International Journal of Neutrosophic Science

The main goal of this paper is to define and study the concept of beta special function defined over the ring of symbolic 2-plithogenic numbers and symbolic 3-plithogenic numbers. Besides, we prove some of the elementary properties of these two versions of beta function by using the isomorphism that connect plithogenic numbers with the classical real numbers. In addition, we represent the relationships between plithogenic beta functions and classical beta functions using the same proposed technique.

The importance of Neutrosophic crisp triple sets and their important effects on our daily lives was and still is aturing point in the history of science, especially mathematical sciences. From here, we began a ƝҪͳ–confused, concept that is based on both ƝҪͳ–interior, and ƝҪͳ– exterior, and important characteristic emerged because of mixing the characteristic of ƝҪͳ– interior and ƝҪͳ– exterior sets. We supported this with various examples.

 In this paper, we present novel techniques for the logarithmic neutrosophic interaction (LogNI) aggregating operator. The new averaging and geometric operations of LogNI numbers are studied using the universal aggregation function. The LogNI are satisfied some algebraic properties. Four novel aggregating operators are presented: LogNI weighted averaging, LogNI weighted geometric, generalized LogNI weighted averaging, and generalized LogNI weighted geometric.

In this paper, we will use the family of regular⁺-open subsets to present and examine two new operators (.){PR⁺}⊛ and Cl{PR⁺}⊛. We demonstrate that, in contrast to the operator (.){PR⁺}⊛, the operator Cl{PR⁺}⊛ is a Kuratowski closure operator. We show that each of these operators lies between two previously defined operators where for each subset H⊆S, H_Pᶲ⊆H_{PR⁺}⊛⊆H_PRᶲ and H⊆Cl_Pᶲ(H)⊆Cl_{PR⁺}⊛(H)⊆Cl_{PR}ᶲ(H). Furthermore, we show that the topology, denoted by T_{PR⁺}⊛, which is obtained by Cl_{PR⁺}⊛ is independent from T and it is finer than T_η⁺, where T_η⁺ is the family of all unions of regular⁺-open subsets of (S, T). Then we demonstrate several fundamental results concerning this new structure and present many illustrative examples that relate to our conclusions. Finally, by using the operator Cl_{PR⁺}⊛ we introduce a new notion namely, P-generalized closed sets, and study some of their basic properties.

The most effectual tools for demonstrating uncertainty in decision-making issues are the neutrosophic set (NS) and its additions, like interval NS (INS), complex NS (CNS), and interval complex NS (ICNS). NS delivers an effectual and precise method for defining an imbalance of information as per the data features. In present times, students’ academic performances have been evaluated on the base of regular examinations or memory-related tests and by equating their performances to recognize the features for forecasting their academic excellence. The prediction of student academic performance is involved in Educational data mining (EDM), which mainly focuses on using data mining methods in the educational side. EDM progress models for finding data, which is a result of educational surroundings. This paper presents a Student Academic Performance Prediction Using N-Valued Interval Neutrosophic Sets and Optimization Algorithms (SAPP-NINSOA). The main intention of the SAPP-NINSOA technique is to provide a prevalent technology for predicting students’ academic performance using an advanced optimization algorithm. At first, the data pre-processing stage applies Z-score normalization to convert input data into a beneficial format. Besides, the secretary bird optimization algorithm (SBOA) to select the relevant features from input data has executed the feature selection process. Next, the proposed SAPP-NINSOA model designs the N‐Valued Interval Neutrosophic Sets (NVINS) method for the classification process. Finally, the arithmetic optimization algorithm (AOA) fine-tunes the parameter values of the NVINS model. An extensive range of experimentation was led to certify the performance of the SAPP-NINSOA technique. The simulation outcomes stated that the SAPP-NINSOA algorithm emphasized furtherance when compared to other existing systems.

