aspg-21-2226-1791475961 20261008161241 American Scientific Publishing Group admin@americaspg.com American Scientific Publishing Group International Journal of Neutrosophic Science IJNS 2692-6148 2690-6805 2024 23 1 A. Manshath Department of Mathematics & Acturial Science, B.S.Abdur Rahman Crescent Institute of Science and Technology, Kanchipuram-600048, Tamil Nadu, India E. Kungumaraj Sakthi Institute of Information and Management Studies, Pollachi, Coimbatore, Tamil Nadu - 642001, India E. Lathanayagam Akshaya College of Engineering and Technology, Kinathukadavu, Coimbatore, Tamil Nadu - 642109, India M. C. Joe Anand Department of Mathematics, Mount Carmel College (Autonomous), Affiliated to Bengaluru City University, Bengaluru - 560052, Karnataka, India Nivetha Martin Department of Mathematics, Arul Anandar College, Karumathur-625514, Tamil Nadu, India Elangovan Muniyandy Department of Biosciences, Saveetha School of Engineering, Saveetha Institute of Medical and Technical Sciences, Chennai- 602105, Tamil Nadu, India. S. Indrakumar Department of Computer Technology (UG), Kongu Engineering College, Erodu-638052, Tamil Nadu, India Neutrosophic mathematics is a branch of mathematics that deals with ambiguity, indeterminacy, and incompleteness in mathematical objects and procedures. To account for Neutrosophic uncertainty, several mathematical concepts—including the reduction formula, partial fractions, and area finding—are extended in this field. The Neutrosophic reduction formula is a technique for summarising simpler words from a complex mathematical expression when the coefficientss a nd/or values may be ambiguous or unknown. By taking the potential of insufficient information into account, expands the traditional reduction formula. A rational function can be broken down using the Neutrosophic partial fraction into several simpler expressions, where the coefficients and/or values may be ambiguous or unknown. By considering, this expands the traditional partial fraction. The potential for inaccurate information. A method for calculating the area under a curve where the curve's form or position may be unknown or ambiguous is area finding via neutrosophic integration. By considering the potential of having insufficient information, this expands the traditional area of searching. These ideas can be used in fields like decision-making, expert systems, and artificial intelligence and are crucial for handling problems in the real world that entail uncertainty, indeterminacy, and incompleteness. 2024 08 16 2226 https://creativecommons.org/licenses/by/4.0/ 10.54216/IJNS.230101 https://www.americaspg.com/journal/21/article/2226 https://www.americaspg.com/storage/11737493681.pdf