ASPG

Fixed point results in ωt-distance mappings for Geraghty type contractions

Ammar Al-tawil , Ayman. A Hazaymeh , Anwar Bataihah

In this study, we establish fixed point theorems for Pωt-contractions within b-metric spaces by utilizing ωtdistance mappings. Subsequently, we demonstrate fixed point results pertaining to nonlinear contraction conditions of the Geraghty type, again employing ωt-distance mappings in the context of a complete b-metric space. Additionally, we bolster our findings with appropriate examples to illustrate the applicability of our results.

Vol. 26 Issue. 1 PP. 01-14, (2025)

Lexicographic Approach for Integer Programming Problem under Triangular Neutrosophic Fuzzy Environment and it’s Application

Yuvashri P. , Saraswathi A. , Broumi Said

Linear programming is an effective way in mathematical programming for solving optimization problems with linear objectives and linear constraints. There is determinant and indeterminant information in the actual world. As a result, the indeterminate problem is veritable and must be considered in the optimization problem,To handle this situation the neutrosophic theory is formed from extension of fuzzy set theory and is a helpful tool for dealing with inconsistent, indeterminate, and incomplete information.In this paper, we examine the coefficient of single valued triangular neutrosophic numbers to solve the neutrosophic integer programming problem.The neutrosophic integer programming problem are formulated with highest truth membership (T), indeterminancy membership and falsity membership function. The neutrosophic objective function involving a neutrosophic number, and then constructs a neutrosophic integer programming problem technique to handle neutrosophic optimization.In this paper we propose a strategy by using lexicographic approach in fractional dual algorthim to obtaining the basic solution and optimal solution as single valued neutrosophic triangular numbers.To gauge the efficacy of the model we solved few examples.

Vol. 26 Issue. 1 PP. 15-32, (2025)

Subfamilies of analytic functions associated with Rabotnov function

Ahlam Fallatah , Tariq Al-Hawary , Mourad Oqla Massa’deh , Feras Yousef

The aim of this paper is to investigate various subfamilies of analytic functions to find inclusion properties, and necessary and sufficient conditions for the Rabotnov function to be in these subfamilies. Furthermore, several corollaries will be implied from our main results.

Vol. 26 Issue. 1 PP. 33-39, (2025)

Extended Refined Neutrosophic Vector Spaces, Subspaces and their Application

T. Sathinathan , J. Aldring , S. John Borg , D. Ajay

The objective of this paper is to present a perspective of Refined Neutrosophic Vector Space (r-NVS), Sub spaces and some basic operations on Refined Neutrosophic Sets such as Algebraic sum and Algebraic product. Further some basic propositions, lemma and examples are presented. Finally an application on Refined Neutrosophic Vector Space is presented in the field of e-Commerce buyer oriented product (Smart Phones) ranking to illustrate the advantage of representing r-NVS.

Vol. 26 Issue. 1 PP. 40-54, (2025)

Kamal Transform for Neutrosophic Initial Value Problem

Azal J. Mera , Huda A. Hadi , Sahar M. Jabbar

The manuscript dealt with the problem of the initial value, especially in second-order differential equations with three degrees of Neutrosophic conditions, which are truth, falsity, and indeterminacy. In addition, we exploited the Kamal transformation to solve it.

Vol. 26 Issue. 1 PP. 55-63, (2025)

On Energy of Double Dominating Bipolar Single-Valued Neutrosophic Graph

Siti Nurul Fitriah Mohamad , Roslan Hasni , Florentin Smarandache

Domination and graph energy are fundamental concepts in graph theory for addressing unpredictable phenomena, and they have attracted considerable interest from researchers. In recent developments, the concept of dominating energy has become increasingly significant in the study of graph energies. While fuzzy graphs (FG) sometimes fall short in delivering optimal results, the neutrosophic set (NS) as well as neutrosophic graphs (NG) offer a robust alternative, effectively managing the uncertainties linked with inconsistent and indeterminate information in real-world scenarios. Most existing research on domination energy in the fuzzy environment focus solely on a single membership function. In contrast, bipolar neutrosophic models, which account for both positive and negative influences, provide a more versatile and applicable approach. This paper focuses on advancements in NG theory to address scenarios where imprecision is represented by both positive and negative membership functions. It introduces a new concept called the double dominating energy graph, relying on the currently developed bipolar single-valued neutrosophic graphs (BSVNG). The study further explores the energy of double domination within the BSVNG framework. Specifically, it develops the adjacency matrix of a dominating BSVNG, analyzes the spectrum of this matrix, and elaborates on the associated theoretical aspects using illustrative examples. Additionally, the double domination energy of BSVNG is calculated to demonstrate its applicability. At the end of this study, conclusions are drawn and avenues for future research are discussed.

