A correlation coefficient is a statistical measure, which contributes measure, whichhe degree to which changes in one variable predict changes in another. In this article, we analyze the characteristics of Fermatean Quadripartitioned Neutrosophic sets with improved correlation coefficients. We have also used the same approach in multiple attribute decision-making methodologies including one with a Fermatean Quadripartitioned Neutrosophic environment. Finally, we implemented for above technique to the problem of multiple attribute group decision making.
Read MoreDoi: https://doi.org/10.54216/IJNS.270201
Vol. 27 Issue. 2 PP. 01-07, (2026)
The expanding growth of financial transactions has resulted in the development of fraud systems. These progressions have considerably improved overall productivity, improved corporate management, and reduced operational costs. With the expanded utilization of automated financial transaction, organization and businesses have progressed to digital platform, convert their financial operation. Still, such a change in addition revealed financial systems to new threats, mainly through fraudulent activity and cybercrime. The large datasets, incorporated with the limits of conventional fraud detection techniques, provide a chance to accept Artificial Intelligence (AI) methods. The fraud detection problem is addressed by using Explainable AI (XAI) to give specialists with explained AI predictions over different explanation models. This paper proposes a Financial Transaction Fraud Detection via Dimensionality Reduction with an Explainable Artificial Intelligence Approach (FTFD-DRXAIA) technique. The aim is to develop an effective and intelligent system for accurate fraud detection in financial transaction utilizing progressive deep learning (DL) methods. Initially, the min-max method is used for data pre-processing to convert raw data into an appropriate format. Furthermore, the recursive feature elimination (RFE) system is applied for feature selection. For financial fraud detection process, the Elman recurrent neural network (ERNN) has been utilized. Moreover, the wildebeest herd optimization (WHO) method fine-tunes the ERNN model's hyperparameters, resulting in improved classification performance. Finally, the XAI technique applies LIME and SHAP to interpret complex AI models, enabling auditors and analysts to detect suspicious transaction patterns with greater clarity and confidence. The experimental outcome of FTFD-DRXAIA system is examined under the financial fraud detection database. The comparison analysis of FTFD-DRXAIA algorithm demonstrated an optimum precision value of 98.96% over recent methods.
Read MoreDoi: https://doi.org/10.54216/IJNS.270202
Vol. 27 Issue. 2 PP. 08-22, (2026)
This work presents a neutrosophic extension of the Fréchet distribution to enhance the modeling of extreme values under conditions of indeterminacy and uncertainty. While the classical Fréchet distribution is widely used in fields such as finance, hydrology, and environmental sciences to model extreme maximum values, it does not fully accommodate imprecise, vague, or conflicting data commonly encountered in real-world scenarios. By incorporating the principles of neutrosophic logic the proposed neutrosophic Fréchet distribution provides a more flexible and realistic approach to representing extreme phenomena. The paper introduces its theoretical formulation, outlines key statistical properties, and proposes an estimation method based on maximum likelihood. Through simulations and numerical illustrations, the robustness and applicability of the model are described, especially in contexts where data is incomplete, uncertain, or contradictory. A real industrial dataset is employed to illustrate the applicability of the proposed model.
