International Journal of Neutrosophic Science

In this work, a comparison plan of Agrobank and NBU for the financial years 2021, 2022, 2023, and 2024 is provided via neutrosophic approach in terms of indicators of profitability, liquidity, and solvency. The profits of the banks are analyzed through the application of net profit margin, profitability coefficient, absolute liquidity ratio, and solvency ratios. The economic ratios on profitability and liquidity point out that the NBU bank is performing better than the Agrobank but solvency ratios depict that Agrobank is more stabilized than NBU. This framework will avail a relative comparison of the two banks in terms of the opportunities, threats, strengths and weaknesses of each. In this way, findings can improve the understanding of banking industry’s performance in Uzbekistan and provide useful information to policuemakers and researchers. Continuation of the study could include the consideration of factors outside the firm to determine how they affect financial performance.  

The study examines the dynamics of a predator-prey model that includes temporal delays, concentrating on the impact of these delays on system stability and behavior.It delineates criteria for the global stability of the positive equilibrium using a generalized Lyapunov function and the Razumkin-type theorem, emphasizing the significance of temporal delays in biological systems. The research highlights the Neymark-Saker (NS) bifurcation, examining the impact of fractional configurations on this bifurcation and the system’s overall dynamic stability. The research utilizes the Lyapunov-Razumihin approach to identify bifurcation points and forecast the system’s progression in intricate ecological settings. The research examines the presence of periodic solutions and local stability criteria related to the two delays in predator-prey interactions. Numerical simulations are used to substantiate the theoretical results, specifically for the periodic bifurcation solutions associated with the Neymark-Saker bifurcation.

It is essential to create new mathematical strategies to deal with everyday problems since they require a lot of data and ambiguity. The best tool for doing this is proper functions, which are the most common mathematical technique. In order to generate suitable functions, we investigate several set operators. A connection between symmetry and certain types of proper functions and their classical topologies can be made. As a result of this symmetry, we can examine the traits and behaviors of traditional topological notions through settings, and vice versa. We describe a new class of proper functions in this paper and launch a preliminary investigation into them. These functions are referred to as pairwise local proper functions and pairwise local Lindel¨of proper functions in bitopological spaces. In general topology, we also establish the connection between this new class of proper functions and other classes of generalized functions already in existence. Regarding the new ideas, a number of relationships, necessary and sufficient conditions, examples and counter-examples are provided. In addition, a different argument for the pairwise regularity of a pairwise Hausdorff and pairwise locally compact bitopological space is presented. As part of this research, we also look at the images and inverse images of specific bitopological features under these functions. A few product theorems pertaining to these concepts were finally discovered.

It is shown that if A, B,X, and Y are operators acting on a finite dimensional Hilbert space, then. ωu (AXB∗ ± BYA∗) ≤ 2 ∥A∥ ∥B∥ ωu ([0 X, Y 0]) where ωu (T ), ∥T ∥, are, respectively, the U-numerical radius, the spectral norm, of an operator T .

In this paper, we study the relationships between the Neutrosophic quasi-Frobenius rings and the Neutrosophic of local rings and Artinian rings. In addition, we present study the relationship between the Neutrosophic quasi-Frobenius ring and some concepts such as Neutrosophic semisimple ring, Neutrosophic module injective and Neutrosophic Noetherian ring. Finally, we introduce some mathematical formulas with an commutative, coherent and Neutrosophic perfect ring, through which we obtain the Neutrosophic quasi-Frobenius ring.

In recent years, there has been a surge of attention to the Conjugate Gradient Method (CGM) and its applications. This is because the algorithm of CGM does not require the computation of the second derivative or an approximation during the iteration process. In this study, a four-term descent CGM is proposed by utilizing the famous Polak–Ribiere–Polyak (PRP) conjugate gradient formula. The direction of the proposed method achieves the descent property without line search consideration. In addition, the convergence properties are met to generate the stationary points. Findings from numerical experiments on unconstrained optimization and robotic motion control problems demonstrate that the novel approach outperforms some existing methods including the famous CG-Descent conjugate gradient method.

