International Journal of Neutrosophic Science

The Type-II Diophantine neutrosophic interval valued soft set (Type-II DioNSIVSS) and related similarity measure are presented in this study. An extension of the neutrosophic interval valued soft set (NSIVSS) and the Diophantine fuzzy soft set is the Type-II DioNSIVSS. The suggested measure for Type-II DioNSIVSS assessment. We support a method of solving the problem using the Type-II soft set model. To demonstrate how they can be applied to successfully handle uncertainty-related challenges, illustrative examples are given.

In a world where efficiency and sustainability in poultry production are crucial, the need arises to find natural additives that enhance the growth of broiler chickens  ̣Recent research has put ginger powder under the microscope, evaluating its impact as a growth promoter through a detailed analysis of plithogenic statistics  ̣This study not only focuses on the quantitative aspects of weight gain and improved feed conversion, but also on the qualitative effects that this additive may have on the general health and well-being of the birds  ̣ The methodology used involves a rigorous and multifaceted approach, integrating biological and nutritional variables, which allows a deep and holistic understanding of the benefits of ginger powder in poultry farming  ̣Preliminary results suggest that ginger powder could be a viable alternative to synthetic growth promoters, showing significant improvement in growth parameters of broilers  ̣ However, plithogenic analysis reveals complex nuances that require careful interpretation, as variations in bird response indicate that factors such as dosage and administration time are crucial to maximizing benefits  ̣ This finding opens a range of possibilities for future research and practical applications, pointing towards more natural and sustainable poultry production  ̣ Additionally, it raises important questions about the integration of herbal supplements into animal diets, inviting a broader debate about science and ethics in the food industry. 

The development of Neutrosophic Cognitive Maps (NCM) for the evaluation and ranking of the main causes of the appearance of fruit fly pests represents a significant advance in the field of agriculture and entomology  ̣This innovative approach allows for a holistic and integrated view of the complex and often interdependent factors that contribute to the proliferation of these destructive pests  ̣Using neutrosophic theory, which incorporates degrees of truth, falsehood, and indeterminacy, NCMs offer a powerful tool for identifying and prioritizing critical variables  ̣In this way, a more nuanced and precise understanding of the phenomenon is facilitated, enabling the design of more effective and sustainable management strategies  ̣The methodology applied in the construction of the NCM is characterized by its ability to manage the uncertainty and ambiguity inherent to ecological and agricultural systems  ̣Through the participation of experts and the analysis of empirical data, maps can be outlined that reflect the real complexity of the problem  ̣These maps not only highlight direct causes, such as weather conditions and poor agricultural practices, but also address underlying and systemic factors  ̣Thus, the use of NCM provides a robust conceptual framework for informed decision making, improving the efficiency of interventions and contributing significantly to crop protection and global food security.

In the fast-paced world of business decision-making, where clarity and precision are vital, an integrated approach that combines the indeterminate Likert scale with the neutrosophic Analytical Hierarchy Process (AHP) offers a fresh and enriching perspective for SWOT analysis. This innovative methodology not only allows us to capture the ambiguity inherent in human evaluations, but also enhances analytical depth by incorporating neutrosophic thinking, which considers elements of truth, falsehood and indeterminacy. Instead of traditional methods that often oversimplify complexities, this integrated approach facilitates a more nuanced and holistic assessment of strengths, weaknesses, opportunities and threats, thus providing a more robust and reliable basis for formulating business strategies. Additionally, the adoption of the indeterminate Likert scale, fused with the neutrosophic AHP, introduces conceptual flexibility that is particularly useful in contexts of uncertainty and changing market dynamics. This approach not only allows decision makers to better capture the subjective and often contradictory perceptions of experts, but also facilitates the weighing of multiple criteria in a coherent and logical manner. Doing so ensures that the strategies developed are not only thoughtful and detailed, but also adaptable to the fluctuating realities of the modern business environment. In short, this integrated approach is presented as a powerful and versatile tool for strategic planning, capable of transforming complex challenges into tangible opportunities through a deep and balanced understanding of organizational reality.