Read MoreDoi: https://doi.org/10.54216/IJNS.270203
Vol. 27 Issue. 2 PP. 23-32, (2026)
The neutrosophic set (NS) is a powerful tool for representing uncertain information in decision-making, extending conventional, fuzzy sets (FS), and intuitionistic fuzzy sets (IFS) by incorporating three degrees: truth, falsity, and indeterminacy. Sales prediction analysis wishes for intellectual data mining systems with precise predictive methods and higher trustworthiness. In the majority of cases, business depends heavily on information in addition to demand prediction of sales performance. The B2B data can offer information on how a business has to manage its products, sales team, and budget flows. Clear prediction techniques were analysed and examined using the model of machine learning (ML) to improve future sales predictions. It is challenging to manage sales prediction precision and big data (BD) when the technique of classic prediction is applied. Thus, the ML method can also be used to analyze the B2B sales reliability. This study proposes an Intelligent Business to Business Sales Estimation Framework Using Neutrosophic Soft Set (IB2BSEF-NSSS) method. The primary purpose of IB2BSEF- NSSS method is to develop an effective system for B2B sales estimation using advanced techniques for greater predictive precision. Initially, the min-max method is adopted in the data pre-processing phase to normalize input data. Additionally, the IB2BSEF-NSSS model leverages the zebra optimization algorithm (ZOA) technique for feature selection. Additionally, the generalized q-rung neutrosophic soft set (GqRNSSS) methodology is exploited for the sales prediction operation. To further increase prediction performance, the Kepler Optimizer Algorithm (KOA) model is employed for model fine-tuning, assuring optimum hyperparameter selection for upgraded accuracy. To expose the better performance of the IB2BSEF- NSSS technique, a wide-ranging experimental analysis is conducted under the B2B sales and customer insight analysis dataset. The comparison study of the IB2BSEF- NSSS technique exposed greater predictive performance, accomplishing the lowest MSE of 0.00670, indicating its efficacy over each other evaluated techniques.
Read MoreDoi: https://doi.org/10.54216/IJNS.270204
Vol. 27 Issue. 2 PP. 33-47, (2026)
In this paper, we introduce a new extension of the transmuted Lindley distribution (TLD) by utilizing neutrosophic logic to handle uncertainties that are often found in real life data. As classical probability models are not flexible enough for dealing with vague, imprecise, ambiguous, and incomplete information, neutrosophic theory is more general as it handles indeterminacy part associated with data. The proposed neutrosophic transmuted Lindey distribution (NTLD) combines indeterminacy concept, yielding a powerful statistical distribution, which is suitable for modeling both randomness and indeterminacy. Major functions such as probability density function (PDF), cumulative function (CDF), reliability function (RF) and hazard rate function (HRF) are established in this framework. Graphical analysis and simulated data are used to illustrate the performance of the model. Moreover, important moments such as mean, variance, skewness, and kurtosis are computed for different values of the neutrosophic parameters. The proposed distribution provides a generalized approach to model complex and uncertain data in reliability engineering, survival analysis, and decision-making. A real electricity consumption data from energy sector is utilized to show the proposed model applicability.
Read MoreDoi: https://doi.org/10.54216/IJNS.270205
Vol. 27 Issue. 2 PP. 48-57, (2026)
The primary aim of this study is to explore the integration of symbolic 2-plithogenic and 3 plithogenic rational functions by formulating explicit and simplified rules to facilitate their evaluation, by using the division symbolic 2-plithogenic and symbolic 3-plithogenic rational numbers respectively. In addition to the theoretical proof of these rules, relevant examples are provided to illustrate these ideas.
Read MoreDoi: https://doi.org/10.54216/IJNS.270206
Vol. 27 Issue. 2 PP. 58-67, (2026)
Healthcare data often involve uncertainty, imprecision, and partial information that are hardly handled by classical statistical models. Here, we propose a new generalization of the Gamma Lomax (GL) distribution under the neutrosophic environment, referred to as the neutrosophic Gamma Lomax (NGL) distribution, to overcome this drawback. In addition, the proposed model can be generalized to handle precise as well as uncertain healthcare data by incorporating neutrosophic logic including truth, falsity and indeterminacy. The classical properties of the Gamma-Lomax (GL) distribution are examined alongside their neutrosophic counterparts. Graphical representations, including density plots and associated reliability functions of the proposed model, are presented. The maximum likelihood estimation (MLE) is applied to find unknown parameters. The neutrosophic model is capable of modeling interval-valued results and uncertainties in practical data, and its effectiveness is verified by simulation studies and an illustration with infant mortality rates. The new method is conducive to the interpretability and credibility of statistical inference under uncertainty and is of high utility in health decision-making scenarios.