Vol. 26 Issue. 1 PP. 64-81, (2025)

Solution of Second Order Fuzzy Differential Equations using Sumudu Transform under Neutrosophic Environment

B. Divya , K. Ganesan

Fuzzy differential equations (FDEs) are used to represent dynamical systems under uncertain environments. Finding solutions for fuzzy differential equations (FDEs) is highly challenging. This work employs the neutrosophic version of the Sumudu transform method to determine the solution to fuzzy differential equations (FDEs) that incorporate Neutrosophic Numbers (NNs). By utilising a novel fuzzy arithmetic operations on the parametric representations of NNs, significant theorems are established to demonstrate the characteristics of Neutrosophic Sumudu Transform (NST). The proposed NST approach is efficient in approximating the solutions of FDEs without converting them into their crisp equivalent forms. An illustrative numerical example is provided to demonstrate the efficacy of the proposed methodology.

Vol. 26 Issue. 1 PP. 82-93, (2025)

Smarandache Fuzzy Semigroups Using (3, 2) Fuzzy Sets

M. Mala , M. Mary Jansirani

This paper introduces the concept of -(3,2) &fnof;uzzy ᵴemigroups within an -ᵴemigroup and explore their characterizations. Various comparable conditions for -(3,2) &fnof;uzzy normal subᵴemigroups are established. Additionally, the -(3,2) &fnof;uzzy coset, -(3,2) &fnof;uzzy ideal, -(3,2) &fnof;uzzy symmetric ᵴemigroup and -(3,2) &fnof;uzzy normal subᵴemigroups are defined. The idea of conjugate -(3,2) &fnof;uzzy ᵴemigroups is also introduced, and the order of an -(3,2) &fnof;uzzy ᵴemigroup is determined. The (3,2) &fnof;uzzy semigroup condition applied to decision making process also.

Vol. 26 Issue. 1 PP. 94-107, (2025)

Analyzing the Relationship Between Project Management and Social Responsibility at Peruvian University Los Andes: Graduate Perceptions for 2024 Using Plithogenic Statistics and the Indeterminate Likert Scale

Michael Raiser Vásquez-Ramírez , Ketty Marilú Moscoso-Paucarchuco , Kathy Lesslie Javier-Palacios , Neftali Llihua-Carrasco , Williams Ronald Olivera-Acuña , Maria Del Pilar Ureta-Vila , Manuel Michael Beraún-Espíritu

The university's mission as established in the World Declaration on Higher Education is to contribute to sustainable development and improve society, which implies training highly qualified professionals. This paper aims to determine to what extent Project Management is related to Social Responsibility at the Universidad Peruana Los Andes, 2024. For the study, a survey is applied to a sample of 384 graduates from a total population of 5823 distributed by faculties, in 2024 regarding the attitude of this university's Center on Project Management and University Social Responsibility. For data representation, we use an Indeterminate Likert Scale. This type of scale consists of the quantitative score of each of the possible nominal values, in this way the opinion of each respondent is captured more faithfully. On the other hand, we use the Plithogenic Statistics, because there are several variables to study, some of them with indeterminacies.

Vol. 26 Issue. 1 PP. 108-116, (2025)

On fuzzy completely γ-irresolute and weakly completely γ-irresolute functions

Wadei Faris AL-Omeri

In this paper, fuzzy γ-open sets, and fuzzy γ-irresolute functions are used to define and investigate a new class of functions called fuzzy completely γ-irresolute functions, fuzzy completely weakly γ-irresolute between fuzzy topological spaces. We obtain their characterizations and their basic properties.

Vol. 26 Issue. 1 PP. 117-126, (2025)

Advances in Hypothesis Testing with Neutrosophic Sets: A Framework for Uncertainty

Ronnason Chinram , Sasiwimon Iwsakul

In this paper, we extend statistical hypothesis testing to data represented as neutrosophic sets, encompassing membership, indeterminacy, and non-membership components. Two distinct scenarios are considered: first, where all three components are independent, and second, where all three components are dependent.

