Depending on the geometric isometry (AH-Isometry), it has been proven that every Neutrosophic real function is equivalent to three real functions. Then, the foundation of the Refined Netrusophic calculus was established, where new definitions of Refined Netrusophic integration and Refined Netrusophic differentiation were introduced, along with some illustrative examples. Following that, definitions for the Refined Netrusophic gamma function and Refined Netrusophic beta function were presented to pave the way towards achieving the desired goal, which is Refined Netrusophic Fractional calculus.
Read MoreDoi: https://doi.org/10.54216/IJNS.240201
Vol. 24 Issue. 2 PP. 08-18, (2024)
In this paper, maximum likelihood estimation method (MLEM), one of the most well-liked and frequently applied classic methods, is used to estimate the two scale and one shape parameters of the Generalized Exponential-Rayleigh distribution for type-I censored data, which is one of the most Rights censored data. Based on an iterative process to get approximated values for these two scale parameters and one shape parameter using the Newton-Raphson method to locate estimate value for these parameters by using the simulation procedure utilizing monte-Carlo technique to find Reliability function underneath various sample sizes and the initial values are different for the parameters for all estimated parameters of Generalized Exponential-Rayleigh by implement the initial value in the MATLAP program, Subsequently, conducting a comparative analysis between the estimated reliability function and its non-estimated counterpart employing the mean squares error methodology. In the last finding the pdf function f (t), reliability function R (t) and hazard function h (t) for simulation data. Also, we provide some examples to clarify how can we apply our results on fuzzy data tables
Read MoreDoi: https://doi.org/10.54216/IJNS.240202
Vol. 24 Issue. 2 PP. 19-29, (2024)
The theory of Plithogeny is primarily attribute based. Plithogenic Sociogram (PS) and Plithogenic cognitive maps (PCM) are distinct decision-making approaches developed to deal with attributes. This paper proposes an integrated decision-making model combining the approaches of PS with PCM and this sets the beginning of new genre of PCM. The development of this model is applied in investigating the association between the factors pertinent to the promotion of sustainable industries. This work also compares the working of the proposed integrated model of PCM with PS and the independent working of PCM model. The results are more promising to the proposed integrated approach and this paper strongly emphasises the efficacy of this hybrid approach. The blended model of PCM with PS is efficient in handling complex decision circumstances and this approach shall be extended to other kinds of Plithogenic representations.
Read MoreDoi: https://doi.org/10.54216/IJNS.240203
Vol. 24 Issue. 2 PP. 30-41, (2024)
This article explores the implementation of Neutrosophic TOPSIS, an advanced decision-making framework that extends classical and fuzzy set theories to handle the complexities of project selection amid uncertainty and indeterminacy. Neutrosophic sets are characterized by three parameters: truth, indeterminacy, and falsehood, which allow for a nuanced assessment of alternatives against defined criteria. Utilizing neutrosophic scales and expert evaluations, this method prioritizes projects by efficiently balancing multiple truth levels and addressing specific challenges such as judicial process optimization and labor education enhancement. The case study within the article demonstrates the application of Neutrosophic TOPSIS to select the most suitable project for improving labor relations and judicial efficiency in a post-pandemic world. The methodology proved effective in identifying the Digital Platform for Labor Education project as the optimal solution, given its alignment with strategic objectives and potential to handle identified challenges robustly. Future work could integrate Neutrosophic TOPSIS with other decision-making models and expand its application to more complex scenarios, potentially incorporating automated tools for a broader and more dynamic evaluation process.
Read MoreDoi: https://doi.org/10.54216/IJNS.240204
Vol. 24 Issue. 2 PP. 42-49, (2024)
This study utilized Neutrosophic Cognitive Maps (NCMs) integrated with the D-OWA operator to analyze the nutritional rights of pregnant women in Ecuador, with a focus on the crucial role of nutrition education. The innovative application of the D-OWA operator enabled the computation of a composite centrality measure by merging key centrality indicators—degree, closeness, and betweenness—each appropriately weighted according to its relevance to the analysis. This methodology provided a sophisticated evaluation of the factors impacting maternal nutrition, demonstrating how combining various centrality measures offers a deeper and more comprehensive insight into the dynamics of complex systems. The calculated composite centrality measures revealed the system’s intricate structure, pinpointing critical nodes and pathways that could be targeted most effectively through interventions. The findings underscore the significant benefits of using composite centrality measures to enhance decision-making in public health and other sectors characterized by complexity and uncertainty. The potential for refining and expanding this approach in future research suggests that it could be further supported by technological advancements, enabling more efficient analysis and scalability across diverse complex systems.
