International Journal of Neutrosophic Science

In this article, we introduce and establish a novel concept called ’cubic spherical linguistic neutrosophic topological spaces’ by employing cubic spherical linguistic neutrosophic sets and topological frameworks. Various foundational definitions, theorems, and properties are provided along with illustrative examples.

In this study, the lindel”of property of spaces will be examined across nth topologies, referred to as nthlindel” of spaces. Furthermore, the characteristics of these spaces will be analyzed in relation to lindel¨o]f spaces and tri-Lindelf spaces. Several theoretical results have been presented and proven, and various well-known theorems concerning Lindel?f spaces have been extended to accommodate nth topologies. An illustrative examples are provided to support the findings.

One of the traditional problems in survey sampling is to estimate the population parameter like mean variance etc. This article investigates the mathematical derivations and application of neutrosophic statistics to address the challenges posed by imprecise, indeterminacies or ambiguous data, such as daily stock prices, weather forecast, social media sentiment and temperatures. The suggested estimators are highly useful for computing results while working with unclear, hazy, and neutrosophic-type data. These estimators produce answers that are interval-form rather than single-valued, which may give our population parameter a better chance of being off. We propose three novel neutrosophic exponential ratio-type estimators for the population mean, utilizing information of neutrosophic auxiliary variables. Expressions for bias and mean square error (MSE) of these estimators are derived using first-order approximations to assess their performance in terms of accuracy. To demonstrate their effectiveness, we apply the proposed estimators to real-life neutrosophic data sets. Additionally, a simulation study shows that our estimators outperform existing methods in terms of MSEs and percentage relative efficiency (PREs). This study further expands its originality by including pre-existing estimators into the neutrosophic framework, showcasing its versatility and adaptability. The results suggest that neutrosophic statistics provide a robust framework for analyzing uncertain data, facilitating more reliable decision-making in various applications.

The study of chemical compounds’ molecular structures is one of the most cutting-edge uses of graph theory, along with computer science, nanochemistry, network design in electrical and electronic engineering, and the depiction of graphs in Google Maps. The degree and distance between vertices of a graph are the basis for examining topological indices. The formula for computing the Weighted Padmakar Ivan index (WPI) of a graph G is PIw(G) = P e∈E(G) [(dG(u) + dG(v)][|V (G)| − NG(e)].

In this paper, we prove new spectral radius inequalities for sums, differences and commutators involving accretive-dissipative matrices of Hilbert space. Earlier well-known results used the spectral radius for its importance for general matrices. In our paper, we focus on some results related to spectral radius for special kind of matrices which are accretive-dissipative. A particular example is also presented in this work.

This paper is dedicated to studying for the first time the building of a topological space based on the intervals defined over 4-refined neutrosophic real numbers and 5-refined neutrosophic real numbers, where we define a special partial order relation on these rings, and we use it to study the structure of the corresponding intervals generated from this relation. Also, we characterize the formula of open sets through these two topological spaces with some illustrated examples.

Wireless Body Area Networks (WBANs) play a pivotal role in modern healthcare by enabling continuous monitoring of physiological data through sensors placed on or around the human body. Despite their significant benefits, WBANs face challenges such as data uncertainty, complex decision-making processes, and dynamic network conditions. These challenges can lead to inaccuracies and inefficiencies in health monitoring and diagnostics. The paper's main aim is to incorporate neutrosophic theory into Wireless Body Area Networks to provide enhancements in decision-making. In modern healthcare, the use of WBANs for monitoring physiological data by sensors, which are attached to or around the human body, can be continuous. Despite huge advantages, the main challenges that WBANs face are the uncertainties in data, complex decision-making processes, and dynamic network conditions, making health monitoring and diagnostics inaccurate and inefficient. In this paper, authors propose a robust framework to map sensor data into the neutrosophic domain and apply neutrosophic logic for enhanced accuracy and reliability of decision-making. In this paper, a Neutrosophic Decision-Making Algorithm is proposed, and its performance is compared with other decision-making techniques in terms of accuracy, response time, energy efficiency, and reliability. Experimental results show major improvements of around 95.3% in accuracy and a reduction of up to 25% in response time and energy consumption. Results underline the potential of neutrosophic theory for revolutionizing decision-making processes within WBANs to ensure more reliable and efficient health monitoring. This approach enables not only operational life but also improves patient outcome, avoiding a wrong diagnosis, during long-term health monitoring applications using WBAN devices.