Vol. 26 Issue. 1 PP. 127-135,, (2025)

Analyzing the Perspective of Circular Economy and Sustainable Development in the Junín Region of Peru Using Neutrosophic Cognitive Maps

Michael Raiser Vásquez-Ramírez , Ketty Marilú Moscoso-Paucarchuco , Percy Tito Avila-Zanabria , Omar Arturo Vivanco-Nuñez , Paul Cesar Calderon-Fernandez , Williams Ronald Olivera-Acuña , Manuel Michael Beraún-Espíritu

The Sustainable Development of a country is a relatively new concept, where the right of each country to achieve decent economic and social development is accepted, and where there is well-being for the population. At the same time, the environment is respected. On the other hand, the Circular Economy is another recent concept where the efficient and effective use of resources and products is proposed, where the fundamental principle is the reuse of waste as far as possible and its rational use, to reduce environmental pollution, and providing economic savings for the country. This paper aims to study the relationship between the concepts of Circular Economy and Sustainable Development contextualized in the Peruvian department of Junín. To examine this relationship and its future behavior, there are challenges such as the existence of indirect relationships between these two concepts, dependent on other concepts; and relationships between concepts that are unknown, at least partially. Taking all this into account, a group of three experts on the subject in Junín was asked for their opinion to determine the relationship between the selected concepts. This allowed the representation of knowledge with the help of a Neutrosophic Cognitive Map (NCM) and the study of the dynamic behavior of concepts with the help of the Method for Hidden Patterns.

Vol. 26 Issue. 1 PP. 136-143, (2025)

Comparing Teachers’ Critical Thinking Skills in Terms of the School Types through Classical Logic and Fuzzy Logic

Çiğdem Apaydin , Abdullah Kargin , Sevilay Şahin

This study is an attempt to explore the value of the teachers’ critical thinking skills with fuzzy expert systems. The study employed this system to obtain an objective and authentic evaluation in an abstract or ambiguous assessment. The working group consisted of 275 teachers working in public schools in Antalya central districts during the 2021-2022 academic year. This study deployed The Critical Thinking Appraisal (CTA) developed by Özelçi (2012). In the first stage, the data obtained from the teachers' critical thinking skill scale were analyzed through classical logic. Validity (explanatory and confirmatory factor analysis) and reliability analyzes (Cronbach Alpha) were performed during data analysis. Besides, the data regarding the teachers' critical thinking skill scale were also examined through the fuzzy logic approach. Different results emerged when comparing both methods. The findings revealed that the result on the fuzzy logic approach, which underpins artificial intelligence applications and which is used in various decision-making applications, is more consistent and objective. This study may shed light onto the researchers to obtain results that are more objective by conducting studies based on fuzzy logic-based survey. Besides, the validity and reliability analyzes made through the classical method with a similar method may also be carried out through the fuzzy logic method. These new results may be compared with those of the classical method. Thus, the objectivity of classical validity and reliability analyzes may also be examined.

Vol. 26 Issue. 1 PP. 144-158, (2025)

Pentapartitioned Neutrosophic Dombi Weighted Aggregation Operator for MADM

R. Radha , R. Rajalakshmi , B. Indhumathi , R. Poornima , M. Karthika , M. Mary Victoria Florence

This paper introduces the concept of Pentapartitioned Neutrosophic Numbers (PNNs) and proposes score and accuracy functions to effectively rank PNNs based on their score values. Utilizing the adaptability of Dombi operators to accommodate various parameters, the study applies these operators to address complex Multicriteria Attribute Group Decision Making (MAGDM) problems. To achieve precise aggregation under neutrosophic conditions, Dombi T-norm and T-conorm operations for two PNNs are defined. Building upon these Dombi operations, the paper presents two weighted aggregation operators—PNDWAA (Pentapartitioned Neutrosophic Dombi Weighted Arithmetic Average) and PNDWGA (Pentapartitioned Neutrosophic Dombi Weighted Geometric Average)—and investigates their properties within the pentapartitioned neutrosophic environment. Furthermore, the study explores a Multicriteria Attribute Decision Making (MADM) approach that utilizes either the PNDWAA or PNDWGA operators for decision-making.An illustrative example is provided to demonstrate the proposed method, offering a detailed step-by-step process that highlights the effectiveness of the approach in determining the optimal alternative based on ranking order.

Vol. 26 Issue. 1 PP. 159-170, (2025)

Some results on fixed point in generalized metric spaces via an auxiliary function

Maryam Hajjat , Anwar Bataihah , Ayman. A Hazaymeh

In this manuscript, we elegantly delineate the concept of JSφ-contractions within the realm of JS-metric spaces, as articulated by Jleli and Samet. Utilizing these contractions, we have formulated a groundbreaking fixed point theorem that paves the way for a diverse array of fixed point results. Additionally, we demonstrate a fixed point result specifically for P-contractions in JS-metric spaces. To further enrich our discourse, we provide several examples that vividly illustrate the essence of our principal theorem.

