On fundamental algebraic characterizations of complex intuitionistic Q-fuzzy subfield
The main objective of this study is to propose a new notion of a complex intuitionistic Q-fuzzy subfield of a field F that is developed from the concept of a complex fuzzy subfield of a field F by adding the notion of intuitionistic Q-fuzzy into a complex fuzzy subfield. We establish a new structure...
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| Format: | Article |
| Language: | English |
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AIMS Press
2023-01-01
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| Series: | AIMS Mathematics |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/math.2023355?viewType=HTML |
| _version_ | 1797936923772190720 |
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| author | Adela Khamis Abd Ghafur Ahmad |
| author_facet | Adela Khamis Abd Ghafur Ahmad |
| author_sort | Adela Khamis |
| collection | DOAJ |
| description | The main objective of this study is to propose a new notion of a complex intuitionistic Q-fuzzy subfield of a field F that is developed from the concept of a complex fuzzy subfield of a field F by adding the notion of intuitionistic Q-fuzzy into a complex fuzzy subfield. We establish a new structure of complex fuzzy subfields which is called complex intuitionistic Q-fuzzy subfield. The most significant advantage of this addition appears to be that it broadens the scope of the investigation from membership function values to membership and non-membership function values. The range of complex fuzzy subfields is expanded to the unit disc in the complex plane for both membership and non-membership functions. Some fundamental operations, especially the intersection, union, and complement of complex intuitionistic Q-fuzzy subfields are studied. We define the necessity and possibility operators on a complex intuitionistic Q-fuzzy subfield. Moreover, we show that each complex intuitionistic Q-fuzzy subfield generates two intuitionistic Q-fuzzy subfields. Subsequently, several related theorems are proven. |
| first_indexed | 2024-04-10T18:36:48Z |
| format | Article |
| id | doaj.art-dbaad247154b4c8e9d38d5ae4315d2b5 |
| institution | Directory Open Access Journal |
| issn | 2473-6988 |
| language | English |
| last_indexed | 2024-04-10T18:36:48Z |
| publishDate | 2023-01-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | AIMS Mathematics |
| spelling | doaj.art-dbaad247154b4c8e9d38d5ae4315d2b52023-02-02T01:11:49ZengAIMS PressAIMS Mathematics2473-69882023-01-01837032706010.3934/math.2023355On fundamental algebraic characterizations of complex intuitionistic Q-fuzzy subfieldAdela Khamis0Abd Ghafur Ahmad 11. Department of Mathematics, Faculty of Education, Seiyun University, Hadhramout, Yemen 2. Department of Mathematical Science, Faculty of Sciences and Technology, Universiti Kebangsaan Malaysia, 43600 UKM Bangi, Selangor, Malaysia2. Department of Mathematical Science, Faculty of Sciences and Technology, Universiti Kebangsaan Malaysia, 43600 UKM Bangi, Selangor, MalaysiaThe main objective of this study is to propose a new notion of a complex intuitionistic Q-fuzzy subfield of a field F that is developed from the concept of a complex fuzzy subfield of a field F by adding the notion of intuitionistic Q-fuzzy into a complex fuzzy subfield. We establish a new structure of complex fuzzy subfields which is called complex intuitionistic Q-fuzzy subfield. The most significant advantage of this addition appears to be that it broadens the scope of the investigation from membership function values to membership and non-membership function values. The range of complex fuzzy subfields is expanded to the unit disc in the complex plane for both membership and non-membership functions. Some fundamental operations, especially the intersection, union, and complement of complex intuitionistic Q-fuzzy subfields are studied. We define the necessity and possibility operators on a complex intuitionistic Q-fuzzy subfield. Moreover, we show that each complex intuitionistic Q-fuzzy subfield generates two intuitionistic Q-fuzzy subfields. Subsequently, several related theorems are proven.https://www.aimspress.com/article/doi/10.3934/math.2023355?viewType=HTMLfuzzy subfieldq-fuzzy setq-fuzzy subfieldcomplex q-fuzzy setcomplex intuitionistic q-fuzzy setcomplex intuitionistic q-fuzzy subfield |
| spellingShingle | Adela Khamis Abd Ghafur Ahmad On fundamental algebraic characterizations of complex intuitionistic Q-fuzzy subfield AIMS Mathematics fuzzy subfield q-fuzzy set q-fuzzy subfield complex q-fuzzy set complex intuitionistic q-fuzzy set complex intuitionistic q-fuzzy subfield |
| title | On fundamental algebraic characterizations of complex intuitionistic Q-fuzzy subfield |
| title_full | On fundamental algebraic characterizations of complex intuitionistic Q-fuzzy subfield |
| title_fullStr | On fundamental algebraic characterizations of complex intuitionistic Q-fuzzy subfield |
| title_full_unstemmed | On fundamental algebraic characterizations of complex intuitionistic Q-fuzzy subfield |
| title_short | On fundamental algebraic characterizations of complex intuitionistic Q-fuzzy subfield |
| title_sort | on fundamental algebraic characterizations of complex intuitionistic q fuzzy subfield |
| topic | fuzzy subfield q-fuzzy set q-fuzzy subfield complex q-fuzzy set complex intuitionistic q-fuzzy set complex intuitionistic q-fuzzy subfield |
| url | https://www.aimspress.com/article/doi/10.3934/math.2023355?viewType=HTML |
| work_keys_str_mv | AT adelakhamis onfundamentalalgebraiccharacterizationsofcomplexintuitionisticqfuzzysubfield AT abdghafurahmad onfundamentalalgebraiccharacterizationsofcomplexintuitionisticqfuzzysubfield |