International Journal of Neutrosophic Science

An irreversible k-threshold conversion process on a graph G=(V,E) is an iterative process that studies the spread of a one way change (from state 0 to 1) on V(G). The process begins by choosing a set S_0⊆V. For each step t(t=1,2,…,), S_t is obtained from S_(t-1) by adjoining all vertices that have at least k neighbors in S_(t-1). We call S_0 the seed set of the k-threshold conversion process and if S_t=V(G) for some t≥0, then S_0 is called an irreversible k-threshold conversion set (IkCS) of G. The k-threshold conversion number of G (denoted by (c_k (G)) is the minimum cardinality of all the IkCSs of G. In this paper, we study IkCSs of toroidal grids and the tensor product of two paths. We determine c_2 (C_3×C_n )  and we present upper and lower bounds for c_2 (C_m×C_n) for m,n≥3. We also determine c_2 (P_2×P_n ),c_2 (P_3×P_n ) and present an upper bound for c_2 (P_m×P_n) when m,n>3. Then we determine c_3 (P_m×P_n) for m=2,3,4 and arbitrary n. Finally, we determine c_4 (P_m×P_n) for arbitrary m,n. . Also, we study the same concepts over some neutrosophic graphs with suggestions for future neutrosophic and fuzzy generalizations.

This study delves into the innovative use of sentiment analysis in conjunction with neutrosophic time series to forecast stock market trends in various contexts. By meticulously analyzing financial news and social media data, sentiment scores are derived and subsequently integrated into a neutrosophic time series model. This model is uniquely adept at managing uncertainty and indeterminacy, providing a robust framework for prediction. The findings indicate that this integrated approach significantly enhances predictive accuracy and reliability over traditional time series models. This research presents a novel methodology for tackling the intrinsic unpredictability of stock markets, offering a more reliable tool for investors and analysts across diverse financial environments. Additionally, by incorporating sentiment scores from a wide range of sources, the model captures a comprehensive view of market sentiment, reflecting the collective mood and opinions of investors. This comprehensive approach ensures that the predictions are not only accurate but also reflective of real-time market dynamics. Finally, this work highlights the possibility of merging sentiment analysis with sophisticated modeling approaches to change stock market prediction, as well as providing a promising avenue for future financial forecasting research.

This paper presents a modified homotopy perturbation method (HPM), which aimed at solving systems of ordinary differential equations (ODEs). The MHPM, which combines the HPM, Laplace transform, and Padé approximants, offers an alternative approach to address the challenges associated with solving such problems. By employing this method, it becomes feasible to overcome these challenges and obtain a dependable approximation for the exact solution. The effectiveness and applicability of the proposed scheme are demonstrated through preliminary results derived from illustrative examples, all of which correspond to exact solutions.

In this paper, we have defined the concept of two-fold maximal units in finite two-fold neutrosophic rings modulo integers, where a sufficient and necessary condition for such class of generalized units will be provided. We characterize all maximal units in the following two-fold neutrosophic rings(Z_n (I))_(f_I ) for nE{2,3,4,5}.

Quality control (QC) charts are essential for ensuring industry process stability, but imprecise data make traditional methods unuseful in such a case. Neutrosophic control charts are available to handle the imprecise data. This article learns fuzzy logic as an approach of handling uncertainty more suitably than neutrosophic approaches. Fuzzy QC charts make use of fuzzy numbers, membership functions and fuzzy control limits and as such are more realistic compared to conventional charts. The study introduces a Fuzzy Adaptive Exponentially Weighted Moving Average (FAEWMA) chart, specifically designed for univariate data in a fuzzy atmosphere. The FAEWMA chart, incorporating α-cuts, is engineered to detect shifts in process means, showcasing its effectiveness through both theoretical development and practical applications. This approach improves decision-making in process control and represents a significant advancement over traditional QC methods.

