aspg-21-3618-1791472384 20261008151304 American Scientific Publishing Group admin@americaspg.com American Scientific Publishing Group International Journal of Neutrosophic Science IJNS 2692-6148 2690-6805 2025 26 1 M. Mala Research Scholar, School of Sciences, Division of Mathematics, SRM- Institute of Science and Technology; Tiruchirappalli Campus, SRM Nagar, Trichy – Chennai Highway, Near Samayapuram, Tiruchi M. Mary Jansirani Associate Professor, School of Sciences, Division of Mathematics, SRM- Institute of Science and Technology; Tiruchirappalli Campus, SRM Nagar, Trichy – Chennai Highway, Near Samayapuram, Tiru This paper introduces the concept of m:val="̆"/> mso-bidi-font-size:10.0pt;font-family:"Cambria Math",serif;mso-ascii-font-family: "Cambria Math";mso-hansi-font-family:"Cambria Math";mso-bidi-font-family: "Times New Roman";mso-bidi-theme-font:major-bidi'> style='font-size:10.0pt;font-family:"Cambria Math",serif;mso-bidi-font-family: "Times New Roman";mso-bidi-theme-font:major-bidi'> m:val="p"/>S -(3,2) ƒuzzy ᵴemigroups within an m:val="̆"/> mso-bidi-font-size:10.0pt;font-family:"Cambria Math",serif;mso-ascii-font-family: "Cambria Math";mso-hansi-font-family:"Cambria Math";mso-bidi-font-family: "Times New Roman";mso-bidi-theme-font:major-bidi'> style='font-size:10.0pt;font-family:"Cambria Math",serif;mso-bidi-font-family: "Times New Roman";mso-bidi-theme-font:major-bidi'> m:val="p"/>S -ᵴemigroup and explore their characterizations. Various comparable conditions for m:val="̆"/> mso-bidi-font-size:10.0pt;font-family:"Cambria Math",serif;mso-ascii-font-family: "Cambria Math";mso-hansi-font-family:"Cambria Math";mso-bidi-font-family: "Times New Roman";mso-bidi-theme-font:major-bidi'> style='font-size:10.0pt;font-family:"Cambria Math",serif;mso-bidi-font-family: "Times New Roman";mso-bidi-theme-font:major-bidi'> m:val="p"/>S -(3,2) ƒuzzy normal subᵴemigroups are established. Additionally, the m:val="̆"/> mso-bidi-font-size:10.0pt;font-family:"Cambria Math",serif;mso-ascii-font-family: "Cambria Math";mso-hansi-font-family:"Cambria Math";mso-bidi-font-family: "Times New Roman";mso-bidi-theme-font:major-bidi'> style='font-size:10.0pt;font-family:"Cambria Math",serif;mso-bidi-font-family: "Times New Roman";mso-bidi-theme-font:major-bidi'> m:val="p"/>S -(3,2) ƒuzzy coset, style='font-size:10.0pt;mso-ansi-font-size:10.0pt;mso-bidi-font-size:10.0pt; font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math"; mso-hansi-font-family:"Cambria Math";mso-bidi-font-family:"Times New Roman"; mso-bidi-theme-font:major-bidi'> style='font-size:10.0pt;font-family:"Cambria Math",serif;mso-bidi-font-family: "Times New Roman";mso-bidi-theme-font:major-bidi'> m:val="p"/>S -(3,2) ƒuzzy ideal, style='font-size:10.0pt;mso-ansi-font-size:10.0pt;mso-bidi-font-size:10.0pt; font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math"; mso-hansi-font-family:"Cambria Math";mso-bidi-font-family:"Times New Roman"; mso-bidi-theme-font:major-bidi'> style='font-size:10.0pt;font-family:"Cambria Math",serif;mso-bidi-font-family: "Times New Roman";mso-bidi-theme-font:major-bidi'> m:val="p"/>S -(3,2) ƒuzzy symmetric ᵴemigroup and m:val="̆"/> mso-bidi-font-size:10.0pt;font-family:"Cambria Math",serif;mso-ascii-font-family: "Cambria Math";mso-hansi-font-family:"Cambria Math";mso-bidi-font-family: "Times New Roman";mso-bidi-theme-font:major-bidi'> style='font-size:10.0pt;font-family:"Cambria Math",serif;mso-bidi-font-family: "Times New Roman";mso-bidi-theme-font:major-bidi'> m:val="p"/>S -(3,2) ƒuzzy normal subᵴemigroups are defined. The idea of conjugate m:val="̆"/> mso-bidi-font-size:10.0pt;font-family:"Cambria Math",serif;mso-ascii-font-family: "Cambria Math";mso-hansi-font-family:"Cambria Math";mso-bidi-font-family: "Times New Roman";mso-bidi-theme-font:major-bidi'> style='font-size:10.0pt;font-family:"Cambria Math",serif;mso-bidi-font-family: "Times New Roman";mso-bidi-theme-font:major-bidi'> m:val="p"/>S -(3,2) ƒuzzy ᵴemigroups is also introduced, and the order of an m:val="̆"/> mso-bidi-font-size:10.0pt;font-family:"Cambria Math",serif;mso-ascii-font-family: "Cambria Math";mso-hansi-font-family:"Cambria Math";mso-bidi-font-family: "Times New Roman";mso-bidi-theme-font:major-bidi'> style='font-size:10.0pt;font-family:"Cambria Math",serif;mso-bidi-font-family: "Times New Roman";mso-bidi-theme-font:major-bidi'> m:val="p"/>S -(3,2) ƒuzzy ᵴemigroup is determined. The (3,2) ƒuzzy semigroup condition applied to decision making process also. 2025 94 107 3618 https://creativecommons.org/licenses/by/4.0/ 10.54216/IJNS.260108 https://www.americaspg.com/journal/21/article/3618 https://www.americaspg.com/storage/41740127154.pdf