Read MoreDoi: https://doi.org/10.54216/IJNS.270207
Vol. 27 Issue. 2 PP. 68-78, (2026)
The neutrosophic set (NS) concept from the philosophical perspective extends and simplifies the principles of fuzzy set (FS) and intuitionistic FS (IFS). A NS is defined by truth, indeterminacy, and falsity membership functions, with each value belonging to the non-standard intervals (−0, 1+). In contrast to IFSs, there is no limitation in the membership function in NS, and the hesitancy degree is incorporated in NS. Arrhythmia is a medical illness wherein the regular pumping mechanism of the human heart becomes abnormal. The arrhythmia detection is one of the most essential steps to identify the disorder that can play a significant role in helping cardiologist with their decision. The initial identification of abnormal heart disease is critical for patients with heart disorders. Computer-aided diagnosis (CAD) has gained popularity in the arrhythmia domain recently, as artificial intelligence (AI) technology has matured. Still, the AI-based deep learning (DL) techniques are applied frequently to classify and detect arrhythmia. This paper presents an Enhanced Diagnostic Model for Cardiac Arrhythmia using Principal Component Analysis and Pythagorean Neutrosophic Bonferroni Mean (DMCA-PCAPNBM) technique in Cardiovascular Signal Processing. The objective is in the automated arrhythmia detection using advanced techniques. Initially, the DMCA-PCAPNBM model applies the min-max scaler-based data pre-processing technique for transforming input data into an appropriate format. In addition, the principal component analysis (PCA) method is applied for the feature subset selection model to pick out the optimal attributes from the dataset. For the procedure of arrhythmia detection, the PNBM model is utilized. Finally, the improved dung beetle optimization (IDBO) approach is applied for parameter tuning, resulting in enhanced classification performance. A comprehensive experimentation is implemented to verify the superior outcome of the DMCA-PCAPNBM model on the ECG arrhythmia classification dataset. The experimental validation of the DMCA-PCAPNBM approach illustrated an improved accuracy value of 99.06% over recent techniques.
Read MoreDoi: https://doi.org/10.54216/IJNS.270208
Vol. 27 Issue. 2 PP. 79-94, (2026)
Uncertainty, imprecision, and incomplete information are commonly found in complex economic and financial systems, and traditional probabilistic models are thus inadequate to accurately model and forecast these systems. In this work, a new extension of the Muth distribution in the neutrosophic environment is presented leading to the neutrosophic Muth distribution (NMD). This new model introduces neutrosophic parameters aiming to quantify vague and uncertain information and provides a flexible and robust approach to modeling right-skewed economic data. Some key characteristics including the density function and cumulative distribution function, moment generating function, and origin moments are obtained in the neutrosophic framework. The study of a model treated under uncertainty is described and an inferential method transforming it into neutrosophic maximum likelihood by interval-valued data is discussed. A real-world financial dataset is considered in order to prove the usefulness of the proposed distribution. The findings emphasize that the proposed distribution has the potential to be a comprehensive, flexible, and potential model for handling uncertainty in economics and finance data.
Read MoreDoi: https://doi.org/10.54216/IJNS.270209
Vol. 27 Issue. 2 PP. 95-109, (2026)
This study investigates the second-order Hankel determinant in the context of certain analytic functions to find upper bounds, incorporating neutrosophic logic to handle uncertainty in coefficient estimation. The normalized conditions ×’)0)=0 ×’′(0) = 1 are analyzed through both classical and neutrosophic frameworks. We derive: • Sharp neutrosophic bounds for |H2,2,ϖ| when ϖ ∈ (1, 3/2] • Optimal bounds for |H2,3| at ϖ = 3/2 in G(ϖ) and Q(ϖ) • Neutrosophic logarithmic coefficient determinants with τ -ι-φ membership degrees The framework demonstrates robustness when coefficients exhibit simultaneous membership/non-membership characteristics.
