## International Journal of Neutrosophic Science

##### Journal DOI

https://doi.org/10.54216/IJNS

2690-6805ISSN (Online) 2692-6148ISSN (Print)

#### Neutrosophic Integrals by Reduction Formula and Partial Fraction Methods for Indefinite Integrals

##### A. Manshath , E. Kungumaraj , E. Lathanayagam , M. C. Joe Anand , Nivetha Martin , Elangovan Muniyandy , 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&mdash;including the reduction formula, partial fractions, and area finding&mdash;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.

Vol. 23 Issue. 1 PP. 08-16, (2024)

#### Î´-separation Axioms on Fuzzy Hypersoft Topological Spaces

##### P. Surendra , A. Vadivel , K. Chitirakala

In this article, the concept of fuzzy hypersoft &delta; (resp. semi, pre, &delta; semi &amp; &delta; pre)-separation axioms in fuzzy hypersoft topological spaces are introduced by developing fuzzy hypersoft &delta; (resp. semi, pre, &delta; semi &amp; &delta; pre)-neighbourhood with respect to fuzzy hypersoft points. Also, the properties and relations between fuzzy hypersoft &delta; (resp. semi, pre, &delta; semi &amp; &delta; pre)- Ti- spaces (i = 0, 1, 2, 3, 4) are discussed.

Vol. 23 Issue. 1 PP. 17-26, (2024)

#### Effective Neutrosophic Soft Expert Set and Its Application

##### Sumyyah Al-Hijjawi , Abd Ghafur Ahmad , Shawkat Alkhazaleh

The neutrosophic soft set emerges as a highly valuable and efficient adaptation of soft sets, specifically addressing parameterized values of alternatives. However, numerous decision-making algorithms rooted in neutrosophic soft sets often neglect the external factors impacting their effectiveness. This paper introduces the innovative concept of an effective neutrosophic soft expert set, meticulously crafted to encapsulate external influences on both neutrosophic soft sets and expert opinions within a unified model. This eliminates the necessity for additional operations. Notably, our groundbreaking approach seamlessly amalgamates the strengths of the neutrosophic soft expert set and the effective set, resulting in heightened efficiency and realism in this domain. The article comprehensively explores the fundamental operations of an effective neutrosophic soft expert set, elucidating these processes through apt examples. Finally, the paper showcases the practical application of this concept in decision-making problems, providing algorithms and illustrative examples to underscore its efficacy.

Vol. 23 Issue. 1 PP. 27-50, (2024)

#### Fuzzy Logic Used to Solve ODEs of Second Order Under Neutrosophic Initial Conditions

##### Sahar M. Jabbar , Azal Mera , Ameera N. Alkiffai

The Mohand transform method, which has the benefit of unit preservation property over the well-established Laplace transform method, is used in this study to solve the ordinary differential equation of second order with neutrosophic numbers as initial conditions. Moreover, the solution obtained at different&nbsp;&nbsp;&ndash;cut .

Vol. 23 Issue. 1 PP. 51-58, (2024)