Picture Fuzzy Ideals of Near-Rings
A picture fuzzy set (PFS) is an augmentation of Atanassov’s intuitionistic fuzzy set (IFS). The PFS-based models are useful in the circumstances when we face uncertain and vague information, especially in the case when we need more answers of the form “indeed,” “avoid,” “no,” and “refusal.” It has b...
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| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
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Wiley
2020-01-01
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| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2020/8857459 |
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| _version_ | 1832554001881628672 |
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| author | Awais Asif Hassen Aydi Muhammad Arshad Abdul Rehman Usman Tariq |
| author_facet | Awais Asif Hassen Aydi Muhammad Arshad Abdul Rehman Usman Tariq |
| author_sort | Awais Asif |
| collection | DOAJ |
| description | A picture fuzzy set (PFS) is an augmentation of Atanassov’s intuitionistic fuzzy set (IFS). The PFS-based models are useful in the circumstances when we face uncertain and vague information, especially in the case when we need more answers of the form “indeed,” “avoid,” “no,” and “refusal.” It has been considered as an essential tool to deal with unsure data during an investigation. In this manuscript, we explore the idea of a picture fuzzy near-ring (PFNR) and a picture fuzzy ideal (PFI) of a near-ring (NR). We illustrate some basic properties such as union, intersection, homomorphic image, and preimage of PFIs of a NR. Furthermore, there is discussion about the direct product of PFIs of a NR. |
| format | Article |
| id | doaj-art-372237189e684fecbd0e01df764f0588 |
| institution | Kabale University |
| issn | 2314-4629 2314-4785 |
| language | English |
| publishDate | 2020-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj-art-372237189e684fecbd0e01df764f05882025-02-03T05:52:30ZengWileyJournal of Mathematics2314-46292314-47852020-01-01202010.1155/2020/88574598857459Picture Fuzzy Ideals of Near-RingsAwais Asif0Hassen Aydi1Muhammad Arshad2Abdul Rehman3Usman Tariq4Department of Math & Stats, International Islamic University Islamabad, PakistanNonlinear Analysis Research Group, Ton Duc Thang University, Ho Chi Minh City, VietnamDepartment of Math & Stats, International Islamic University Islamabad, PakistanDepartment of Computer Science and Engineering, Kyungpook National University, Daegu 41566, Republic of KoreaDepartment of Computer Science, Nankai University Tianjin, Tianjin 300071, ChinaA picture fuzzy set (PFS) is an augmentation of Atanassov’s intuitionistic fuzzy set (IFS). The PFS-based models are useful in the circumstances when we face uncertain and vague information, especially in the case when we need more answers of the form “indeed,” “avoid,” “no,” and “refusal.” It has been considered as an essential tool to deal with unsure data during an investigation. In this manuscript, we explore the idea of a picture fuzzy near-ring (PFNR) and a picture fuzzy ideal (PFI) of a near-ring (NR). We illustrate some basic properties such as union, intersection, homomorphic image, and preimage of PFIs of a NR. Furthermore, there is discussion about the direct product of PFIs of a NR.http://dx.doi.org/10.1155/2020/8857459 |
| spellingShingle | Awais Asif Hassen Aydi Muhammad Arshad Abdul Rehman Usman Tariq Picture Fuzzy Ideals of Near-Rings Journal of Mathematics |
| title | Picture Fuzzy Ideals of Near-Rings |
| title_full | Picture Fuzzy Ideals of Near-Rings |
| title_fullStr | Picture Fuzzy Ideals of Near-Rings |
| title_full_unstemmed | Picture Fuzzy Ideals of Near-Rings |
| title_short | Picture Fuzzy Ideals of Near-Rings |
| title_sort | picture fuzzy ideals of near rings |
| url | http://dx.doi.org/10.1155/2020/8857459 |
| work_keys_str_mv | AT awaisasif picturefuzzyidealsofnearrings AT hassenaydi picturefuzzyidealsofnearrings AT muhammadarshad picturefuzzyidealsofnearrings AT abdulrehman picturefuzzyidealsofnearrings AT usmantariq picturefuzzyidealsofnearrings |