Read MoreDoi: https://doi.org/10.54216/IJNS.270210
Vol. 27 Issue. 2 PP. 110-122, (2026)
Ram Awadh (RA) distribution is flexible to handle skewedness and heavy tailed observations, which are frequent in financial risk management. With flexible structure, it has potential to be a reliable model in financial data modeling and decision-making process in the scenarios of indeterminacy. The new one parameter lifetime distribution is proposed and called as the neutrosophic RA distribution ( ) in this article. We obtain the raw and central moments of it and investigate some important statistical properties such as the coefficient of variation, skewness, kurtosis and index of dispersion. Moreover, some reliability properties such as the hazard rate function mean residual life function, and stochastic orderings of the distribution are considered. The method of maximum likelihood estimation (MLE) is utilized for parameter estimation. A comprehensive simulation study is carried out to evaluate the behavior of the distribution and its statistical properties. Finally, a real-world dataset of economic sector is utilized to illustrate its practical importance.
Read MoreDoi: https://doi.org/10.54216/IJNS.270211
Vol. 27 Issue. 2 PP. 123-131, (2026)
In this paper, I_g^*- closed sets, and I_g^*- open are used to investigate and define a new class of functions is said to be I_g^*-Continues functions, I_g^*-irresolute functions in ideal topological space topological spaces. Morover, I introduce I_g^*- compact spaces and I_g^*-connected spaces, and maximal I_g^*-closed sets. I obtain their characterizations and study their basic properties.
Read MoreDoi: https://doi.org/10.54216/IJNS.270212
Vol. 27 Issue. 2 PP. 132-143, (2026)
This paper introduces a novel extension of the multi-attributive border approximation area comparison (MABAC) method based on circular bipolar complex dual valued fuzzy uncertain linguistic sets (CBCDVFULSs) using Frank power aggregation operators. In order to effectively integrate aspects of fuzzy set theory, bipolarity, complex-valued, and uncertain linguistic information, this paper presents a novel framework based on CBCD- VFULSs. Frank power aggregation operators is used specifically for CBCDVFULSs in order to handle and aggregate such complex data. These operators maintain the circular and bipolar properties of the fuzzy linguistic data by utilizing the adaptability of Frank t-norms pFT N q and t-conorms pFT CN q. In contrast to current approaches, the suggested method’s superior handling of complex uncertain linguistic environments, flexibility, and applicability are demonstrated through a numerical example. A group message prioritization system for WhatsApp that involve deciding on the priority under complex, uncertain, and bipolar linguistic evaluations is used to demonstrate the efficacy of the suggested approach.
Read MoreDoi: https://doi.org/10.54216/IJNS.270213
Vol. 27 Issue. 2 PP. 144-168, (2026)
Average edge connectivity is a fundamental concept in graph theory, widely employed to evaluate the robustness of networks through the analysis of local edge cuts. Classical fuzzy extensions allow for graded membership, yet they fail to clearly distinguish between inherent uncertainty and definite absence of edges. To overcome this limitation, we introduce the notion of neutrosophic average edge connectivity, a tri-valued connectivity measure formulated within the framework of single-valued neutrosophic graphs (SVNGs). In this study, we rigorously define neutrosophic local edge cuts, establish key theoretical results including bounds and monotonicity properties, and design efficient algorithms tailored for particular families of graphs. The applicability of the proposed framework is demonstrated through a detailed communication-network case study, which highlights its capacity to capture structural resilience under indeterminate conditions. Overall, the proposed approach generalizes classical robustness indicators and provides a comprehensive tool for analyzing connectivity in networks characterized by vagueness, indeterminacy, and incomplete information.
Read MoreDoi: https://doi.org/10.54216/IJNS.270214
Vol. 27 Issue. 2 PP. 167-174, (2026)
The neutrosophic framework offers a promising direction for modeling data affected by uncertainty. Many quality characteristics in the production industry follow the asymmetric structure of the Maxwell distribution. The neutrosophic VSQ chart serves as a novel tool for monitoring parameters of the neutrosophic Maxwell distribution. However, the existing structure of the neutrosophic VSQ chart, based on the basic Shewhart model, is generally unable to detect small shifts in the production process. In this study, a new control chart designed following the structure of the EWMA chart is developed to efficiently monitor Maxwell-distributed neutrosophic data. The run length properties of the proposed scheme are studied, and Monte Carlo simulations are performed to investigate its statistical characteristics. Numerical results indicate that the proposed chart is effective in detecting small shifts in the process. The practical utility of the proposed chart is demonstrated through a real-world industrial dataset affected by uncertainty.