The neutrosophic set, a mathematical framework that accounts for truth, indeterminacy, and falsity, plays a crucial role in enhancing artificial intelligence (AI)-driven language education. By integrating neutrosophic logic, AI systems can better handle linguistic ambiguities, dynamically adapt learning materials, and offer more precise and personalized feedback. This paper explores the application of neutrosophic theory in intelligent tutoring systems (ITS), natural language processing (NLP), and AI-assisted feedback mechanisms, all within an uncertainty-based framework. Through the incorporation of neutrosophic models, AI can more effectively assess learner responses by considering elements of truth, uncertainty, and falsehood, leading to more adaptive and context-aware language instruction. Furthermore, the study highlights how AI, powered by neutrosophic logic, contributes to breaking language barriers, increasing accessibility, and fostering inclusive learning environments. Ethical concerns, bias mitigation, and data privacy challenges in AI-driven language learning are also addressed, emphasizing the need for responsible AI implementation. Finally, the paper underscores the synergistic balance between AI and human educators, advocating for adaptive AI frameworks that enhance linguistic comprehension while ensuring pedagogical integrity. Future research directions focus on leveraging neutrosophic logic to further improve AI's reliability, adaptability, and overall effectiveness in personalized language education.

Assume R is a commutative ring with unity. The clean graph CL(R) is defined in which every vertex has the form (a, v), where a is an idempotent in R and v is a unit. In CL(R), two distinct vertices (a1, v1) and (a2, v2) are adjacent if a1a2 = a2a1 = 0 or v1v2 = v2v1 = 1. In this paper, we show that the clean graph CL(R) over a ring of order p2 can be defined only if R is one of the rings: Zp2 ,Zp ⊕Zp,Zp(+)Zp and GF(p2). Then, we study the spectrum, the biclique partition number, and the eigensharp property for the these clean graphs.

The new theory of £ukasiewicz įntuitionistic ꞙuzzy set and £ukasiewicz įntuitionistic ꞙuzzy ꞙilter is introduced. Some properties of £ukasiewicz įntuitionistic ꞙuzzy ꞙilter is presented. It is explored that under what circumstances, the £ukasiewicz įntuitionistic ꞙuzzy set can be a £ukasiewicz įntuitionistic ꞙuzzy ꞙilter. An algorithm for diagnosing disease is developed and provided with demonstration.

Regression modeling is a significant statistical tool aimed at quantifying and understanding the nature of relations between the predictor and response variables. The routine parameter estimation procedures, like OLS and ML, are based heavily on the assumption of normality in data, which will not be the case for most real-world data scenarios. The paper presents a Neutrosophic approach for the estimation of parameters in multiple linear regression models, making use of the Neutrosophic principles to treat uncertainties, indeterminacies, and inconsistencies in actual data, a proposed method is called the Simple Averaging Method, or SAM. This is a robust alternative to traditional methods and provides reliable results even if the assumptions of normality are not held. SAM performance is tested using real-time crime data in the USA and demonstrates its capabilities to deal with complex datasets. The comparative analysis between the OLS model and the same model is done via RMSE and MAD metrics. The results show that SAM significantly outperforms OLS with an RMSE of 34.37598 in contrast to 58.05248 for OLS. Graphical analysis further confirms SAM's performance over and above OLS. Critical issues of regression modeling with incorporation of neutrosophic logic cover their critical challenges, especially when standard assumptions are violated.