Read MoreDoi: https://doi.org/10.54216/IJNS.240205
Vol. 24 Issue. 2 PP. 50-57, (2024)
The integration of the Analytic Hierarchy Process (AHP), the Delphi method, and neutrosophic logic provides a powerful framework for complex decision-making, allowing for an enhanced handling of uncertainties and multiple criteria that characterizes many strategic planning and policy formulation scenarios. AHP’s structured approach helps decompose decision-making into manageable sub-problems, while the Delphi method facilitates expert consensus through iterative rounds, enriching the decision-making process with diverse expert insights. The inclusion of neutrosophic logic allows for better representation and processing of uncertainty, offering a flexible way to handle indeterminate and contradictory information. This robust methodology not only improves the precision of decisions but also adapts to the nuanced requirements of multifaceted decision environments. Future research could benefit from integrating these methods with technological advancements like artificial intelligence to automate and optimize the decision-making process further. Applying this integrated approach in various sectors such as healthcare, environmental management, and urban planning could also provide valuable insights into its effectiveness and scalability.
Read MoreDoi: https://doi.org/10.54216/IJNS.240206
Vol. 24 Issue. 2 PP. 58-67, (2024)
Industry has developed greatly nowadays, and it has been accompanied by great complexity in machines and devices. Researches that seeks to obtain high efficiencies for these machines have emerged , such as reliability theory. Due to the verity and complexity of the machines, we resort to using the neutrosophic reliability that includes cases excluded from classical reliability. The aim of this paper is to define the neutrosophic parallel system and study neutrosophic methods of calculating the neutrosophic reliability, where the basic concept neutrosophic adjacency matrix of system are present by defined neutrosophic adjacency matrix of neutrosophic graph. Two methods for calculate the neutrosophic reliability are defined conformity to neutrosophic logic which are neutrosophic minimal path method and neutrosophic tracing method. some applications have been introduced.
Read MoreDoi: https://doi.org/10.54216/IJNS.240207
Vol. 24 Issue. 2 PP. 68-79, (2024)
Industrialization and urbanization air is getting polluted due to human activities. CO, NO, C6H6, etc., are the major air pollutants. The focus of air pollutants in ambient air is controlled by the climatological parameters including wind direction, atmospheric speed of wind, temperature, and humidity. Air pollution prediction is a critical sector where machine learning (ML) technique plays a major role. Its main purpose is to tackle and understand the damaging effects of air pollutants on the environment and human health. By using a range of ML techniques such as neural networks, regression, and decision trees, we could analyze historical data on air quality alongside geographical and meteorological factors. This allows us to design model that could detect patterns and predict pollution levels. By taking proactive measures such as providing timely alerts to the public, adjusting controls on emissions, and, implementing strategies to reduce pollution, we can work towards creating healthier and cleaner environments. Embracing the potential of artificial intelligence (AI) in air pollution prediction empowers us to protect the well-being of our communities and make informed decisions. Therefore, this study develops an Improved Sine Trigonometric Single Valued Neutrosophic Information based Air Pollution Prediction (ISTSVNI-APP) approach. The major objective of the ISTSVNI-APP technique is to exploit AI concepts with neutrosophic sets (NS) models for the forecasting of air pollution. To do so, the ISTSVNI-APP technique makes use of min-max normalization as the initial preprocessing step. For predicting air pollution, the ISTSVNI-APP technique uses STSVNI approach. To improve the performance of the ISTSVNI-APP technique, modified crow search algorithm (MCSA) is used for the parameter tuning of the STSVNI system. The performance evaluation of the ISTSVNI-APP method is verified utilizing benchmark dataset. The experimental outcomes stated that the ISTSVNI-APP technique gains better performance in predicting air pollution
Read MoreDoi: https://doi.org/10.54216/IJNS.240208
Vol. 24 Issue. 2 PP. 80-93, (2024)
