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

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 exist...

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Bibliographic Details
Published inJournal of fuzzy extension & applications (Online) Vol. 4; no. 2; pp. 125 - 135
Main Authors Vishnu Mishra, Tarun Kumar, Mukesh Sharma, Laxmi Rathour
Format Journal Article
LanguageEnglish
Published Ayandegan Institute of Higher Education 01.06.2023
Subjects
fermatean fuzzy subgroups
fuzzy sets
pythagorean fuzzy subgroups
s ̃-conorm
t ̃-norm
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Summary: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.
ISSN:2783-1442
2717-3453
DOI:10.22105/jfea.2023.396751.1262