The Frechet distribution is a versatile probability distribution that is used within a loose range in many important statistical fields, such as image processing, data analysis, and pattern recognition. It aims to explore and study the estimation of the parameters of the Frechet distribution using the noise-robust least squares method, as in the research paper, and it also has uses. There are many real-world scenarios. It is known that there is a growing challenge in estimating the parameter because of the noisy data. Depending on rigorous simulations and experimental analysis, we provide a novel powerful way to estimate the parameters for the Frechet Distribution Robust Least Squares approach to be flexible. Also, the results approach of this work will be very helpful in estimating the Frechet distribution parameters for diverse statistical applications. Also, we generalize our results to include the generalized neutrosophic case of this distribution dealing with neutrosophic numbers.
Read MoreDoi: https://doi.org/10.54216/IJNS.250301
Vol. 25 Issue. 3 PP. 01-13, (2025)
We employ the Laplace Residual Power Series Method to approximate analytical solutions for differential equations and neutrosophic differential equations with associated parameters, including non-homogeneous equations and fractional formulas in partial differential equations (PDEs). This approach showcases the method's simplicity, effectiveness, and robustness in deriving analytical series solutions for PDEs that involve associated parameters, especially in the context of fractional differential equations. Several practical uses of LRPSM with an emphasis on non-homogeneous and partial differential equations and neutrosophic equations with fractions (PDEs). These applications are significant in a variety of scientific and engineering domains that simulate complicated dynamic system such as anomalous diffusion in physics, viscoelastic material modeling in engineering and signal processing.
Read MoreDoi: https://doi.org/10.54216/IJNS.250302
Vol. 25 Issue. 3 PP. 14-24, (2025)
This paper uses finite difference methods to study the numerical solution for neutrosophic Sine-Gordon system in one dimension. We use the explicit method and Crank-Nicholson method. Also, an effective comparison between the results of the two methods has been made, where we obtain the result that Crank-Nicholson method is more accurate than the explicit method, but the explicit method is easier. We also study the stability analysis for each method by using Fourier (Von-Neumann) method and get that Crank-Nicholson method is unconditionally stable while the Explicit method is stable under the condition 𝑟2≤1𝑐2 and 𝑟2≤1.
Read MoreDoi: https://doi.org/10.54216/IJNS.250303
Vol. 25 Issue. 3 PP. 25-36, (2025)
In this study, we define time-fuzzy soft set (T-FSS) as an extension of fuzzy soft set. We will also define and investigate the features of its main operations (complement, union intersection, ”AND” and ”OR”). Finally, we’ll apply this approach to decision-making difficulties.
Read MoreDoi: https://doi.org/10.54216/IJNS.250304
Vol. 25 Issue. 3 PP. 37-50, (2025)
This study develops a new version of the lognormal distribution, the neutrosophic lognormal distribution (NLND), to address uncertainties commonly exist in reliability studies within the engineering field. The NLND is suitable for analyzing complex data with symmetrical or right-skewed patterns. The paper discusses the mathematical characteristics of the NLND, including concepts of reliability like mean time failure, hazard rate, cumulative failure rate, and reliability function. The model is based on real-life examples from life-test data and uses the maximum likelihood method to determine two key parameters. A simulation experiment was conducted to evaluate the accuracy of the estimated parameters, showing that maximum likelihood estimators can effectively estimate unknown parameters, especially with a large sample size. Finally, a real-world data is used to demonstrate the adequacy of the proposed model in a practical scenario.
Read MoreDoi: https://doi.org/10.54216/IJNS.250305
Vol. 25 Issue. 3 PP. 51-59, ()
In this paper, the basic properties of the convex fuzzy metric space will be presented. In particular, the proof of the fixed-point theorem for the fuzzy contraction single valued functions will be discussed. Furthermore, the solution system of linear equations, Volterra equations and Fredholm integral equations will be obtained as a direct application of the fixed-point theorem.
Read MoreDoi: https://doi.org/10.54216/IJNS.250306
Vol. 25 Issue. 3 PP. 60-69, (2025)
The research started from Salama's generalization to both ideal and local function through NCSs. We presented some results and properties to reinforce the concept of the generalized local function, which though its properties was used to deduce the properties of the 𝜓Ν𝐶- operator that we generalized through NCSS.
Read MoreDoi: https://doi.org/10.54216/IJNS.250307
Vol. 25 Issue. 3 PP. 70-75, (2025)
This work is dedicated to advancing the approximation of initial value problems through the introduction of an innovative and superior method inspired by the Euler-Maclaurin formula. This results in a higher-order implicit corrected method that outperforms the Runge-Kutta method in terms of accuracy. We derive an error bound for the Euler-Maclaurin higher-order method, showcasing its stability, convergence, and greater efficiency compared to the conventional Runge-Kutta method. To substantiate our claims, numerical experiments are provided, highlighting the exceptional efficiency of our proposed method over the traditional well-known methods. In conclusion, the proposed method consistently outperforms the Runge-Kutta method experimentally in all practical problems.
Read MoreDoi: https://doi.org/10.54216/IJNS.250308
Vol. 25 Issue. 3 PP. 76-91, (2025)
We present the neutrosophic interval-valued set applied to the q-rung logarithmic operator (q-RLOANIVS). One might develop a q-rung neutrosophic interval-valued set by extending the Pythagorean interval-valued fuzzy set (PIVFS) and neutrosophic set (NS). We discuss the q-Rlogarithimic operator applied neutrosophic interval-valued weighted averaging (q-RLOANIVWA), q-Rlogarithimic operator applied neutrosophic intervalvalued weighted geometric (q-RLOANIVWG), extended q-Rlogarithimic operator applied neutrosophic intervalvalued weighted averaging (q-RELOANIVWA) and extended q-Rlogarithimic operator applied neutrosophic interval-valued weighted geometric (q-RELOANIVWG). Several algebraic attributes have been established, including distributivity, idempotency, and associativity of q-RLOANIVSs.