Neutrosophic set (NS) and logic are powerful mathematical approaches for managing different uncertainties. Amongst different approaches for examining NS statistics, rough set theory (RST) offers a valuable instrument in the domain of NS statistics, and masses of researchers have been motivated by NS combination of RST. Recently, there have been no wide-ranging statistics and literature reviews of the universal RST and its applications. The Financial Crisis Prediction mechanism leverages cutting-edge computation methods to predict possible disruptions or economic downturns. By investigating past fiscal information, marketplace gauges, and macroeconomic features, the typical recognizes primary caution indications of imminent disasters. This practical method helps financial institutions, policymakers, and investors in applying pre-emptive procedures to alleviate fiscal marketplaces and threats. In this paper, we develop a Financial Crisis Prediction Model using Neutrosophic Fusion of Rough Set Theory (FCPM-NFRST) methodology. The suggested FCPM-NFRST method for financial crises incorporates numerous forward-thinking systems to improve predictive performance. It is initiated by the Firefly Algorithm (FFA) based feature selection to detect the fittest fiscal gauges. Consequently, the Neutrosophic Fusion of RST (NFRST) is exploited for strong cataloguing and successful management of vagueness and roughness in economic information. Lastly, the Whale Optimization Algorithm (WOA) is exploited for parameter fine-tuning, enhancing the system's accuracy. Investigational study displays that the FCPM-NFRST ensemble mechanism is more robust and superior than its complements. Accordingly, this study powerfully suggests that the suggested FCPM-NFRST method is very competitive than conventional and other existing algorithms.

Neutrosophic set (NS) and Neutrosophic logic (NL) play a major part in approximation theory. They are generalizations of intuitionistic fuzzy sets and logic correspondingly. Rough NS (RNS) combines the concepts of RS and NL to deal with vagueness, uncertainty, and imprecision in information. By integrating truth, indeterminacy, and false degrees, RNS provides a more solid basis for analyzing and classifying complicated data. Particularly, this makes it powerful in applications where incompleteness and ambiguity of data are ubiquitous. Smart cities are a current trend to contain information and communication technologies (ICTs) in the progression of great urban cities. It would be beneficial in defining the city's movement by monitoring the regular flow of traffic jams and visitors. One important characteristic of smart cities is Crowd management, which assists in safety and enjoyable experiences for the residents and visitors. Since the crowd density (CD) classification method encounters tasks including inter-scene, non-uniform density, and intra-scene deviations, occlusion and convolutional neural networks (CNNs) approaches were beneficial. This work focuses on the design of Automated Crowd Density Recognition using the Rough Neutrosophic Set for Smart Cities (ACDR-RNSSC) method in urban management. The presented ACDR-RNSSC method focuses on identifying various types of crowd densities in smart cities. Firstly, the ACDR-RNSSC method utilizes the ResNet50 method for feature extraction. Second, the classification is done using RNS. RNS is utilized for its ability to manage the vagueness and uncertainty in crowd density statistics. Lastly, the parameter is fine-tuned using the Fruit Fly Optimization Algorithm (FOA). This ensures that the model attains high robustness and accuracy in forecasting crowd density. The empirical analysis of the ACDR-RNSSC method is examined under benchmark crowd dataset and the outcomes are tested using various metrics. This study states the improvement of the ACDR-RNSSC method over existing techniques.

We construct and analyze the concept of complex cubic anti neutrosophic subbisemiring (ComCANSBS). We analyze the important properties and homomorphic aspects of ComCANSBS. For bisemirings, we propose the ComCANSBS level sets. A complex neutrosophic subset of bisemiring Ⓢ is represented by the symbol Γ if and only if each non-empty level set R(℘,κ), where R) = |ℜ⊤Γ ·eiθ z}|{ℑ⊤Γ ,z}|{ℜ גΓ ·eiθz}|{ℑ גΓ ,z}|{ℜΓ ·eiθz}|{ℑΓ ,ℜ⊤Γ ·eiθℑ⊤Γ ,ℜ גΓ · eiθℑ גΓ,ℜΓ · eiθℑΓ ) is a ComCANSBS of Ⓢ. Let Υ be a ComCANSBS of bisemiring Ⓢ. If and only if Υ is a ComCANSBS of Ⓢ × Ⓢ, then Γ is a ComCANSBS of bisemiring Ⓢ. Let Γ be the strongest complex anti neutrosophic relation of bisemiring Ⓢ. We show that homomorphic images of all ComCANSBSs are ComCANSBSs, and homomorphic pre-images of all ComCANSBSs are ComCANSBSs. There are examples given to illustrate our results.