Let R be a G-graded ring and M be a G-graded R-module. The graded second spectrum of M, denoted by Specs G(M), is the set of all graded second submodules of M. In this paper, we define a topology on Specs G(M) which is analogous to that for SpecG(R), and investigate several topological properties of this topology.

This manuscript presents a novel approach for solving first-order initial value problems by leveraging the Fuzzy Kamal Transform within a Neutrosophic framework. By integrating fuzzy logic with Neutrosophic set theory, the method adeptly addresses uncertainties inherent in differential equations. The efficacy of this method is demonstrated through the exposition of various illustrative examples.

Decision-making theory is an effective way to help the decision-maker take the right path to solve a problem. Among the applications of this theory is the medical field, i.e. allowing the decision maker (doctor) to analyze patient data and judge the result of this analysis as to whether the patient is infected or not. In this path and to enrich this theory with more flexible mathematical methods, we present in this work a more flexible expanded method for a previous concept called Interval-valued Q-neutrosophic soft matrix (IV-Q-NSM) as a new generalization of previous mathematical tools. These tools deal with the two-dimensional uncertainty issues that exist in many areas of life. Next, some ordinary algebraic properties and matrix operations have also been studied. After that, we present a new methodology for the decision-making (DM) selection problems in medical diagnoses.

To handle incomplete and indeterminate data, neutrosophic logic/set/probability was recognized. The neutrosophic falsehood, truth, and indeterminacy modules show symmetry as the truth and the falsehood appear the similar and perform in a symmetrical method with esteem to the indeterminacy module which aids as a line of the symmetry. Soft set is a general mathematical device to deal with uncertainty. Sentiment analysis (SA) is the foremost task of natural language processing (NLP), where judgments, opinions, thoughts, or attitudes toward an exact subject are removed. Web is a rich foundation of information and unstructured covering numerous text documents with reviews and opinions. The detection of sentiment will be useful for governments, discrete business groups, and decision-makers. With this motivation, this study develops a Data Analytics Framework for Sentiment Classification Using Pythagorean Neutrosophic Bonferroni Mean (DAFSC-PNBM) technique on Product Reviews. The presented DAFSC-PNBM technique mainly aims to determine the nature of sentiments based on product reviews. Primarily, data preprocessing is performed to increase the product review qualities. For the word embedding process, word2vec model is used. Besides, the DAFSC-PNBM model uses the Pythagorean Neutrosophic Bonferroni Mean (PNBM) technique for classification. To enhance the SA performance of the PNBM model, the grey wolf optimizer (GWO) model has been applied as a hyperparameter tune process. The experimentation outcome analysis of the DAFSC-PNBM method occurs and the outcomes are investigated under several features. The experimental study indicated the improvement of the DAFSC-PNBM method across the modern techniques

Neutrosophy is the neutralities study and prolongs the discussion of the truth of opinions. Neutrosophic logic might be used in all sectors, to provide the solution for the indeterminate challenges. Some real-time data experience issues like inconsistency, incompleteness, and indeterminacy. A fuzzy set (FS) offers an uncertain solution, and an intuitionistic fuzzy set (IFS) processes partial data, but both fail to handle uncertain data. Financial fraud, believed as a deceptive strategy to gain financial assistance, has recently become a common threat in organizations and companies. Traditional methods namely manual inspections and verifications are costly, time-consuming, and imprecise to identify such fraudulent actions. With the development of artificial intelligence (AI), machine learning (ML)-based algorithms are applied logically to identify fraud transactions by investigating a larger amount of financial data. Therefore, the study offers an Optimizing Financial Fraud Detection using Bayesian Optimization and Variable Selection with Neutrosophic Vague Soft Set (OFFDBO-VSNVS) Algorithm. The OFFDBO-VSNVS model presents an optimized framework for fraud detection by integrating advanced variable selection techniques and classification models. Initially, the OFFDBO-VSNVS technique applies the Z-score data normalization technique to transform input data into a compatible layout. Next, the grey wolf optimizer (GWO)--based feature selection to effectively reduce dimensionality and highlight the most relevant features. For the classification and detection of financial fraud, the neutrosophic vague soft set (NVS) model can be employed. Eventually, the Bayesian optimization (BO) model adjusts the hyperparameter values of the NVS algorithm optimally and outcomes in greater classification performance. The stimulated outcome study of the OFFDBO-VSNVS model occurs and the outcomes are examined in terms of changing features. The experimental study represented the superiority of the OFFDBO-VSNVS method across the existing state-of-the-art methods