Read MoreDoi: https://doi.org/10.54216/IJNS.250309
Vol. 25 Issue. 3 PP. 92-105, (2025)
In light of the great development witnessed by our contemporary world, it has become necessary to focus on scientific methods and use the quantitative method to reach more accurate decisions, appropriate to the surrounding circumstances and factors. The process of decision-making and choosing the optimal alternative depends on the type and quality of data that describes the issue for which the decision is to be made. Regarding it, in this chapter we present a study of the issue of determining the ideal advertising medium to display a company’s products. This issue is considered one of the issues of decision-making in the case of confirmed data, so we build the appropriate mathematical model and through the optimal solution to it we can make the ideal decision through which the company achieves its goal from the campaign. Informative, we will divide this study into two parts. In the first section, we will develop a general formula for this issue, and the data will be classical values. We will obtain a linear mathematical model. In the second section, we will formulate the issue from the perspective of neutrosophic science, meaning we will take the data as neutrosophic values, obtaining a linear neutrosophic model.
Read MoreDoi: https://doi.org/10.54216/IJNS.250310
Vol. 25 Issue. 3 PP. 106-114, (2025)
The aim of this study is to compare common and previously used numerical algorithms for nonlinear problems under different conditions. This study proposes a parallel implementation of two free derivative optimization methods, Powell's method and Nelder-Mead's method, combined with two restart strategies to achieve a global search. In terms of total time, the Powell method converges faster than the Nelder-Mead method. The final function value obtained by the Powell method is slightly lower. Both are optimization techniques used to find the minimum of an objective function in multidimensional space, without requiring derivatives. Also, we extend our results to apply to some neutrosophic non-linear problems under different neutrosophic-based conditions with many examples that explain the validity of our approach.
Read MoreDoi: https://doi.org/10.54216/IJNS.250311
Vol. 25 Issue. 3 PP. 115-122, (2025)
In this investigation, we present a new collection of analytic functions that includes Touchard polynomials. We then aim to calculate the Maclaurin coefficients |𝑎2 | and |𝑎3 | and address the Fekete-Szegö functional problem within this specific subfamily. Additionally, we demonstrate several new outcomes by specifying the parameters used in our main findings.
Read MoreDoi: https://doi.org/10.54216/IJNS.250312
Vol. 25 Issue. 3 PP. 123-131, (2025)
The cyclical nature of credit is a pivotal component of the broader business cycle, with credit expansion serving as a crucial mechanism for economic resurgence post-crisis. This paper delves into the ramifications of stringent financial regulations implemented in the wake of the 2007–2008 financial crisis, which notably decelerated the credit expansion phase, culminating in an anomalously extended period of credit contraction within the non-financial private sector. From a Neutrosophic Science perspective, this study posits that the typical progression of the credit cycle was significantly altered due to the heightened requirements under Basel III and the overhaul of the United States financial system. Distinct from prior crises, the post-2007–2008 period witnessed a more languid recuperation in credit activity, with the credit volume to the non-financial private sector yet to attain pre-crisis levels. This article offers a comparative analysis, scrutinizing the temporal dynamics of credit recovery following various crises. Drawing on Minsky’s financial instability hypothesis, Crotty’s theory of endogenous credit standard formation, and the Neutrosophic Science framework, the research investigates the phenomenon termed "credit paralysis." It hypothesizes that banking credit standards are intrinsically linked to macroeconomic variables such as GDP levels, interest rates, and loan volumes. Employing a vector autoregressive model, the study examines the alterations in credit activity vis-à-vis shifts in credit standards and explores the genesis of these standards in relation to macroeconomic indicators. The analysis leads to the conclusion that the augmented credit standards, necessitated by Basel III's implementation in crisis response, disrupted the normal trajectory of the credit cycle. The research culminates in the development of a stylized model of the U.S. credit cycle, which incorporates specific factors from the 2007–2008 crisis, including pre-crisis financial innovations, the subsequent intensification of financial regulations, and the principles of Neutrosophic Science.
Read MoreDoi: https://doi.org/10.54216/IJNS.250313
Vol. 25 Issue. 3 PP. 132-143, (2025)
In this paper, we explore the theoretical foundations of neutrosophics type-2 fuzzy sets by investigating its algebraic properties, demonstrating how neutrosophics type-2 fuzzy sets can generalize and extend existing operations in Type-1 and traditional Type-2 fuzzy sets. We also provide illustrative examples to clarify the practical applications of these operations, showcasing the potential of neutrosophics type-2 fuzzy sets in areas requiring sophisticated decision-making tools and uncertainty management.
Read MoreDoi: https://doi.org/10.54216/IJNS.250314
Vol. 25 Issue. 3 PP. 144-154, (2025)
In this study, I introduce time-fuzzy soft expert set (T-FSES) as an extension of fuzzy soft set. I will also define and investigate the features of its main operations (complement, union intersection, AND and OR). Finally, I’ll apply this approach to decision-making difficulties.
Read MoreDoi: https://doi.org/10.54216/IJNS.250315
Vol. 25 Issue. 3 PP. 155-176, (2025)
In this manuscript, we present the concept of E -Geraghty contractions, demonstrating several fixed point results.Additionally, we provide an illustrative example to highlight our principal findings.
Read MoreDoi: https://doi.org/10.54216/IJNS.250316
Vol. 25 Issue. 3 PP. 177-186, (2025)