Read MoreDoi: https://doi.org/10.54216/IJNS.270215
Vol. 27 Issue. 2 PP. 175-187, (2026)
Let G be a group with identity e. Let T be a commutative G-graded ring with non-zero identity, W be a graded T-module and S ⊆ h(T) a multiplicatively closed subset of T. In this article, we introduce and study the concept of graded S-semiprime submodules. A graded submodule K of W with (K :T W) ∩ S = ∅ is said to be graded S-semiprime, if there exists a fixed st ∈ S such that whenever rn i mj ∈ K for some ri ∈ h(T), mj ∈ h(W), t, i, j ∈ G, and n ∈ N, then strimj ∈ K. Some characterizations and properties of graded S-semiprime submodules are given.
Read MoreDoi: https://doi.org/10.54216/IJNS.270216
Vol. 27 Issue. 2 PP. 188-194, (2026)
In this work, we use the symbolic 2-plithogenic integers and refined neutrosophic numbers to get a generalized version of HXDTRU with a strict approach includes three symbolic 2-plithogenic and refined neutrosophic private keys with one public symbolic 2-pithogenic and refined neutrosophic key to improve the security. In addition, we analyse the complexity of the generalized systems numerically.
Read MoreDoi: https://doi.org/10.54216/IJNS.270217
Vol. 27 Issue. 2 PP. 195-203, (2026)
A variety of mathematical frameworks—such as fuzzy sets, intuitionistic fuzzy sets, neutrosophic sets, soft sets, rough sets, and plithogenic sets—have been developed to model uncertainty, with wide applications in decision making, data analysis, and artificial intelligence. Within soft set theory, extensions like hypersoft sets, indeterm-soft sets, indeterm-hypersoft sets, bipolar soft sets, and bipolar hypersoft sets have further enhanced its expressive power. In this paper, we introduce two new constructs: bipolar indeterm-soft sets and bipolar indeterm-hypersoft sets. We provide their formal definitions, establish key algebraic properties, and demonstrate how they naturally combine bipolar evaluation with inherent indeterminacy. These models offer a versatile toolkit for capturing complex forms of uncertainty and lay the groundwork for future theoretical advances and practical applications in soft set theory.
Read MoreDoi: https://doi.org/10.54216/IJNS.270218
Vol. 27 Issue. 2 PP. 204-222, (2026)
The Travelling Salesman Problem (TSP) possesses a significant challenge in optimization, complicated by real-world uncertainties such as fluctuating traffic conditions, weather variability and inconsistent travel durations. Traditional mathematical formulation fails to adequately incorporate these uncertainties, thus limiting their effectiveness. This paper introduces a modified approach to solving the TSP by employing Single-Valued Triangular Neutrosophic Sets (SVTNS), which effectively manages the indeterminate and ambiguous data. The proposed methodology to transform the neutrosophic fuzzy data into crisp numbers using a specifically modified score function. A stepwise procedure is introduced, encompassing crisp conversion, range evaluation and iterative optimization processes to attain an optimal and practically viable solution. The proposed methodology is validated through numerical computation to demonstrate its efficiency in determining the minimal crisp travelling costs and optimizing travelling schedules under the various weighting scenarios. This research advances the applicability of neutrosophic sets in decision-making to provide a reliable framework to address the uncertainties inherent in practical travelling Salesman issues.
Read MoreDoi: https://doi.org/10.54216/IJNS.270219
Vol. 27 Issue. 2 PP. 223-234, (2026)
The purpose of this research is to introduce the notion of neutrosophic bipolar Ti – spaces (i = 0, 1, 2, 3, 4) via neutrosophic bipolar fuzzy topological spaces, and investigate their different properties. By defining neutrosophic bipolar Ti – spaces (i = 0, 1, 2, 3, 4), some interesting results on neutrosophic bipolar separation axioms via neutrosophic bipolar fuzzy topological spaces are proved.