Vol. 26 Issue. 1 PP. 171-180, (2025)

The novel algebraic structure trigonometric Pythagorean neutrosophic set provides the basis for interaction weighted aggregating operators

P. Srikanth Rao , R. Balaji , Nasreen kausar , Tonguc Cagin

We introduce new methods for the trigonometric Pythagorean neutrosophic set (TPNSS) via interaction aggregating operator in this study. A combination of the trigonometric operator and the Pythagorean neutrosophic set. The universal aggregation function is used to study the novel averaging and geometric interaction operations of Pythagorean neutrosophic numbers. The TPNSS are commutative, associative, idempotent, and boundedness compatible. TPNSS interaction weighted averaging, TPNSS interaction weighted geometric, generalized TPNSS interaction weighted averaging, and generalized TPNSS interaction weighted geometric are the four new interaction aggregating operators that are introduced. The Euclidean distance, Hamming distance, and score values are often assumed to represent the aggregation functions.

Vol. 26 Issue. 1 PP. 181-191, (2025)

Multi Criteria Decision Making Using Linguistic Fermatean Neutrosophic Number

E. Madhavan Pillai , S. Vijayan , R. Sundareswaran , Said Broumi

The article aims to introduce the Linguistic Fermatean Neutrosophic set (LFNS) which is an important mathematical tool that helps to solve decision-making problems. LFNS is a generalization of the Linguistic Fermatean Fuzzy set (LFFS), by adding the truth, falsity and indeterminacy membership degrees to denote the uncertain information. Score and Accuracy functions are introduced to distinguish any two or more linguistic Pythagorean Neutrosophic Numbers. Weighted averaging and geometric aggregation operators with respect to linguistic Pythagorean neutrosophic weighted average and geometric, ordered weighted average are proposed. OEE (Overall Equipment Effectiveness) is the industry standard for measuring manufacturing productivity. It defines the percentage of manufacturing time that is productive. A 100% OEE score means that you are creating only high-quality products as soon as possible, with no downtime. By measuring OEE and the underlying losses, you will gain critical insights on how to systematically optimize your manufacturing process. OEE is the single most effective measure for detecting losses, assessing progress, and improving manufacturing equipment productivity (i.e., reducing waste). To adopt OEE practices in manufacturing industries, we must first understand, measure, and enhance OEE. The purpose of this research is to better understand OEE practices and their crucial aspects. The Human Arena, Engineering, Management, and Social elements are assessed, with sub-factors aggregated by similarity and analyzed using a LFNN. This method helps to comprehend the impact of each factor and ranks the group based on their influence in implementing the OEE practices effectively in an organization. The Engineering aspects and the Management aspects contribute a major role in the success of OEE. In this study, the assessment of numerous components and sub-factors involving determining the influence factor leading to OEE is translated into a Multi-Attribute Group Decision Making (MAGDM) problem and illustrated in the last section utilizing LFNN.

Vol. 26 Issue. 1 PP. 192-205, (2025)

Continuous Maps and Irresolute Maps Via Fuzzy Hypersoft θ Open set

P. Revathi , B. Premamalini , K. Chitirakala , A. Vadivel

The purpose of this paper is to introduce and study fuzzy hypersoft θ continuous maps, fuzzy hypersoft θ semi continuous maps, fuzzy hypersoft θ pre continuous maps and fuzzy hypersoft θ irresolute maps in fuzzy hypersoft topological spaces with examples. Further, we derived some useful results and properties related to them.

Vol. 26 Issue. 1 PP. 206-222, (2025)

On the characterization of Harmonized fuzzy subgroups θ Open set

Eman A. AbuHijleh , Sara A. Khalil , Sana Abu-Ghurra , Ghada Alafifi

In this paper, we continue to discuss the concept of harmonized fuzzy subgroups. We present the harmonized fuzzy coset and harmonized fuzzy normal subgroup and their properties. We also study the effect of group homomorphism on harmonized fuzzy subgroups. Finally, we define and study the cartesian product of two harmonized fuzzy subgroups.