This research work examines the critical challenge of enhancing educational environments through social media feedback, often impeded by the very uncertainties and complexities offered by textual data. Existing approaches either may indulge in sentiment analysis or may take the approach of basic data mining; nevertheless, they seldom consider ambiguity, contextual subtlety, and dynamic interventions. We propose an entirely new framework using Hybrid Neutrosophic Decision Optimization (HNDO) and Neutrosophic Sentiment Fusion (NSF) with deep learning-for advanced feature extraction-and reinforcement learning-for adaptive intervention strategies, with Explainable AI (XAI) for transparency. Presenting a new Neutrosophic Quantum Squirrel-Whale Decision Optimization (NQSWDO) framework to optimize educational enhancements based on feedback surveys and social media sentiment analysis, where it can collect, preprocess, extract features, fuse sentiments, optimize decisions, and detect concerns through reinforcement learning before interpreting feedbacks. A Neutrosophic Sentiment Fusion (NSF) model is applied to bring improvement into the accuracy of sentiment classification. Further refinement of educational improvements will come through the new application of hybrid neutrosophic decision optimization (HNDO), which incorporates multi-criteria decision analysis (MCDA) and fuzzy logic. For identification of key concerns, the VGG-Darknet detection model will be used, as well as a deep Q-network (DQN)-based reinforcement-learning system that dynamically intervenes in topic analysis. The last phase will comprehensively interpret feedback and adopt decision-making strategies to avoid wasting time in properly formulating useful educational policies. The results from the experiments indicate the practicality of the proposed framework for improving education decision-making through advanced methodologies on sentiment analysis, optimization, and reinforcement learning.

This article introduces a neutrosophic methodological framework for conducting personnel marketing research in the rural labor market of Uzbekistan. Given the inherent uncertainty and indeterminacy in labor market dynamics, the study applies neutrosophic logic to enhance the reliability of marketing data regarding labor demand and supply. The research outlines the interrelated stages of personnel marketing analysis, incorporating neutrosophic sets to better identify discrepancies between labor demand and supply, the scale and causes of rural unemployment, and the structural needs for new professions. Key areas of focus include problem identification, goal formulation, data collection and analysis, forecasting labor market trends, and developing targeted interventions to mitigate unemployment and improve workforce qualifications. Additionally, the study proposes strategic marketing initiatives for rural employment assistance centers, integrating neutrosophic decision-making models to optimize labor market strategies. By adopting neutrosophic approaches, the study provides a robust, uncertainty-aware methodology for balancing labor market proportions and formulating evidence-based policies to enhance rural employment opportunities.

In this paper, we introduce a novel extension of the symmetry operational matrix method specifically designed to tackle tempered fractional differential equations (FDE) that incorporate an additional function. Our approach leverages the framework of shifted Legendre polynomials (SLP), which are well-suited for this context. While the operational matrix method has been widely recognized for its efficacy in addressing a range of problems within fractional calculus, its application to tempered fractional differential equations remains relatively uncharted territory. To bridge this gap, we begin by deriving the analytical expression for the tempered fractional derivative (TFD) of the term τ p. This crucial step paves the way for the formulation of a new operational matrix that captures the behavior of fractional derivatives in conjunction with another function. We use a method that combines a limited number of terms from the shifted Legendre polynomial basis. This allows us to accurately solve tempered fractional differential equations that include an additional function. We show that our approach works well through several numerical examples, demonstrating how effective and accurate our results are in tackling these complex equations.  

In the present paper, we introduced a new generalized parametric measure of fuzzy directed divergence of order σ with the proof of its validity. The particular case and some elegant properties of fuzzy directed divergence measure are studied. Total ambiguity , fuzzy information improvement measure and reduction in improvement measure are given for the proposed measure. A comparative study of proposed measure with existing generalized fuzzy directed divergence measure is computed numerically and represented by using graphical representation. The application of proposed fuzzy directed divergence measure in multi criteria decision making problem is demonstrated by using numerical example.

In a neutrosophic environment, a single-valued neutrosophic multi-set, and an intuitionistic fuzzy-valued neutrosophic multi-set are defined by sequences of acceptance, indeterminacy, and rejection grades. The structure of these sets enables the incorporation of multiple layers of information across acceptance, indeterminacy, and rejection grades, making them particularly valuable for multi-criteria decision-making processes. This paper presents the N-valued T-spherical fuzzy neutrosophic set as an advanced extension of neutrosophic sets, aimed at improving uncertainty management and imprecision in complex, real-world scenarios. Building upon previous models such as neutrosophic sets, intuitionistic fuzzy-valued neutrosophic sets, Pythagorean fuzzy neutrosophic sets, and T-spherical fuzzy neutrosophic sets, this new approach introduces greater flexibility in handling indeterminacy. The authors define N-valued T-spherical fuzzy neutrosophic sets and numbers, incorporating new mathematical operations and comparison functions. A significant contribution of the work is the development of simplified neutrosophic-valued distance-based similarity measures for N-valued T-spherical fuzzy neutrosophic sets, along with a score function to rank simplified neutrosophic values. To illustrate the practical utility of this framework, an algorithm is applied to a real-world problem of site selection for solid waste management systems, effectively addressing decision-making scenarios with disjoint criteria. The results and discussions show that the N-valued T-spherical fuzzy neutrosophic set outperforms existing methods by providing more accurate and precise results, specifically in multi-criteria decision-making contexts. The site choice example for solid waste management highlights how this new approach enhances accuracy.