Read MoreDoi: https://doi.org/10.54216/IJNS.270220
Vol. 27 Issue. 2 PP. 235-249, (2026)
The utilization of neutrosophic concept to forecast patron purchase conduct has been thoroughly tested in preceding research using various fashions. This study examines the number one elements affecting clients' selections to shop for mobile phones, dividing them into 4 separate ranges consistent with their purchasing behaviours. The tiers, from the first to the fourth layer, characterize exclusive ranges of customer hobby and participation. The main intention is to create an efficient neutrosophic predictive version that examines purchaser conduct thru pertinent traits that signify their opportunity of buying. We utilize the Neutrosophic Radial Basis Function (NRBF) model for neutrosophic class to do that. The results indicate a minimal blunders fee and improved neutrosophic category accuracy, mainly in contrast to the BIC version, which exhibited lower accuracy. NRBF exhibited a sturdy location below the curve (AUC) rating, underscoring the model's efficacy. These findings provide big insights into consumer preferences and decision-making methods, enhancing procedures for market analysis and cantered advertising initiatives.
Read MoreDoi: https://doi.org/10.54216/IJNS.270221
Vol. 27 Issue. 2 PP. 250-261, (2026)
Video codecs based on lossy compression techniques take advantage of removing redundant data in spatial and frequency domains. The various modes of intra- and inter-predictions help to reduce the redundant information in the spatial domain in standard video codecs like AVC, HEVC, and VVC. Further, the removal of redundant information in the frequency domain is achieved by adaptive quantization of transformed frames obtained after DCT-II or DST transformation techniques. In traditional video codec standards, adaptive quantization matrices are derived using the Human Visual System (HVS) model and display resolution parameters, which adjust the quantization step size to preserve perceptually significant pixel information in transformed blocks. The Neutrosophic (NS)-based approach introduces a more refined mechanism for generating the quantization matrix, utilizing Neutrosophic set membership values (true, indeterminate, and false) assigned to each region or frequency component of the transformed block. These values reflect the certainty of pixel relevance, enabling a more adaptive, perceptually driven quantization process. The proposed method incorporates NS logic in combination with the Human Visual System (HVS) model and display resolution parameters. By blending these factors, the quantization step size is optimally tuned to enhance visual quality. The HLS implementation of the transformation and quantization technique suitable for video codec acceleration using the OpenCL framework is adopted in our work. The design was implemented and tested on the Xilinx ZCU-104 board using a standard test sequence from the JCTVC and UVG datasets of various resolutions and diversified content. The testing showed an optimized resource utilization of 60.36%, with notable metrics indicating perceptually good results. The objective metrics showed an improvement of 3.77% in PSNR and 1.83% in SSIM compared to standard HVS-based quantization.
Read MoreDoi: https://doi.org/10.54216/IJNS.270222
Vol. 27 Issue. 2 PP. 262-274, (2026)
The transportation problem is a linear programming challenge focused on allocating resources efficiently across multiple locations while minimizing costs. Widely used in operations research, the transportation problem has numerous practical applications. Traditional approaches often struggle with imprecise data, which membership grades and fuzzy set theory can be used to address. Fuzzy sets concept provides a valuable framework for analysing transportation models under uncertainty. Neutrosophic sets have gained significant attention as a powerful tool for handling incomplete, ambiguous, and inconsistent data. Their ability to manage indeterminacy has made them increasingly popular in decision-making research, leading to extensive studies on their applications. This paper explores the use of imprecise parameters to improve transportation problem solution methods, emphasizing the versatility and advancements of neutrosophic sets. While various techniques exist for interpreting neutrosophic sets, certain limitations and field-specific requirements persist. In this study, trapezoidal fuzzy neutrosophic numbers make up fundamental components with respect to transportation problem. The proposed mathematical operations, algorithmic process, and framework achieve a 95% confidence level in clarifying uncertainties compared to the results with other methods. The effectiveness has been demonstrated with a numerical example for this approach, with comparisons to existing methods highlighting its advantages.
