International Journal of Neutrosophic Science IJNS 2690-6805 2692-6148 10.54216/IJNS https://www.americaspg.com/journals/show/2226 2020 2020 Department of Mathematics & Acturial Science, B.S.Abdur Rahman Crescent Institute of Science and Technology, Kanchipuram-600048, Tamil Nadu, India A. A. Sakthi Institute of Information and Management Studies, Pollachi, Coimbatore, Tamil Nadu - 642001, India E. Kungumaraj Akshaya College of Engineering and Technology, Kinathukadavu, Coimbatore, Tamil Nadu - 642109, India E. Lathanayagam Department of Mathematics, Mount Carmel College (Autonomous), Affiliated to Bengaluru City University, Bengaluru - 560052, Karnataka, India M. C. Joe Anand Department of Mathematics, Arul Anandar College, Karumathur-625514, Tamil Nadu, India Nivetha Martin Department of Biosciences, Saveetha School of Engineering, Saveetha Institute of Medical and Technical Sciences, Chennai- 602105, Tamil Nadu, India. Elangovan Muniyandy Department of Computer Technology (UG), Kongu Engineering College, Erodu-638052, Tamil Nadu, India S. Indrakumar 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 ndor 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 andor 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 2024 08 16 10.54216/IJNS.230101 https://www.americaspg.com/articleinfo/21/show/2226