In this paper, we introduce the concepts of neutrosophic subgroups and neutrosophic normal subgroups of groups and investigate several properties. We investigate relations between neutrosophic subgroups (neutrosophic normal subgroups) and their neutrosophic level subsets of a group. We also look at the homomorphic image and inverse image of the neutrosophic subgroups and neutrosophic normal subgroups of groups, as well as some related properties.

This paper investigates a fractional-order SEIR model to study the dynamics of infectious diseases, specifically COVID-19, by incorporating memory effects through fractional derivatives. The model’s formulation enhances the understanding of epidemic dynamics by considering disease transmission, recovery, and mortality rates under fractional calculus. Stability analyses are conducted for the disease-free equilibrium (DFE) and the pandemic fixed point (PFP), identifying critical conditions for finite-time stability using Lyapunov functions and fractional derivatives. Numerical simulations validate theoretical findings, demonstrating finitetime stabilization around the equilibrium points under realistic parameter settings. The results underscore the advantages of fractional-order modeling in capturing complex epidemic dynamics and highlight its potential to inform public health intervention strategies.

In this careful study , through the concept possibility interval valued neutrosophic hyper soft set (abbreviated as piv-NHSS) which is combined from the hypersoft set (HSS) and Interval-valued neutrosophic set under the posobolity degree and each iv-NHSS is assigned a possibility degree in the interval [0, 1]. Based on this concept, we present a more flexible, expanded method for a previous concept named possibility interval valued neutrosophic hyper soft matrix (piv-NHSM) as a new generalization of piv-NHSS. In this work, we also present nseveral algebraic operations and also all the mathematical properties associated with this model. In addition to the above, we have presented a clear algorithm based on the matrix properties of this model, which has been used to solve one of the multi-property decision-making problems. Finally, the correlation coefficient for this concept was defined and explained in detail according to an approved mechanism, with a numerical example provided to illustrate the mechanism of use. Moreover, we develop a new algorithm for solving the decision-making issue based on the proposed correlation coefficient for piv-NHSS .

The most important stage of data mining is clustering. Several distinct clustering approaches like grid-based, density-based, partitioning, graph-based, model-based, and hierarchical clustering are used for cluster analysis. We can cluster data objects into hierarchical trees by using the hierarchical clustering approach. Hierarchical clustering, with its agglomerative and divisive types, uses nodes to represent clusters. Agglomerative clustering is favored, and high-quality clusters are essential for successful cluster analysis. Up to this point, numerous alternatives to the clustering technique have been proposed, including the fuzzy k-mean approach. The uncertainty resulting from numerical variations or unpredictable natural occurrences may be handled by any data mining techniques now in use. However, indeterminacy components may be present in current data mining challenges in real-world scenarios. Neutrosophic logic, applicable in various sectors, is gaining traction due to its efficiency and accuracy, attracting investment for its potential to improve human lives. The suggested approach outperforms current methods like fuzzy logic and k-means in its ability to forecast the number of clusters.

In this work, we present novel techniques for the reciprocal fractional floor function applied neutrosophic set (RFFFNS) via interaction aggregating operator. The neutrosophic set combined with the reciprocal fractional floor operator. The geometric interaction operations of neutrosophic numbers and their new averaging are studied using the universal aggregation function. The RFFFNS are idempotent, boundedness compatible, commutative, and associative. Four new interaction aggregating operators are introduced: RFFFNS interaction weighted averaging, RFFFNS interaction weighted geometric, generalized RFFFNS interaction weighted averaging, and generalized RFFFNS interaction weighted geometric. The aggregation functions are commonly assumed to be represented by the Euclidean distance, Hamming distance, and score values.