Neutrosophic set (NS) is particularly appropriate in applications where data is incomplete, unclear, or inconsistent, which offers an effectual means for analyzing and exhibiting complex mechanisms. An NS is a mathematical technique to manage uncertainty, indeterminacy, and imprecision. It enlarges classical sets, IF sets, and fuzzy sets by presenting three degrees such as indeterminacy (I), false (F), and truth (T). Financial technology (Fintech) plays an essential part in advancing modern society, technology, economies, and various fields. Financial crisis prediction (FCP) plays a crucial role in shaping economic outcomes. Past research has predominantly focused on using deep learning (DL), machine learning (ML), and statistical methods to forecast the financial stability of business. In this manuscript, we focus on the development of Effective Data Classification using Interval Neutrosophic Covering Rough Sets based on Neighborhoods and Multi-Strategy Improved Butterfly Optimization (EDCINCRS-MSIBO) Algorithm for FinTech Applications. It contains distinct kinds of stages such as data normalization, feature selection, classification, and parameter tuning. In the EDCINCRS-MSIBO technique, a min-max normalization-based data pre-processing model to scale the raw data into a uniform format. For feature subset selection, the whale optimizer algorithm (WOA) is employed to reduce the dimensionality and improve model efficiency by selecting the most relevant features. In addition, the EDCINCRS-MSIBO technique takes place interval neutrosophic covering rough sets (INCRS) classifier is utilized for detection and classification of a financial crisis. Finally, a multi-strategy improved butterfly optimization algorithm (MSIBOA) is exploited for the optimum parameter adjustment of the INCRS model. To confirm the better predictive solution of the EDCINCRS-MSIBO model, a wide range of simulations are executed on the two benchmark databases. The comparative result analysis displays the encouraging outcomes of the EDCINCRS-MSIBO method on the existing techniques

In decision-making, NS permits the representation of information with three membership functions: indeterminacy (I), false (F), and truth (T). All components in an NS have indeterminacy, non-, and membership degrees that are autonomous and vary from (0-1). This generates NS particularly appropriate in composite decision-making situations where information is incomplete, ambiguous, or contradictory, which allows strong and more complex solutions and analysis. Detecting road damage accurately and quickly enables the capability of road maintenance agencies to generate timely maintenance to road surfaces, retain optimum road conditions, enhance the safety of transportation, and reduce transportation charges. Research on road damage detection using AI models achieved more attention at present, particularly in smart cities. This paper develops a Boosting Road Damage Detection using DEMATEL with Bipolar Neutrosophic Dombi and Siberian Tiger Optimization (BRDD-DBNDSTO) algorithm. The presented BRDD-DBNDSTO technique is mainly intended to improve the accuracy and reliability of road damage classification for intelligent smart city infrastructure. To accomplish this, the BRDD-DBNDSTO technique employs adaptive bilateral filtering (ABF) using image preprocessing to effectively enhance image quality by reducing noise. Then, the SqueezeNet method was used to create a collection of feature vectors. For the classification and detection of road damage, the DEMATEL with bipolar neutrosophic Dombi model is exploited. At last, the Siberian tiger optimization (STO) algorithm is used to adjust the parameters related to the classifier model. To guarantee the improved performance of the BRDD-DBNDSTO method, an extensive experimental study was carried out and the gained outcomes illustrate the improvement of the BRDD-DBNDSTO model across the existing techniques.

The generalization for interval fuzzy set name as neutrosophic set employed to construct a measurable space in this work. The measurable space with respect to a ring of sets that is closed under difference and union, is studied. The objective of this study is to extend the notion of a ring of sets by using neutrosophic sets. Neutrosophic set concept has gained popularity in various fields of mathematics, probability, and other sciences due to its many uses, especially when dealing with uncertainties. Several different properties of neutrosophic ring are studied. Examples and characterizations to the proposed extension are given.