In this paper, we present sentiment analysis on Twitter data by employing Neutrosophic Sentiment Analysis (NSA). NSA captures sentiments by considering three aspects: truth, falsehood, and indeterminacy, offering a more nuanced understanding of sentiment in tweets. To enhance this analysis, we integrate the results from Neutrosophic logic (NL) sentiment analysis into a Bi-directional Long Short-Term Memory (LSTM) model. This integration takes use of NL's capacity to manage uncertainty and indeterminacy in social media material, as well as the Bi-directional LSTM's capability to capture temporal relationships in sequential data. Our combined NL-Bidirectional LSTM technique attempts to increase the precision of forecasting, particularly when it comes to predicting stock market patterns based on Twitter sentiment. Through comprehensive evaluation, we demonstrate the effectiveness of this approach, highlighting its potential to address the inherent uncertainties and indeterminacies in social media data and thereby provide more reliable predictions for stock market movements.

The objective of this paper is to extend the concept of standard soft sets to pentapartitioned neutrosophic vague soft sets (PNVSSs) by applying soft set theory to pentapartitioned neutrosophic vague sets (PNVSs)to make them stronger and more usable. We additionally describe its null, absolute, and fundamental operations, such as complement, subset, equality, union, and intersection, using examples. In addition, we defined the Pentaprtitioned Neutrosophic Vague multiset and the Possibility Pentaprtitioned Neutrosophic Vague sets (PPNVSs). We also look at several related properties and the proofs for them. Finally, this concept is applied to a decision-making problem, and its viability is demonstrated using an example. Related properties and the proofs for them. Finally, this concept is applied to a decision-making problem, and its viability is demonstrated using an example.

A neutrosophic is a strong framework to characterize novel mathematical structures. This framework is more suitable and flexible set side by side to fuzzy sets and intuitionistic fuzzy sets. In this work, we focus on some famous mathematical spaces like Ls,p (u)when we work on displaying a feature the immediate and contrary theorems of unrestrained functions in the spaceLs,p (u)are considered. Also, some characteristics of modification symmetric and modulus of neutrosophic smoothness have been discussed. Moreover, the identical among approximate tools such as the neutrosophic K-functional and neutrosophic modulus of softness.

Sentiment Analysis (SA) is a crucial task for analyzing online content over languages for processes such as content moderation and opinion mining. However advanced NLP modeling approaches frequently need an abundance of training datasets to accomplish their outcomes. SA is a classification task where the polarity of text dataset is detected, viz., to analyze a document or sentence expressing a positive, negative, or neutral sentiment. Deep learning (DL) becomes predominant in resolving Natural Language Processing (NLP) tasks. On the other hand, this technique requires a significantly enormous quantity of annotated corpus, which is not easier to attain, particularly under these lower resource settings. Neutrosophic Net-RBF Neural Network (NNRBFNN) combines the principle of neutrosophic logic (NL) with RBF-NNs for handling data indeterminacy and uncertainty. This combined strategy optimizes conventional NNs by incorporating the possibility of addressing incomplete and imprecise data, augmenting decision-making in challenging circumstances. This paper introduces a Neutrosophic Net-RBF Neural Network with Sentiment Analysis on a Low Resource Language (NNRBFNN-SALRL) model. To accomplish this, the NNRBFNN-SALRL method undertakes data pre-processing to transform the input dataset into a helpful format, and Term Frequency Inverse Document Frequency (TF-IDF) technique is utilized for the process of word embedding. For the classification method, the NNRBFNN model is used. To optimize the recognition outcomes of the NNRBFNN method, the hyperparameter tuning technique can be done using the Bayesian Optimization Algorithm (BOA). Wide-ranging experiments were conducted to validate the superior outcomes of the NNRBFNN-SALRL method. The empirical findings indicated that the NNRBFNN-SALRL method emphasized betterment over other approaches.

