applications in Electromagnetic Signals and Solar Activities
In the present communication, a new concept of a cohesive fuzzy set (CHFS) has been proposed as a synchronized generalization of complex fuzzy sets and hesitant fuzzy sets in a systematic way. The novelty of the introduced notion lies in the selection of the best alternative among the available mult...
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| Format: | Article |
| Language: | English |
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MDPI AG
2023-02-01
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| Series: | Symmetry |
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| Online Access: | https://www.mdpi.com/2073-8994/15/3/595 |
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| author | Xingsi Xue Mahima Poonia Ghaida Muttashar Abdulsahib Rakesh Kumar Bajaj Osamah Ibrahim Khalaf Himanshu Dhumras Varun Shukla |
| author_facet | Xingsi Xue Mahima Poonia Ghaida Muttashar Abdulsahib Rakesh Kumar Bajaj Osamah Ibrahim Khalaf Himanshu Dhumras Varun Shukla |
| author_sort | Xingsi Xue |
| collection | DOAJ |
| description | In the present communication, a new concept of a cohesive fuzzy set (CHFS) has been proposed as a synchronized generalization of complex fuzzy sets and hesitant fuzzy sets in a systematic way. The novelty of the introduced notion lies in the selection of the best alternative among the available multiple favorable situations, where the possibility of its range is in the extended unit circle of the complex plane. We study the relationship between the CHFS and the complex intuitionistic fuzzy set (CIFS), along with validation of the obtained results. On the basis of the proposed notion, various properties, operations, and identities have been established with their necessary proof. The applications of CHFS in the process of filtering the signals for obtaining the reference signal using the necessary Fourier cosine transform or inverse Fourier cosine transform and identifying the maximum number of sunspots in a particular interval of solar activity have been suitably discussed with illustrative numerical examples. Some advantages of incorporating the proposed notion have also been tabulated for better understanding. |
| first_indexed | 2024-03-11T05:50:45Z |
| format | Article |
| id | doaj.art-f600224b4a3e453bbe4c633826e086a5 |
| institution | Directory Open Access Journal |
| issn | 2073-8994 |
| language | English |
| last_indexed | 2024-03-11T05:50:45Z |
| publishDate | 2023-02-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Symmetry |
| spelling | doaj.art-f600224b4a3e453bbe4c633826e086a52023-11-17T14:08:13ZengMDPI AGSymmetry2073-89942023-02-0115359510.3390/sym15030595On Cohesive Fuzzy Sets, Operations and Properties with Applications in Electromagnetic Signals and Solar ActivitiesXingsi Xue0Mahima Poonia1Ghaida Muttashar Abdulsahib2Rakesh Kumar Bajaj3Osamah Ibrahim Khalaf4Himanshu Dhumras5Varun Shukla6Fujian Provincial Key Laboratory of Big Data Mining and Applications, Fujian University of Technology, Fuzhou 350118, ChinaDepartment of Mathematics, Jaypee University of Information Technology, Solan 173234, IndiaDepartment of Computer Engineering, University of Technology, Baghdad 10066, IraqDepartment of Mathematics, Jaypee University of Information Technology, Solan 173234, IndiaDepartment of Solar, Al-Nahrain Research Center for Renewable Energy, Al-Nahrain University, Baghdad 64040, IraqDepartment of Mathematics, Jaypee University of Information Technology, Solan 173234, IndiaDepartment of Eelectronics & Communication Engineering, Pranveer Singh Institute of Technology, Kanpur 209305, IndiaIn the present communication, a new concept of a cohesive fuzzy set (CHFS) has been proposed as a synchronized generalization of complex fuzzy sets and hesitant fuzzy sets in a systematic way. The novelty of the introduced notion lies in the selection of the best alternative among the available multiple favorable situations, where the possibility of its range is in the extended unit circle of the complex plane. We study the relationship between the CHFS and the complex intuitionistic fuzzy set (CIFS), along with validation of the obtained results. On the basis of the proposed notion, various properties, operations, and identities have been established with their necessary proof. The applications of CHFS in the process of filtering the signals for obtaining the reference signal using the necessary Fourier cosine transform or inverse Fourier cosine transform and identifying the maximum number of sunspots in a particular interval of solar activity have been suitably discussed with illustrative numerical examples. Some advantages of incorporating the proposed notion have also been tabulated for better understanding.https://www.mdpi.com/2073-8994/15/3/595hesitant fuzzy setcomplex fuzzy setcomplex intuitionistic fuzzy setelectromagnetic signalssunspots |
| spellingShingle | Xingsi Xue Mahima Poonia Ghaida Muttashar Abdulsahib Rakesh Kumar Bajaj Osamah Ibrahim Khalaf Himanshu Dhumras Varun Shukla On Cohesive Fuzzy Sets, Operations and Properties with Applications in Electromagnetic Signals and Solar Activities Symmetry hesitant fuzzy set complex fuzzy set complex intuitionistic fuzzy set electromagnetic signals sunspots |
| title | On Cohesive Fuzzy Sets, Operations and Properties with Applications in Electromagnetic Signals and Solar Activities |
| title_full | On Cohesive Fuzzy Sets, Operations and Properties with Applications in Electromagnetic Signals and Solar Activities |
| title_fullStr | On Cohesive Fuzzy Sets, Operations and Properties with Applications in Electromagnetic Signals and Solar Activities |
| title_full_unstemmed | On Cohesive Fuzzy Sets, Operations and Properties with Applications in Electromagnetic Signals and Solar Activities |
| title_short | On Cohesive Fuzzy Sets, Operations and Properties with Applications in Electromagnetic Signals and Solar Activities |
| title_sort | on cohesive fuzzy sets operations and properties with applications in electromagnetic signals and solar activities |
| topic | hesitant fuzzy set complex fuzzy set complex intuitionistic fuzzy set electromagnetic signals sunspots |
| url | https://www.mdpi.com/2073-8994/15/3/595 |
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