Tropical cyclones (TCs) are powerful, low-pressure weather systems attributed to heavy rainfall and strong winds, and have often resulted in extensive damage to coastal regions. TC intensity prediction, an essential aspect of meteorological forecasting, includes evaluating the strength of the storm to facilitate disaster preparedness and alleviate possible risks. Classical approaches for the prediction of TC intensity rely on different oceanic and atmospheric parameters, but the incorporation of artificial intelligence (AI) approaches, especially those leveraging image data, provides positive breakthroughs in efficiency and accuracy. By harnessing AI techniques like deep learning architectures and convolutional neural networks (CNNs), meteorologists could analyze radar data, satellite imagery, and other visual inputs to distinguish complicated patterns indicative of intensity changes and TC development. This combination of weather science and AI-driven image analysis enables more timely and precise predictions and improves our understanding of TC dynamics, eventually fortifying protection against the impacts of formidable storms. This article introduces Neutrosophic TOPSIS with Artificial Intelligence Driven Tropical Cyclone Intensity Estimation (NTOPSIS-TCIE) technique for Weather Prediction. The presented NTOPSIS-TCIE technique determines the intensities of the TC which in turn helps to forecast weather. In the NTOPSIS-TCIE technique, median filtering (MF) approach is used to remove the noise in the images. In addition, the features are extracted using deep convolutional neural network (CNN) model. To enhance the performance of the CNN model, Harris Hawks Optimization (HHO) algorithm is applied. Finally, the NTOPSIS model is employed for the prediction of TC intensities. The performance of the NTOPSIS-TCIE technique can be studied using TC image dataset and the results signify its promising results over other models
Read MoreDoi: https://doi.org/10.54216/IJNS.240209
Vol. 24 Issue. 2 PP. 94-107, (2024)
The purpose of the current paper is study some new concept of sets and called fuzzy neutrosophic rar and fuzzy neutrosophic dense sets in fuzzy neutrosophic opology and investigate some properties. In fact, the subject of fuzzy neutrosophic sets is already conducted by F. M. Mohammed et.al. [1-9]. However, the current study illustrates number of notable examples to shed the light on some novel attributes of recently established terms, as well as showing related interactions among these researches.
Read MoreDoi: https://doi.org/10.54216/IJNS.240210
Vol. 24 Issue. 2 PP. 108-119, (2024)
This paper introduces a new statistical distribution called the Neutrosophic Extended Rayleigh Distribution (NERD), which is specifically developed to handle uncertainty commonly found in industrial applications. We conduct a comprehensive examination of the statistical characteristics of NERD, including important measures such as the quantile function, moments, moment generating function, mean deviation, skewness, kurtosis, reliability measures, uncertainty measures, distributions of order statistics, and L-moments. Parameter estimation is conducted by maximum-likelihood estimation within a neutrosophic framework, guaranteeing resilient inference in practical situations. Through the application of NERD to actual industrial datasets, we evaluate its adaptability and efficiency in simulating industrial processes. A real case study of Al-Kharj region demonstrates the higher performance of NERD. This research highlights the capacity of NERD to greatly improve productivity and efficiency in several industrial sectors.
Read MoreDoi: https://doi.org/10.54216/IJNS.240211
Vol. 24 Issue. 2 PP. 120-130, (2024)
In this study, we introduce a new concept by making Possibility Fermatean fuzzy soft sets into a more general concept, namely Intuitionistic Possibility Fermatean fuzzy soft sets. We present examples of the application of this theory to a decision-making problem. From a theoretical point of view, we review the basic properties of this model and define the operations essential to its framework. Comprehensive definitions of complement, union, and intersection, as well as AND and OR operations are meticulously presented. As a transition from theory to practical application within this innovative context, we present an algorithm for solving decision-making problems, contributing to the practical implementation of this extended concept. This research aims to improve our understanding of the intuitionistic possibility of Fermatean fuzzy soft sets and to bridge the gap between theoretical advances and their real-world utility in decision-making problems.
Read MoreDoi: https://doi.org/10.54216/IJNS.240212
Vol. 24 Issue. 2 PP. 131-146, (2024)
We introduce the concept of sine trigonometric (g1, g2, g3) neutrosophic normal interval valued set. An identifying sine trigonometric (g1, g2, g3)neutrosophic normal interval valued set is a combination of (g1, g2, g3) neutrosophic interval valued set and neutrosophic interval valued set. We communicate the new aggregating operator such as sine trigonometric (g1, g2, g3) neutrosophic normal interval valued weighted averaging, sine trigonometric (g1, g2, g3) neutrosophic normal interval valued weighted geometric, sine trigonometric generalized (g1, g2, g3) neutrosophic normal interval valued weighted averaging and sine trigonometric generalized (g1, g2, g3) neutrosophic normal interval valued weighted geometric.