Cyber-attacks involve a large number of malicious events including phishing, malware attacks, ransomware, social engineering, etc. Automatic cyber-attack recognition and classification are obtained by different technologies and techniques, including artificial intelligence (AI), data analytics, machine learning (ML), deep learning (DL), and other forward-thinking approaches. As a generality of the fuzzy set (FS) and intuitionistic FS (IFS), the Neutrosophic set (NS) can handle incongruous, uncertain, and indeterminacy data where the indeterminate is explicitly measured, and the degree of truth, indeterminacy, and false functions are liberated. It may successfully define inconsistent, uncertain, and incomplete data and overcome certain limitations of the present techniques in representing uncertain decision data. The indeterministic portion of uncertain information, presented in the NS concept, has been instrumented in proper decision-making that is impossible by the IFS concept. Cyber threat detection and classification is a crucial research area that develops intelligent systems that can identify and categorize a variety of cyber-attacks in real time. This article develops an Integrating Machine Learning with Two-Person Intuitionistic Neutrosophic Soft Games for Cyber threat Detection in Blockchain Environment (IMLTPIN-CDBE) system. The main aim of the IMLTPIN-CDBE methodology lies in the automatic recognition of the cyber-threat BC platform.  The initial phase of data normalization using a min-max scalar is conducted in the IMLTPIN-CDBE method. Moreover, the two-person intuitionistic neutrosophic soft games (TPINSSG) technique is applied for cyberattack recognition. Finally, the grasshopper optimization algorithm (GOA) technique is applied for fine-tuning the hyperparameter included in the TPINSSG classifiers. A sequence of experiments has been conducted on the ransomware database to exhibit the great performance of the IMLTPIN-CDBE method. The empirical findings show the supremacy of the IMLTPIN-CDBE method over other current approaches.

A neutrosophic set (NS) is an advanced computational technique that accesses uncertain information via three membership functions. A soft expert set (SES) is derived from the hypothesis of a “soft set” with computer technology. Currently, this method is utilized in various domains such as intelligent systems, measurement theory, probability theory, cybernetics, game theory, and so on. Internet user faces a myriad of risks with the development of malware worldwide. The most prominent type of malware, Ransomware, encrypts confidential data without releasing the files until the user makes a ransom payment. Internet of Things (IoT) framework is a wide region of Internet-related devices with further computation capacities with storage capabilities that can be damaged by malware creators. Ransomware is a cruel and new malware on Internet with increasing attack levels. Ransomware encrypts the whole information to make users incapable of accessing important information and their files. In this article, we propose a Complex Proportional Assessment Based Neutrosophic Approach for Ransomware Detection in Cybersecurity (CPABNA-RDCS) methodology in IoT environment. The objective of the CPABNA-RDCS approach is to identify and categorize the ransomware to accomplish cybersecurity in the IoT network. Primarily, the CPABNA-RDCS method exploits min-max normalization for scaling the input dataset into relevant format. Meanwhile, the ransomware classification takes place via Complex Proportional Assessment Based Neutrosophic (CPABN) method. Finally, grey wolf optimizer (GWO) is employed for optimum hyperparameter choice of the CPABN system. The experimental results of the CPABNA-RDCS method are inspected on benchmark data. The simulation analysis emphasized the developments of the CPABNA-RDCS method over other existing techniques.

Indian agriculture aims at achieving sustainable development, which increases crop production per square unit without damaging the ecosystem and natural resources. Timely and prompt diagnosis and analysis of plant diseases are very beneficial in increasing food crop productivity and plant health and decreasing plant diseases. Plant disease specialists are not accessible in distant regions therefore there is an urgent need for reliable, automatic low-cost, and approachable solutions to detect plant disease without the expert’s opinion and laboratory inspection. Classical machine learning (ML)-based image classification techniques and Deep learning (DL)-based computer vision (CV) approaches such as Convolutional Neural Networks (CNN) was employed to detect plant disease. Neutrosophic set (NS), a generality of fuzzy set (FS) and intuitionistic FS (IFS), presented to characterize inconsistent, uncertain, imprecise, and incomplete data in realistic conditions. Besides, interval NS (INSs) was exactly proposed to resolve the problems with a collection of numbers in the actual entity. On the other hand, there are high levels of operational reliability for INSs, along with the decision-making method and INS aggregation operators. This study presents an Efficient Plant Disease Detection using the Possibility Neutrosophic Hypersoft Set Approach (EPDD-pNSHSS) method. The suggested EPDD-pNSHSS method uses the DL method for the recognition and classification of plant diseases. Initially, the EPDD-pNSHSS method takes place the Median filtering (MF) through the preprocessing to progress image superiority and eliminate noise. In the meantime, the possibility neutrosophic hypersoft set (pNSHSS) classifier is utilized for the detection of diseased and healthy leaf images. To optimize the detection accuracy of the pNSHSS mechanism, the whale optimization algorithm (WOA) is employed for adjusting the hyperparameter value of the DSAE technique. Wide-ranging experiments are implemented to exhibit the supremacy of the EPDD-pNSHSS method. The empirical findings showcased the development of the EPDD-pNSHSS method over other existing techniques.