Read MoreDoi: https://doi.org/10.54216/IJNS.270223
Vol. 27 Issue. 2 PP. 275-286, (2026)
This article defines the central tendency fuzzy measures, which include the weighted fuzzy possiblistic mean and the fuzzy probability mean involving octagonal fuzzy numbers. The same is supported by a fuzzy variant of the Black-Scholes option model, in which uncertain pricing parameters such as volatility, interest rate, and stock price are described using octagonal fuzzy numbers.
Read MoreDoi: https://doi.org/10.54216/IJNS.270224
Vol. 27 Issue. 2 PP. 287-296, (2026)
Let 0 be a group, Υ be a 0-graded commutative ring with unity 1 and M a graded Υ-module. Our goal in this paper, introducing the concept of graded weakly Jgr -classical prime submodule as a generalization of graded weakly classical prime submodule and offering several results pertinent of graded weakly Jgr - classical prime submodules. For instance, we give characterizations of graded weakly Jgr -classical prime submodule. Also, we give some restrictions for graded submodule to be a graded weakly Jgr -classical prime submodule. A proper graded submodule V of M is said to be a graded weakly Jgr -classical prime submodule of M if, whenever 0̸ = abx ∈ V where a, b ∈ h(Υ) and x ∈ h(M), then either ax ∈ V + Jgr (M) or bx ∈ V + Jgr (M), The symbol Jgr (M) indicates the graded Jacobson radical of Υ-module M.
Read MoreDoi: https://doi.org/10.54216/IJNS.270225
Vol. 27 Issue. 2 PP. 297-302, (2026)
An interval-valued neutrosophic set is a type of neutrosophic sets where the membership, indeterminacy, and non-membership degrees are represented by closed intervals within the unit interval [0, 1]. An interval-valued picture fuzzy set is one of special cases of interval-valued neutrosophic sets. In this paper, we apply interval- valued picture fuzzy sets on almost ideals of semigroups. Moreover, we study a relationship between each almost ideal in a semigroup and their interval-valued picture fuzzifications.
Read MoreDoi: https://doi.org/10.54216/IJNS.270226
Vol. 27 Issue. 2 PP. 303-319, (2026)
Our study addresses the intuitionistic fuzzy system of linear Volterra-integro-differential equations of the second kind. Intuitionistic fuzzy General Transform (I-F-G-transform) method has been used to find the exact solution of these systems. We present two numerical examples for illustrating the applicability of the Intuitionistic fuzzy General integral transform method.
Read MoreDoi: https://doi.org/10.54216/IJNS.270227
Vol. 27 Issue. 2 PP. 320-340, (2026)
The main goal of this article is to study the division of symbolic n-plithogenic numbers using the identification method and n-plithogenic AH-isometry. In particular, we discuss the division of symbolic 2-plithogenic numbers and 3-plithogenic numbers, and we generalize these divisions. Additionally, we prove the validity of the formulas using AH-isometry and provide four worked examples to enhance understanding.
Read MoreDoi: https://doi.org/10.54216/IJNS.270228
Vol. 27 Issue. 2 PP. 341-350, (2026)
In this paper, we conduct a comprehensive study of neutrosophic subalgebras of various types within the framework of Sheffer stroke UP-algebras (SUP-algebras). Specifically, we introduce and characterize (∈, ∈), (∈, ∈ ∨q), and (q, ∈ ∨q)-neutrosophic subalgebras based on neutrosophic ∈-subsets, q-subsets, and (∈ ∨q)-subsets. Necessary and sufficient conditions are established for these subsets to form subalgebras under the Sheffer stroke operation. Several theorems demonstrate how these types interrelate and differ in their structural properties, with illustrative examples provided. Furthermore, we identify the conditions under which certain canonical subsets, such as X1 0 = {x ∈ X | T (x) > 0, I(x) > 0, F (x) < 1}, form subalgebras across differ- ent neutrosophic configurations. These results offer a unified perspective and deeper insight into the algebraic behavior of neutrosophic systems in the context of SUP-algebras.
Read MoreDoi: https://doi.org/10.54216/IJNS.270229
Vol. 27 Issue. 2 PP. 351-359, (2026)