In this article, an innovative approach is presented that combines analysis of variance (ANOVA) with the Neutrosophic 2-Tuple linguistic method to explore and analyze the complex interactions between elements in various contexts. ANOVA, known for its ability to decompose variance and detect significant differences between groups, is here merged with the Neutrosophic method, which provides tools to handle the uncertainty and linguistic ambiguity present in many real data sets. This methodological synergy not only expands analytical possibilities, but also allows for a more nuanced and profound interpretation of the relationships between variables, overcoming the limitations of traditional approaches that assume absolute certainty in the data. Through detailed case studies and practical examples, it is demonstrated how this hybrid model can be effectively applied in fields as diverse as scientific research, business management, and public policy evaluation. The results obtained illustrate how the combination of ANOVA and 2-Tuple Neutrosophic not only improves the precision of statistical analysis, but also enriches the understanding of complex phenomena by considering and modeling uncertainty in a more realistic and adaptable way to different contexts and scenarios.

This article explores the innovative application of multi-criteria methods and neutrosophic logic in the analysis of productive factors, highlighting how these approaches can offer a more nuanced and comprehensive view of industrial and business dynamics  ̣ Multicriteria methods allow different aspects to be evaluated simultaneously, considering complex variables that affect productivity and efficiency in various sectors  ̣ On the other hand, neutrosophic logic introduces a theoretical framework that manages the uncertainty and imprecision inherent in many business decisions, offering tools to better interpret and manage the variabilities and ambiguities that influence productive results  ̣ This integrative approach not only seeks to improve accuracy in the evaluation of critical factors such as cost, quality and time, but also to promote more informed and strategic decision making in competitive and changing environments  ̣ By combining rigorous analysis with interpretive flexibility, the door is opened to new methodologies that can effectively adapt to the complexities of the globalized market and the dynamic demands of consumers  ̣ This article examines case studies and practical examples to illustrate how these methods can be successfully applied in the optimization of production processes and in the formulation of business strategies that seek not only to remain competitive, but also to anticipate and proactively respond to emerging challenges  ̣

To address the complex challenges of cyberviolence and gender-based violence among young students, it is crucial to employ analytical approaches that consider the multifaceted nature of these phenomena. The Neutrosophic Analytical Hierarchy (NAHP) method is presented as an innovative tool that allows us to unravel the different layers of influences and factors involved in these behaviors. This approach not only recognizes the diversity of perspectives and experiences that contribute to online and gender-based violence, but also offers a structured framework to assess and prioritize these factors holistically. By applying the NAHP, not only the visible and direct aspects of cyberviolence and gender violence are explored, but also the more subtle and underlying aspects that may go unnoticed in conventional analyses. This method allows us to capture the dynamic complexity of how individual perceptions, social norms, and power dynamics interact to perpetuate these problems in student environments. Thus, a deeper and more nuanced understanding of the triggering and contributing factors is fostered, facilitating the formulation of more effective interventions and policies that are sensitive to the specific needs of affected young people.

Big Data Analytics are said to help in transforming huge amounts of raw data towards valuable information that can be used, but there are formidable challenges in feature selection and classification due to the complexity and high dimensionality of the data. Traditional methods are usually too weak to handle the built-in uncertainty, imprecision, and inconsistency within big data and they often fail to perform well. This paper aims to induce the new methodology on these problems using the sets of neutrosophic in dealing with more flexible and nuanced data analysis. The key contributions to the current approach proposed are threefold. First, generalization of the classical set through extension of the notions of truth, indeterminacy, and falsity by allowing representations of uncertainty in data. The second combines a powerful process for selecting features based upon neutrosophic set theory that is optimal by genetic algorithms and advances a step further by applying these features in training and validating the classification models across a set of different domains. Therefore, the major aim from this study is to increase accuracy and reliability in feature selection and classification in big data analytics. This methodology has been implemented and tested over datasets of the following types: healthcare, finance, social media, and more. Results have proved great improvement against conventional performance metrics, for example, the classification accuracy with an SVM classifier over the Cleveland Heart Disease dataset increases from 83.5% to 87.2%, and of a Random Forest classifier over a financial dataset from 76.4% to 81.9%. For instance, the accuracy of social media sentiment analysis changed to 82.7% from 78.3%. All these findings establish that the neutrosophic set-based method holds good advantages in addressing the limitations of classical alternatives. The proposed approach of neutrosophism, through an explicit model, enhances performances in classifications and, at the same time, augments overall robustness and reliability in big data analytic. The importance of this study lies in establishing the groundwork for further research and practical applications, thus indicating possible further development in this field.

