International Journal of Neutrosophic Science

In this paper, I_g^*- closed sets, and I_g^*- open are used to investigate and define a new class of functions is said to be I_g^*-Continues functions, I_g^*-irresolute functions in ideal topological space topological spaces. Morover, I introduce I_g^*- compact spaces and I_g^*-connected spaces, and maximal I_g^*-closed sets. I obtain their characterizations and study their basic properties.

Ram Awadh (RA) distribution is flexible to handle skewedness and heavy tailed observations, which are frequent in financial risk management. With flexible structure, it has potential to be a reliable model in financial data modeling and decision-making process in the scenarios of indeterminacy. The new one parameter lifetime distribution is proposed and called as the neutrosophic RA distribution ( ) in this article. We obtain the raw and central moments of it and investigate some important statistical properties such as the coefficient of variation, skewness, kurtosis and index of dispersion. Moreover, some reliability properties such as the hazard rate function mean residual life function, and stochastic orderings of the distribution are considered. The method of maximum likelihood estimation (MLE) is utilized for parameter estimation. A comprehensive simulation study is carried out to evaluate the behavior of the distribution and its statistical properties.  Finally, a real-world dataset of economic sector is utilized to illustrate its practical importance.

This study investigates the second-order Hankel determinant in the context of certain analytic functions to find upper bounds, incorporating neutrosophic logic to handle uncertainty in coefficient estimation. The normalized conditions ג)0)=0 ג′(0) = 1 are analyzed through both classical and neutrosophic frameworks. We derive: • Sharp neutrosophic bounds for |H2,2,ϖ| when ϖ ∈ (1, 3/2] • Optimal bounds for |H2,3| at ϖ = 3/2 in G(ϖ) and Q(ϖ) • Neutrosophic logarithmic coefficient determinants with τ -ι-φ membership degrees The framework demonstrates robustness when coefficients exhibit simultaneous membership/non-membership characteristics.

Uncertainty, imprecision, and incomplete information are commonly found in complex economic and financial systems, and traditional probabilistic models are thus inadequate to accurately model and forecast these systems. In this work, a new extension of the Muth distribution in the neutrosophic environment is presented leading to the neutrosophic Muth distribution (NMD). This new model introduces neutrosophic parameters aiming to quantify vague and uncertain information and provides a flexible and robust approach to modeling right-skewed economic data. Some key characteristics including the density function and cumulative distribution function, moment generating function, and origin moments are obtained in the neutrosophic framework. The study of a model treated under uncertainty is described and an inferential method transforming it into neutrosophic maximum likelihood by interval-valued data is discussed. A real-world financial dataset is considered in order to prove the usefulness of the proposed distribution. The findings emphasize that the proposed distribution has the potential to be a comprehensive, flexible, and potential model for handling uncertainty in economics and finance data.

The neutrosophic set (NS) concept from the philosophical perspective extends and simplifies the principles of fuzzy set (FS) and intuitionistic FS (IFS). A NS is defined by truth, indeterminacy, and falsity membership functions, with each value belonging to the non-standard intervals (−0, 1+). In contrast to IFSs, there is no limitation in the membership function in NS, and the hesitancy degree is incorporated in NS. Arrhythmia is a medical illness wherein the regular pumping mechanism of the human heart becomes abnormal. The arrhythmia detection is one of the most essential steps to identify the disorder that can play a significant role in helping cardiologist with their decision. The initial identification of abnormal heart disease is critical for patients with heart disorders. Computer-aided diagnosis (CAD) has gained popularity in the arrhythmia domain recently, as artificial intelligence (AI) technology has matured. Still, the AI-based deep learning (DL) techniques are applied frequently to classify and detect arrhythmia. This paper presents an Enhanced Diagnostic Model for Cardiac Arrhythmia using Principal Component Analysis and Pythagorean Neutrosophic Bonferroni Mean (DMCA-PCAPNBM) technique in Cardiovascular Signal Processing. The objective is in the automated arrhythmia detection using advanced techniques. Initially, the DMCA-PCAPNBM model applies the min-max scaler-based data pre-processing technique for transforming input data into an appropriate format. In addition, the principal component analysis (PCA) method is applied for the feature subset selection model to pick out the optimal attributes from the dataset. For the procedure of arrhythmia detection, the PNBM model is utilized. Finally, the improved dung beetle optimization (IDBO) approach is applied for parameter tuning, resulting in enhanced classification performance. A comprehensive experimentation is implemented to verify the superior outcome of the DMCA-PCAPNBM model on the ECG arrhythmia classification dataset. The experimental validation of the DMCA-PCAPNBM approach illustrated an improved accuracy value of 99.06% over recent techniques.

