International Journal of Neutrosophic Science

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.