Pythagorean and fermatean fuzzy sub-group redefined in context of T ̃-norm and S ̃-conorm

Mishra, Vishnu Narayan; Kumar, Tarun; Sharma, Mukesh Kumar; Rathour, Laxmi

doi:10.22105/jfea.2023.396751.1262

Document Type : Research Paper

Authors

¹ Department of Mathematics, Indira Gandhi National Tribal University, Lalpur, Amarkantak, Anuppur, Madhya Pradesh 484 887, India.

² Department of Mathematics, Chaudhary Charan Singh University, Meerut, India-250004.

³ Ward Number – 16, Bhagatbandh, Anuppur 484 224, Madhya Pradesh, India.

https://doi.org/10.22105/jfea.2023.396751.1262

Abstract

This paper aims to study Pythagorean and Fermatean Fuzzy Subgroups (FFSG) in the context of -norm and -conorm functions. The paper examines the extensions of fuzzy subgroups, specifically "Pythagorean Fuzzy Subgroups (PFSG)" and "FFSG", along with their properties. In the existing literature on Pythagorean and FFSG, the standard properties for membership and non-membership functions are based on the "min" and "max" operations, respectively. However, in this work, we develop a theory that utilizes the -norm for "min" and the -conorm for "max", providing definitions of Pythagorean and FFSG with these functions, along with relevant examples. By incorporating this approach, we introduce multiple options for selecting the minimum and maximum values. Additionally, we prove several results related to Pythagorean and FFSG using the -norm and -conorm, and discuss important properties associated with them.

Keywords

Main Subjects

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Journal of Fuzzy Extension and Applications

Pythagorean and fermatean fuzzy sub-group redefined in context of T ̃-norm and S ̃-conorm

References

References

Volume 4, Issue 2
June 2023
Pages 125-135

Pythagorean and fermatean fuzzy sub-group redefined in context of T ̃-norm and S ̃-conorm

References

References

Volume 4, Issue 2June 2023Pages 125-135

Volume 4, Issue 2
June 2023
Pages 125-135