Vol. 26 Issue. 1 PP. 223-233, (2025)

New form of weighted interaction aggregating operators communicated with the reciprocal fractional floor function via the neutrosophic set

D. Mahendar , R. Balaji , Nasreen kausar , Tonguc Cagin

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.

Vol. 26 Issue. 1 PP. 234-242, (2025)

Neutrosophic Hierarchical Clustering: A Novel Approach for Handling Uncertainty in Multi-Level Data Organization

Sitikantha Mallik , Suneeta Mohanty , Bhabani Shankar Prasad Mishra

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.

Vol. 26 Issue. 1 PP. 243-253, (2025)

Matrices and Correlation Coefficient for possibility interval-valued neutrosophic hypersoft sets and their applications in real-life

Eman Hussein , Yousef Al-Qudah , Abdulqader O. Hamadameen , R.H. Al-Obaidi , Abdullah S. Al-Jawarneh , Faisal Al-Sharqi , Anas Owledat

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 .

Vol. 26 Issue. 1 PP. 254-265, (2025)

Fractional-Order SEIR Model for COVID-19: Finite-Time Stability Analysis and Numerical Validation

Shaher Momani , Iqbal M. Batiha , Mohammad S. Hijazi , Issam Bendib , Adel Ouannas , Nidal Anakira

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.

Vol. 26 Issue. 1 PP. 266-282, (2025)

Neutrosophic subgroups and neutrosophic normal subgroups of groups

Aiyared Iampan , C. Sivakumar , Neelamegarajan Rajesh

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.

Vol. 26 Issue. 1 PP. 283-292, (2025)

A Comprehensive Approach to Solid Waste Management Site Selection Using Simplified Neutrosophic Distance-Based Similarity Measures with N-Valued T-Spherical Fuzzy Neutrosophic Sets

Mahizha J. C. , Immaculate Mary M.

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.

Vol. 26 Issue. 1 PP. 293-310, (2025)

A Generalized Directed Divergence of Fuzzy Entropy

Vaishali Manish Joshi , Javid Gani Dar

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.

Vol. 26 Issue. 1 PP. 311-321, (2025)

An Efficient Symmetric Operational Matrix Method for Solving Tempered Fractional Differential Equations with Respect to Another Function

Mohammad Abdel Aal , Ahmad Arafah

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.  

Vol. 26 Issue. 1 PP. 335-352, (2025)

Neutrosophic Methodological Foundations of Marketing Research in the Rural Labor Market

Kholmuminov Shayzak Rakhmatovich

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.

Vol. 26 Issue. 1 PP. 353-364, (2025)

Enhancing educational environments with Social Media Feedback Evaluation Employing Hybrid Neutrosophic Decision Optimization (HNDO) and Neutrosophic Sentiment Fusion (NSF)

Walaa Fouda , Asmaa Hegazy , Najla M. Alnaqbi , Ebru Ozbilge , Emre Özbilge

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.

Vol. 26 Issue. 1 PP. 365-390, (2025)

Student Academic Performance Classification Using N-Valued Interval Neutrosophic Sets with Optimization Algorithms for Significant Feature Selection

Nahla Moussa , Cuauhtemoc Samaniego , Moustafa Mohamed Abouelnour , Wael F. Ali

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.

Vol. 26 Issue. 1 PP. 391-403, (2025)

The Topology T (PR⋆) ^⊛ in the Frame of Primal Topological Spaces

Amani Rawshdeh , Ahmad Al-Omari

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&sube;S, H_Pᶲ&sube;H_{PR⁺}⊛&sube;H_PRᶲ and H&sube;Cl_Pᶲ(H)&sube;Cl_{PR⁺}⊛(H)&sube;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.

Vol. 26 Issue. 1 PP. 322-334, (2025)

Logarithmic neutrosophic logical communicated to basic interaction aggregating operators using various finite weighted with extension

Nasreen kausar , Swarnakar Dornala , M. S. Malchijah Raj , Ebru Ozbilge , Emre Özbilge

 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.

Vol. 26 Issue. 1 PP. 404-414, (2025)

ƝҪͳ- Confused Neutrosophic Crisp Sets

Asra Mohammed Jasem , L. A. A. Al-Swidi , Ali H. M. Al-Obaidi

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.

Vol. 26 Issue. 1 PP. 415-420, (2025)

Beta Special Function of Symbolic 2-Plithogenic and 3-Plithogenic Real Numbers

Nabil Khuder Salman

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.

Vol. 26 Issue. 1 PP. 421-427, ()

International Journal of Neutrosophic Science

Journal DOI

Journal Menu