The objective of this paper is to introduce for the first time the concept of two-fold neutrosophic and fuzzy topological space defined over real numbers, where we combine the two-fold neutrosophic sets with real numbers to get a novel topological space based on them. Also, we present many of its elementary properties and special subsets such as two-fold neutrosophic open sets, two-fold neutrosophic closed sets, and two-fold neutrosophic closure. Many examples and theorems will be provided to clarify the validity of our approach.

Neutrosophic logic extends conventional and fuzzy logic (FL) by integrating the concepts of indeterminacy, truth, and falsity, enabling for a further extensive management of uncertainty. In classical binary logic, a statement can be either true or false. FL extends this by adding degree of truth, where a statement is partially true or false. The smart city technology shown to be an effective solution to the problems regarding improved urbanization. The practical applications of a smart city technology to video surveillance relies on the ability of processing and gathering large quantities of live urban data. Violence detection is considered as a major challenge in smart city monitoring.  The required computational power is substantial due to the large volume of video data gathered from the extensive camera network. As a result, the algorithm based on handcrafted features utilizing video and image processing fails to provide a promising solution. Deep Learning (DL) and Deep Neural Networks (DNNs) models are more reliable to handle these data. In this study, we introduce a Transfer Learning with Neutrosophic Weighted Extreme Learning Machine for Violence Detection (TL-NWELMVD) technique in smart cities. The TL-NWELMVD technique aims to recognize the presence of the violence in the smart city environment. In the TL-NWELMVD technique, the features can be extracted using SE-RegNet model. To enhance the performance of the TL-NWELMVD technique, a hyperparameter optimizer using monarch butterfly optimization (MBO) is involved. Finally, the NWELM classifier is applied for the identification of violence in the smart city environment. To investigate the accomplishment of the TL-NWELMVD technique, a widespread investigational outcome is involved. The simulation results portrayed that the TL-NWELMVD technique gains better performance compared to other models.

Neutrosophic logic (NL) goes further by introducing a third component: indeterminacy. Each logical proposition in NL belongs to three degrees: truth (T), indeterminacy (I), and false (F), each taking value within the range of zero and one. This allows the processing and representation of uncertain, incomplete, and inconsistent data in a superior way. NL finds it beneficial in partially contradictory, partially known, and partially unknown scenarios, it becomes an effective instrument for applications in fields such as information fusion, artificial intelligence, and data analysis, where logical framework might be unsuccessful in handling the nuances and complexities of real-time data. Recently, Arabic sentiment analysis has become a hot research topic, which mainly intends to recognize sentiments that exist in Arabic social media. Therefore, this study introduces a Single-Valued Linguistic Complex Neutrosophic Set based Arabic Sentiment Classification (SVLCNS-ASC) technique on NLP applications. The presented SVLCNS-ASC technique undergoes Arabic data pre-processing and Glove word embedding process. For sentiment recognition, the SVLCNS-ASC technique applies the SVLCNS model, which enables to identification of various kinds of sentiments. At last, the performance of the SVLCNS model can be boosted by the use of artificial bee colony (ABC) based parameter-tuning approach. The results of the SVLCNS-ASC system has been studied on Arabic database. The experimental values indicate the supremacy of the SVLCNS-ASC approach compared to recent models.

