International Journal of Neutrosophic Science

Accurate and timely recognition of plant diseases is crucial to prevent crop loss and ensure global food security. This paper presents a robust ensemble-based framework that combines six classical and state-of-the-art deep convolutional neural networks (DCNNs), including a ConvNeXt architecture, and integrates Neutrosophic Science to better handle uncertainty in leaf images. The proposed approach features three main components: (1) transfer learning with pre-trained DCNNs, (2) a model-averaging strategy to stabilise individual predictions, and (3) a stacked ensemble design that employs a radial basis function (RBF) meta-learner to refine the classification outputs. Experiments on the Plant Village dataset, comprising 54,305 segmented images of 38 plant diseases, included 10-fold cross-validation. The results show that the final stacking ensemble achieved near-perfect performance with 99.97% accuracy and an F1 score of 99.55% on an unseen test set of 27,160 images. Compared with standalone models, the ensemble demonstrated greater robustness in distinguishing visually similar diseases, benefiting from the complementary strengths of multiple DCNN architectures. The Neutrosophic component further enhances reliability by modelling uncertainties due to noise, occlusions, and environmental variations. Although a higher computational overhead and modest misclassifications remain, especially in certain visually overlapping classes, this study demonstrates the effectiveness of an ensembledriven, uncertainty-aware strategy. These findings hold considerable promise for real-world agricultural applications, where rapid and accurate disease diagnosis is paramount.

In this paper, we apply neutrosophic N-structures in ternary semirings. We consider ternary neutrosophic N-subsemirings of ternary semirings. We investigate the conditions for neutrosophic N-structures to be neutrosophic ternary N-subsemirings. In addition, we show the relation between ternary subsemirins and neutrosophic ternary N-subsemirins. Finally, we showed that the homomorphic preimage of the neutrosophic ternary N-subsemirings is a neutrosophic ternary N-subsemirings and the onto homomorphic image of the neutrosophic ternary N-subsemiring is also a neutrosophic ternary N-subsemirings.

This article presents a tool for international market selection (IMS) that integrates Neutrosophic Analytic Hierarchy Process (Neutrosophic AHP) and Monte Carlo simulation to reduce uncertainty in export decision-making. The methodology begins with a comprehensive literature review identifying five key criteria and twenty-three sub-criteria for IMS, supported by the insights of five notable authors in the field. Using Neutrosophic AHP, the weights of each criterion and sub-criterion are calculated and incorporated into a mathematical model designed for market selection. Data are collected from globally renowned sources and adjusted to probability distributions, enabling scenario simulation through Monte Carlo. The developed algorithm evaluates 193 countries, generating a ranking of potential destinations based on the determined weights and obtained information. The tool is validated by testing hundreds of products from 4,290 tariff lines under the SA 2012 version, confirming its applicability across diverse commercial contexts. The results highlight the tool's ability to accurately and adaptively identify viable export markets, offering a robust model for strategic decision-making in business internationalisation.

In this paper we apply the neutrosophic set on the concept of the UP-algebra to obtain some types of neurosophic sets satisfies certain conditions which are called neutrosophic Up-subalgebras. Several types of these neutrosophic Up-subalgebras are introduced and their properties are investigated. Also, illustrative examples are given when they are needed.

This paper explores the fundamental concepts of sub-level subgroups, element orders, normalizers, and centralizers within the framework of neutrosophic group theory. Additionally, it examines quotient groups and the index of a subgroup, extending classical algebraic structures to a neutrosophic setting. Finally, a generalized formulation of Lagrange’s theorem is presented, demonstrating its applicability in the neutrosophic environment and highlighting its implications for uncertain and indeterminate group structures.

Ranking algorithms are very important tools in decision making. There are two ranking algorithms for nvalued neutrosophic tuplets (Single-Valued MultiNeutrosophic tuplets): The S-ranking algorithm of Single- Valued MultiNeutrosophic tuplets, which is introduced by F.Smarandache in 2023, and the N-ranking algorithm of n-valued neutrosophic tuplets, Which is introduced by V. L. Nayagam and Bharanidharan R. in 2023. In this paper we show (by examples) that these two ranking algorithms are not a total ordering for the set of n-valued neutrosophic tuplets. These algorithms do not taking into account the number of sources, which is a very important factor in neutrosophic n-valued refined sets theory. We introduce two ranking algorithms: The integrated S-ranking algorithm of Single-Valued MultiNeutrosophic tuplets, and the integrated N-ranking algorithm of n-valued neutrosophic tuplets. These algorithms are improvements of the S-ranking algorithm of Single-Valued MultiNeutrosophic tuplets, and the N-ranking algorithm of n-valued neutrosophic tuplets, respectively, and taking the number of sources into account. We construct different examples to show that each step in the integrated ranking algorithms is necessary to make them a total ordering for the set of all n-valued neutrosophic tuplets.