Healthcare data often involve uncertainty, imprecision, and partial information that are hardly handled by classical statistical models. Here, we propose a new generalization of the Gamma Lomax (GL) distribution under the neutrosophic environment, referred to as the neutrosophic Gamma Lomax (NGL) distribution, to overcome this drawback. In addition, the proposed model can be generalized to handle precise as well as uncertain healthcare data by incorporating neutrosophic logic including truth, falsity and indeterminacy. The classical properties of the Gamma-Lomax (GL) distribution are examined alongside their neutrosophic counterparts. Graphical representations, including density plots and associated reliability functions of the proposed model, are presented. The maximum likelihood estimation (MLE) is applied to find unknown parameters. The neutrosophic model is capable of modeling interval-valued results and uncertainties in practical data, and its effectiveness is verified by simulation studies and an illustration with infant mortality rates. The new method is conducive to the interpretability and credibility of statistical inference under uncertainty and is of high utility in health decision-making scenarios.

The primary aim of this study is to explore the integration of symbolic 2-plithogenic and 3 plithogenic rational functions by formulating explicit and simplified rules to facilitate their evaluation, by using the division symbolic 2-plithogenic and symbolic 3-plithogenic rational numbers respectively. In addition to the theoretical proof of these rules, relevant examples are provided to illustrate these ideas.

In this paper, we introduce a new extension of the transmuted Lindley distribution (TLD) by utilizing neutrosophic logic to handle uncertainties that are often found in real life data. As classical probability models are not flexible enough for dealing with vague, imprecise, ambiguous, and incomplete information, neutrosophic theory is more general as it handles indeterminacy part associated with data. The proposed neutrosophic transmuted Lindey distribution (NTLD) combines indeterminacy concept, yielding a powerful statistical distribution, which is suitable for modeling both randomness and indeterminacy. Major functions such as probability density function (PDF), cumulative function (CDF), reliability function (RF) and hazard rate function (HRF) are established in this framework. Graphical analysis and simulated data are used to illustrate the performance of the model. Moreover, important moments such as mean, variance, skewness, and kurtosis are computed for different values of the neutrosophic parameters. The proposed distribution provides a generalized approach to model complex and uncertain data in reliability engineering, survival analysis, and decision-making. A real electricity consumption data from energy sector is utilized to show the proposed model applicability.