In decision-making, neutrosophic set allows for the information representation with three membership functions: truth (T), indeterminacy (I), and false (F). Each component in a neutrosophic set has membership, non-membership, and indeterminacy degrees that are independent and range from 0 to 1. This makes neutrosophic set especially suitable in complex decision-making scenarios where information is contradictory, incomplete, or ambiguous, which enables robust and more nuanced analysis and solutions. A large portion of finance companies experience problems handling vast amounts of data. These data are often left unstructured and unorganized. Therefore, it is necessary to classify them to exploit it. Data classification also simplifies to use, locating, and retrieval of information. It becomes vital while handling risk management, legal discovery, data security, and compliance. Therefore, this manuscript presents an Intuitionistic Fuzzy-Valued Neutrosophic Multiset based Financial Data Classification (IFVNMS-FDC) technique in Complex Systems. The main aim of the IFVNMS-FDC technique is to recognize and categorize the financial data into respective classes. To do so, the IFVNMS-FDC technique initially uses min-max scalar as a pre-processing step. Besides, the high-dimensional financial data can be handled by the design of whale optimization algorithm (WOA) based feature selection. Finally, the IFVNMS-FDC technique derives IFVNMS technique for the identification of various classes related to the financial data. A wide-ranging experiments were involved in exhibiting the performance of the IFVNMS-FDC technique. The experimental values depicted that the IFVNMS-FDC method obtains reasonable performance on financial data recognition.

The financial constraints of companies listed jeopardize the interests of employees and internal managers but also carries significant threats to outer investor and other stakeholders. Thus, there is need to create an effective financial distress predictive system.  The two most pressing issues in finance are assessing credit risk and predicting bankruptcies. Thus, credit scoring and financial distress prediction remain crucial areas of research in the financial industry. Previous research has aimed at the design of ML and statistical approaches to predict the financial distress of the company. Neutrosophic set may be utilized, which is a generality of classical, fuzzy, and intuitionistic fuzzy sets (IFS). They establish a foundation for addressing inconsistency, indeterminacy, and uncertainty associated with real-world challenges. This study presents an Innovative Approach to Financial Distress Prediction using Relative Weighted Neutrosophic Valued Distances (IAFDP-RWNVD) technique. The IAFDP-RWNVD technique intends to estimate the occurrence of financial distress in any firm or organization. In the IAFDP-RWNVD technique, two major processes are comprised. At the primary stage, the IAFDP-RWNVD technique applies RWNVD technique for the identification of financial distress. In the second stage, the IAFDP-RWNVD technique designs fish swarm algorithm (FSA) for finetuning the RWNVD model. The experimental outcomes of the IAFDP-RWNVD method is investigated using distinct aspects. The experimentation outcome shows the improvements of the IAFDP-RWNVD technique.

The article examines the neutrosophic approach as an innovative tool to optimize production in small guinea pig farming systems. Through the exploration of bipolar sets and interval values, the application of this methodology in improving breeding processes is investigated, thus identifying areas of improvement and opportunities for economic and sustainable growth in the sector. The research highlights the importance of considering the uncertainty and imprecision inherent in these systems, proposing a flexible and adaptive framework that allows informed and strategic decision making to increase productivity and profitability. Likewise, the study highlights the need for a holistic and multidisciplinary understanding of the challenges and opportunities in guinea pig farming, recognizing the complexity of the social, economic, and environmental factors involved. Through an interdisciplinary approach, we seek to integrate traditional knowledge and practices with innovative approaches, thus promoting sustainability and the well-being of both producers and animals. Ultimately, this article offers a comprehensive and dynamic perspective on how the neutrosophic approach can significantly contribute to the development and optimization of guinea pig farming systems, thereby driving progress and prosperity in the agricultural sector.

In this study, a thorough evaluation of the impact of whey use in the production of flavored beverages was carried out, using the neutrosophic analysis of variance method as the central research tool· The research focused on analyzing how whey, a byproduct of cheese production, could be used effectively in the production of flavored beverages, exploring its possible benefits and challenges from a comprehensive and multidisciplinary perspective· Through a series of experiments and exhaustive analyses, different variants of flavored beverages were examined, evaluating both their sensory quality and physical-chemical stability, and compared with beverages made without whey, revealing valuable insights about their viability and potential in the beverage industry· food and drinks· The findings of this study not only offer a deeper understanding of the role of whey in the production of flavored beverages, but also highlight the importance of the variance neutrosophic approach in evaluating this complex relationship· By integrating sensory analyzes with physicochemical measurements and stability considerations, a holistic and accurate picture of the effects of whey on the quality and characteristics of beverages could be obtained· These results not only have practical implications for the food industry, but also contribute to the advancement of research in multidimensional analysis methods and their application in the evaluation of innovative and sustainable food products.