A new approach to fuzzy group theory using (𝛼, 𝛽) -Pythagorean fuzzy sets

• Main Authors: Supriya Bhunia, Ganesh Ghorai
• Format: Article
• Language: English
• Published: Prince of Songkla University 2021-02-01
• Series: Songklanakarin Journal of Science and Technology (SJST)
• Subjects: pythagorean fuzzy set; (𝛼; 𝛽) - pythagorean fuzzy set; 𝛽) - pythagorean fuzzy subgroup; 𝛽) - pythagorean fuzzy normal subgroup; 𝛽) - pythagorean fuzzy level subgroup
• Online Access: http://rdo.psu.ac.th/sjstweb/journal/43-1/38.pdf

A Pythagorean fuzzy set (PFS) is a very efficient and powerful tool for handling uncertainty and vagueness. In this paper, we present the notion of (𝛼, 𝛽) -Pythagorean fuzzy set (PFS) as a generalisation of Pythagorean fuzzy set (PFS). We propose a new fuzzy subgroup, called (𝛼, 𝛽) -Pythagorean fuzzy subgroup (PFSG). We investigate properties of our proposed fuzzy subgroup. We present the concept of (𝛼, 𝛽) -Pythagorean fuzzy coset (PFC) and (𝛼, 𝛽) -Pythagorean fuzzy normal subgroup (PFNSG). Furthermore, we define (𝛼, 𝛽) -Pythagorean fuzzy level subgroup (PFLSG) and establish properties of it.