A neutrosophic set (NS) contains 3 modules such as the degree of truth (T), degree of falsity (F), and degree of indeterminacy (I). While fuzzy graphs (FG) occasionally fall short of providing optimum outcomes, the NS and neutrosophic graphs (NG) provide a strong substitute, which efficiently handles the uncertainties related to indeterminate and inconsistent data in real-life scenarios. Conversely, bipolar neutrosophic methods, which account for both negative and positive effects, deliver a more flexible and applicable technique. Financial crisis prediction (FCP) is inherent in the detection of major social and economic impacts that crises of financial might hold on a global measure. It generally outcomes in vast financial losses, redundancy, and losses in values of assets that lead to significantly affected individuals and businesses. In recent times, the credit risk prediction methods have aided businesses in resolving whether to award credit to users who applied. This paper presents the Financial Credit Risk Forecasting Using Bipolar Single-Valued Neutrosophic Graph Sets Approach (FCRF-BSVNGSA) method. The main intention of the FCRF-BSVNGSA method is to develop an effective method for financial credit risk prediction using advanced methods. At first, the data normalization stage utilizes Z-score normalization for converting the input data into a beneficial format. Furthermore, for the financial credit risk classification process, the proposed FCRF-BSVNGSA model employs the bipolar single-valued neutrosophic graphs (BSVNG) approach. Finally, the multi‐objective hippopotamus optimization (MOHO) approach fine-tunes the hyperparameter values of the BSVNG model optimally and results in superior classification performance. An extensive simulation of the FCRF-BSVNGSA approach is performed under the Statlog (German Credit Data) dataset. The experimental validation of the FCRF-BSVNGSA approach portrayed a superior accuracy value of 95.59% over exisitng techniques.

Fuzzy fractional partial differential equations have become a powerful approach to handle uncertainty or imprecision in real-world modeling problems. In this article, two compact finite difference schemes, the compact Crank-Nicolson and the compact center time center space methods, were developed and used to obtain a numerical solution for fuzzy time fractional wave equations in the double parametric form. The principles of fuzzy set theory are utilized to perform a fuzzy analysis and formulate the proposed numerical schemes. The Caputo formula is used to define the time-fractional derivative considered. The stability of the proposed schemes is analyzed by means of the Von Neumann method. To illustrate the practicality of the numerical methods, a specific numerical instance was performed. The outcomes were showcased through tables and figures, revealing the efficacy of the schemes in terms of accuracy and their ability to decrease computational expenses.

In this paper, we defined some new kinds of continuous functions in fuzzy neutrosophic topology and called fuzzy neutrosophic - continuous, fuzzy neutrosophic weakly  continuous, fuzzy neutrosophic strongly - continuous, fuzzy neutrosophic -contra continuous, fuzzy neutrosophic weakly -contra continuous and fuzzy neutrosophic strongly -contra continuous functions. Then, we defined the relationship between the define functions with their comparative.

In this paper, we study the notion of principal (crisp) fuzzy ideals (resp. filters) on the setting of trellises (or weakly associative lattices as called by several authors). More specifically, we introduce the notions of L-fuzzy ideals and L-fuzzy filters on a given trellis and provide basic characterizations of these notions based on their weakly associative meet and join operations. We pay particular attention to the kind of principal L-fuzzy ideals (resp. filters) on a given trellis, which are more complicated in the absence of the (associativity) transitivity property.

Neutrosophic cognitive maps are expansion of fuzzy cognitive maps, containing indetermination in causal relations. Fuzzy cognitive maps do not require an indeterminate relationship, making it less adequate for real-time applications. A logic in which every proposition is projected to have the truth percentage in subset T and the falsity percentage in subset F is named Neutrosophic Logic. This logic is also considered the general form of Intuitionistic fuzzy logic. Stock price prediction is a main topic in economics and finance, which has promoted the priority of investigators in recent years to improve improved predictive methods. Predicting price and tendency of the stock market denote indispensable features of finance and investment. Many scientists have presented their ideas to predict the market price to make money while trading utilizing different methods like statistical and technical analysis. This manuscript proposes a Neutrosophic Cognitive Map-Based Short-Term Financial Stock Market Price Trend Prediction (NCM-SFSMPTP) model. The main goal of NCM-SFSMPTP technique relies on improving the accurate approach for stock market price trend prediction. At first, the min-max normalization methodology is utilized in the data normalization phase to standardize and scale data for consistency, comparability, and efficient processing. For the classification process, the neutrosophic cognitive map (NCM) technique is employed. Finally, the improved arithmetic optimization algorithm (IAOA)-based hyper-parameter selection is implemented to enhance the classification outcomes of the NCM system. The performance validation of the NCM-SFSMPTP methodology is verified under the Apple Stock Price Trend and Indicators dataset and the outcomes are determined regarding to several measures. The experimental validation of the NCM-SFSMPTP method illustrated a superior accuracy value of 94.79% over existing models in stock market price trend prediction process.