The neutrosophic set (NS) is a powerful tool for representing uncertain information in decision-making, extending conventional, fuzzy sets (FS), and intuitionistic fuzzy sets (IFS) by incorporating three degrees: truth, falsity, and indeterminacy. Sales prediction analysis wishes for intellectual data mining systems with precise predictive methods and higher trustworthiness. In the majority of cases, business depends heavily on information in addition to demand prediction of sales performance. The B2B data can offer information on how a business has to manage its products, sales team, and budget flows. Clear prediction techniques were analysed and examined using the model of machine learning (ML) to improve future sales predictions. It is challenging to manage sales prediction precision and big data (BD) when the technique of classic prediction is applied. Thus, the ML method can also be used to analyze the B2B sales reliability. This study proposes an Intelligent Business to Business Sales Estimation Framework Using Neutrosophic Soft Set (IB2BSEF-NSSS) method. The primary purpose of IB2BSEF- NSSS method is to develop an effective system for B2B sales estimation using advanced techniques for greater predictive precision. Initially, the min-max method is adopted in the data pre-processing phase to normalize input data. Additionally, the IB2BSEF-NSSS model leverages the zebra optimization algorithm (ZOA) technique for feature selection. Additionally, the generalized q-rung neutrosophic soft set (GqRNSSS) methodology is exploited for the sales prediction operation. To further increase prediction performance, the Kepler Optimizer Algorithm (KOA) model is employed for model fine-tuning, assuring optimum hyperparameter selection for upgraded accuracy. To expose the better performance of the IB2BSEF- NSSS technique, a wide-ranging experimental analysis is conducted under the B2B sales and customer insight analysis dataset. The comparison study of the IB2BSEF- NSSS technique exposed greater predictive performance, accomplishing the lowest MSE of 0.00670, indicating its efficacy over each other evaluated techniques.

This work presents a neutrosophic extension of the Fréchet distribution to enhance the modeling of extreme values under conditions of indeterminacy and uncertainty. While the classical Fréchet distribution is widely used in fields such as finance, hydrology, and environmental sciences to model extreme maximum values, it does not fully accommodate imprecise, vague, or conflicting data commonly encountered in real-world scenarios. By incorporating the principles of neutrosophic logic the proposed neutrosophic Fréchet distribution provides a more flexible and realistic approach to representing extreme phenomena. The paper introduces its theoretical formulation, outlines key statistical properties, and proposes an estimation method based on maximum likelihood. Through simulations and numerical illustrations, the robustness and applicability of the model are described, especially in contexts where data is incomplete, uncertain, or contradictory. A real industrial dataset is employed to illustrate the applicability of the proposed model.

The expanding growth of financial transactions has resulted in the development of fraud systems. These progressions have considerably improved overall productivity, improved corporate management, and reduced operational costs. With the expanded utilization of automated financial transaction, organization and businesses have progressed to digital platform, convert their financial operation. Still, such a change in addition revealed financial systems to new threats, mainly through fraudulent activity and cybercrime. The large datasets, incorporated with the limits of conventional fraud detection techniques, provide a chance to accept Artificial Intelligence (AI) methods. The fraud detection problem is addressed by using Explainable AI (XAI) to give specialists with explained AI predictions over different explanation models. This paper proposes a Financial Transaction Fraud Detection via Dimensionality Reduction with an Explainable Artificial Intelligence Approach (FTFD-DRXAIA) technique. The aim is to develop an effective and intelligent system for accurate fraud detection in financial transaction utilizing progressive deep learning (DL) methods. Initially, the min-max method is used for data pre-processing to convert raw data into an appropriate format. Furthermore, the recursive feature elimination (RFE) system is applied for feature selection. For financial fraud detection process, the Elman recurrent neural network (ERNN) has been utilized. Moreover, the wildebeest herd optimization (WHO) method fine-tunes the ERNN model's hyperparameters, resulting in improved classification performance. Finally, the XAI technique applies LIME and SHAP to interpret complex AI models, enabling auditors and analysts to detect suspicious transaction patterns with greater clarity and confidence. The experimental outcome of FTFD-DRXAIA system is examined under the financial fraud detection database. The comparison analysis of FTFD-DRXAIA algorithm demonstrated an optimum precision value of 98.96% over recent methods.

A correlation coefficient is a statistical measure, which contributes measure, whichhe degree to which changes in one variable predict changes in another. In this article, we analyze the characteristics of Fermatean Quadripartitioned Neutrosophic sets with improved correlation coefficients. We have also used the same approach in multiple attribute decision-making methodologies including one with a Fermatean Quadripartitioned Neutrosophic environment. Finally, we implemented for above technique to the problem of multiple attribute group decision making.