Read MoreDoi: https://doi.org/10.54216/IJNS.240213
Vol. 24 Issue. 2 PP. 147-162, (2024)
In this paper an idea of neutrosophic convex structures (briefly, NC-structures) is given and some of their properties are explored. Also, NC-sets, neutrosophic concave sets and neutrosophic convex hull are defined and their properties are investigated. Moreover, the notions of NC-derived operator and NC-base are studied and their relationship to NC-structures are established.
Read MoreDoi: https://doi.org/10.54216/IJNS.240214
Vol. 24 Issue. 2 PP. 163-175, (2024)
The notion of a neutrosophic Abelian subgroup of a group is introduced. The characterizations of a neutrosophic Abelian subgroup are investigated. We show that the homomorphic preimage of a neutrosophic Abelian subgroup of a group is a neutrosophic Abelian subgroup, and the onto homomorphic image of a neutrosophic Abelian subgroup of a group is a neutrosophic Abelian subgroup.
Read MoreDoi: https://doi.org/10.54216/IJNS.240215
Vol. 24 Issue. 2 PP. 176-186, (2024)
Fuzzy concepts have been widely used to treat imprecision in many fields of natural and social sciences. In most of the natural science fields such as applied mathematics, physics, chemistry, and engineering, triangular and trapezoidal fuzzy numbers are commonly used and arithmetic operations on those numbers are studied in detail. On the other hand, in engineering and social science fields such as sociology and psychology, while treating the uncertainties, these numbers are not applicable and fuzzy numbers with more parameters and clear definitions of their arithmetic operations are needed. In order to fill this gap in the literature, in this study we propose the generalized pentagonal fuzzy numbers, and we define fuzzy arithmetic operations based on both extension and the function principle.
Read MoreDoi: https://doi.org/10.54216/IJNS.240216
Vol. 24 Issue. 2 PP. 187-197, (2024)
Lifetime analyses comprise the techniques dealing with observations obtained from the occurrence of a specified event(s). In most of the situations dealing with lifetime observations, some units are recorded as censored observations. Dealing with censored observations makes these techniques unique. Countless standard statistical tools are available for inference based on censored lifetime observations. These classical techniques consider lifetime observations as precise numbers and ignore the uncertainty of single observations. Whereas in practical applications it is not possible to measure life times as precise numbers, they are always more or less nonprecise. The imprecision in measurements can be covered by neutrosophic set. Fuzzy estimators for life time distributions potentially use neutrosophic system to model and analyze the inherent uncertainties and neutalities present in the data and the parameter estimates. This study aimed to obtain estimators for the Weibull parameters and two exponential parameters based on the up-to-date fuzzy number approach, a special case for neutrosophic set. The suggested estimators incorporate fuzziness in addition to random variation, which makes these estimators more realistic. The same techniques need to be extended to fuzzy and neutrosophic sets.
Read MoreDoi: https://doi.org/10.54216/IJNS.240217
Vol. 24 Issue. 2 PP. 198-209, (2024)
This paper introduces a new Neutrosophic Adaptive Neuro-Fuzzy Inference System paired with Explainable Artificial Intelligence to classify oral cancer from clinical photos. The ANFIS model’s interpretability and accuracy have been enhanced in resolving challenging medical images by deploying Neutrosophic logic on a 1000-image dataset to solve the word indeterminacy. A combination of Neutrosophic sets addresses ambiguity, enabling an adaptive neuro-fuzzy network to learn from data to accurately classify oral cancer. This exhibits the benefits of fuzzy logic and neural networks in action. The parameters of this model have been changed meticulously to increase sensitivity, specificity, and accuracy toward diagnostic readiness. These results reflect a substantive enhancement in the model’s ability to distinguish between benign and malignant lesions by delivering accurate and understandable diagnostic decisions existence for clinical adoption. AI medical diagnostic confidence increases the understanding of how the model makes decisions. The ideal objective is to develop a strong, dependable, and easy-to-understand tool to diagnose cancer early. The experimentation on this model can be improved as it may lead to real-time testing, more data for the testing dataset, and using how many types of cancer the model can be applied.
Read MoreDoi: https://doi.org/10.54216/IJNS.240218
Vol. 24 Issue. 2 PP. 198-221, (2024)