aspg-21-3902-1791475889 20261008161129 American Scientific Publishing Group admin@americaspg.com American Scientific Publishing Group International Journal of Neutrosophic Science IJNS 2692-6148 2690-6805 2025 26 4 A Study on Subsequent Expansions of the Operators S(A), Algebraic Sum, and Geometric Product over IVTNFSS K. Rajesh Department of Mathematics, Pachaiyappa’s College for Men, Kanchipuram, and Tamil Nadu – 631 501, India Nasreen kausar Department of Mathematics, Faculty of Arts and Science, Balikesir University, 10145 Balikesir, Turkey M. Kaviyarasu Department of Mathematics, Vel Tech Rangarajan Dr. Sagunthala R&D Institute of Science and Technology, Avad-600 062, Chennai, India Behzad Omidi Koma College of Engineering, American University of the Middle East, Kuwait In this work, subsequent expansions of the operators style='mso-bidi-font-style:normal'> 107%;font-family:"Cambria Math",serif;mso-fareast-font-family:Calibri; mso-fareast-theme-font:minor-latin;mso-bidi-font-family:"Times New Roman"; mso-ansi-language:EN-US;mso-fareast-language:EN-US;mso-bidi-language:AR-SA'> S(A) , algebraic sum and geometric product over IVTNFs. The first of style='mso-bidi-font-style:normal'> 107%;font-family:"Cambria Math",serif;mso-fareast-font-family:Calibri; mso-fareast-theme-font:minor-latin;mso-bidi-font-family:"Times New Roman"; mso-ansi-language:EN-US;mso-fareast-language:EN-US;mso-bidi-language:AR-SA'>S(α,β) is called the shrinking operator and the second, which is an extension of the first, is called style='mso-bidi-font-style:normal'> 107%;font-family:"Cambria Math",serif;mso-fareast-font-family:Calibri; mso-fareast-theme-font:minor-latin;mso-bidi-font-family:"Times New Roman"; mso-ansi-language:EN-US;mso-fareast-language:EN-US;mso-bidi-language:AR-SA'>(α, β) - shrink operator. The membership values & the values of non-membership be not completion our for all time possible, although in the branch of IVTNFS, it plays an additional significant character at this time, since the interval valued temporal neutrosophic fuzzy sets provides the best solution for finding the shortest distance in deciding one's career, judgment making and image processing and many more areas. Especially in medical diagnosis, when using this concept, there is a real chance that there will be a non-zero fraction of hesitation at any point in the assessment. 2025 143 154 3902 https://creativecommons.org/licenses/by/4.0/ 10.54216/IJNS.260414 https://www.americaspg.com/journal/21/article/3902 https://www.americaspg.com/storage/01749759403.pdf