On fundamental algebraic characterizations of complex intuitionistic <i>Q</i>-fuzzy subfield

Adela Khamis; Abd Ghafur Ahmad; Adela Khamis; Abd Ghafur Ahmad

doi:10.3934/math.2023355

AIMS Mathematics

2023, Volume 8, Issue 3: 7032-7060. doi: 10.3934/math.2023355

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On fundamental algebraic characterizations of complex intuitionistic Q-fuzzy subfield

Adela Khamis ^{1,2
,
,},
Abd Ghafur Ahmad ²

1.
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, Malaysia

Received: 16 October 2022 Revised: 30 November 2022 Accepted: 12 December 2022 Published: 11 January 2023
MSC : 06F35, 03B52, 03B05

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.
- fuzzy subfield,
- $ Q $-fuzzy set,
- $ Q $-fuzzy subfield,
- complex $ Q $-fuzzy set,
- complex intuitionistic $ Q $-fuzzy set,
- complex intuitionistic $ Q $-fuzzy subfield
Citation: Adela Khamis, Abd Ghafur Ahmad. On fundamental algebraic characterizations of complex intuitionistic Q-fuzzy subfield[J]. AIMS Mathematics, 2023, 8(3): 7032-7060. doi: 10.3934/math.2023355

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Abstract

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.

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