Background: Neutrosophy is the subject area of philosophy that researches all associated with neutralities, owing to the contradictory information, lack of information, imprecise and paradoxical information, among them. The scale's design is organized to take the subjective quality of opinion, being responsible for either uncertainty or the indeterminacy of the respondents' opinions. It relies on the triple refined indeterminate neutrosophic sets (NS) for improved accuracy in understanding the agreement or disagreement level on particular items, like the competence of activities cost and financial management inside the legal services. Currently, customer abrasion is more and more serious in commercial banks, mainly, high-valued customers in retail banking. Therefore, it is stimulated to advance a prediction mechanism and recognize this customer may be at attrition risk. Thus, recognizing and lowering customer churn has become important for financial institutions trying to maintain customers. Currently, several researchers concentrate on customer attrition rate studies utilizing sophisticated machine learning (ML) and deep learning (DL) methods. Methodology: This study develops a Customer Attrition Prediction Using Triple Refined Indeterminate Neutrosophic Sets with an Optimization Algorithm (CAP-TRINSOA) technique. The main aim of the CAP-TRINSOA technique is to improve the attrition prediction of a customer in large-scale financial sectors using state-of-the-art techniques. In the initial stage, the data normalization employs mean normalization to transfer input data into an even format. Furthermore, the classification process is performed by implementing the triple refined indeterminate neutrosophic sets (TRINS). Finally, the honey badger algorithm (HBA) alters the parameter tuning value of the TRINS method optimally and results in greater performance of classification. Results: An extensive set of simulations is accomplished to exhibit the promising results of the CAP-TRINSOA method under the bank customer churn prediction dataset. The experimental validation of the CAP-TRINSOA technique portrayed a superior accuracy value of 97.65% over exisitng model in the customer attrition prediction process.

The aim of this article is proposed the notion of Correlation Measure for Neutrosophic Filter (NF). Additionally using correlation measure for neutrosophic set the application of medical diagnosis were discussed with numerical example.

This work analyzes neutrosophic fuzzification in algebra, applies novel classes of neutrosophic fuzzy () to algebra, and explores the ideas of ideal (), subalgebra (), δ-homomorphism, and ideal (), exploring some of their descriptions. We shall demonstrate a variety of applications, including the notations  and  on  /  is  of }. We will also investigate their equivalence classes, evaluate our findings in light of the unique ideas offered in this work, and investigate related characteristics.

The first appearance of COVID-19 in late 2019 and spread rapidly throughout the world until it became a global pandemic, and the World Health Organization announced some vaccines, and the emergence of a mutated version of COVID-19 was reported in several countries, including Iraq, and we will take care of conducting a study on the spread and dynamics of a virus, this work will be based on the study of the dynamics 3D harvesting predator (COVID-19) differential-algebraic predator-prey economic model (DA-PPM) with functional responses of Holing type-II. The appropriate and realistic description with high accuracy of this phenomenon, which may be natural and emerging as such models, has proven the sentimentality and existence of the solution to the system, and the stability of the system, was discussed in a manner similar to the stability of Matignon. The numerical results showed that the variables of stable unhappy situations have an effect, and this important study can be used as one of the methods of health science to control the spread of COVID-19 and its advanced models.  One of the critical aspects of sustainable development is building resilient health systems capable of dealing with epidemics and other crises, the mathematical model (DA-PPM) was applied to analyze the sustainability of health systems under the pressure of Covid-19 and evaluate how long-term public health policies and interventions can prevent overexploitation of resources. Ensuring equitable access to care. The application of the mathematical model to understand the spread of the epidemic is discussed to observe the spread of the epidemic, the possibility of coexistence with it, its close relationship with sustainable development, and to emphasize the importance of the flexibility of the health system. In addition, we apply our results on the neutrosophic supposed data that deals with uncertainty in real-life measurements and compare it with the classical results.