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A Novel Neutrosophic Decision-Making Approach For Optimizing Metaverse Headphone Design: Balancing Technical Performance And User Emotional Needs, Mai Mohamed, Amira Salam, Karam Sallam, Bilal Arain

Neutrosophic Systems with Applications

The concept of the metaverse, which combines various technologies to create a wide range of virtual experiences, has gained significant popularity in recent years. To fully engage in these metaverse environments, users rely on access devices such as virtual reality (VR) headsets and smartphones for augmented reality (AR). These devices must be lightweight, compact, and user-friendly to ensure comfort and enhance customer satisfaction. There is a growing focus on innovating and designing products that not only meet technical requirements but also address the emotional needs of users, ultimately improving the overall experience. Selecting the ideal design for Metaverse headphones is …

A Comprehensive Intelligent Traffic Monitoring System Based On A Novel Integration Of Neutrosophic Multi-Criteria Decision-Making Techniques, Mai Mohamed, Amira Salam, Rana Muhammad Zulqarnain, Muhammad Gulistan

Neutrosophic Systems with Applications

With the spread of road accidents and traffic congestion that costs countries and governments a lot of money in addition to the loss of human lives, and since traditional methods of monitoring traffic have not been as effective as desired, attention has been drawn to the search for more effective solutions to the problem of monitoring and regulating traffic. With the spread of technology and the Internet of Things, UAVs have emerged as a promising tool for monitoring traffic, as they can fly for a sufficient period and operate in difficult climatic conditions, in addition to their ability to monitor …

Nash Equilibrium Solutions For Continuous Static Games Under Neutrosophic Environment, M. G. Brikaa

Neutrosophic Systems with Applications

Neutrosophic set theory plays an important role in dealing with the impreciseness and inconsistency in data encountered in solving real life problems. This paper presents a novel approach to solving a new class of continuous static games within a neutrosophic framework. In the proposed methodology, the neutrosophic continuous static games are redefined into two separate crisp problems: the lower problem and the upper problem. The study further establishes the necessary conditions for determining equilibrium strategies in neutrosophic continuous static games. To demonstrate its effectiveness and practical applicability, the proposed method is validated through a numerical example.

A Neutrosophic Micro Vague Correlation Measure: Application To Multi-Criteria Decision Making Problems, Vargees Vahini T, Trinita Pricilla M

Neutrosophic Systems with Applications

Statistical methods called correlation measures are employed to express the degree of association or relationship between two variables. The correlation coefficient which may be computed in a variety of ways is the most often used kind of correlation measure in many disciplines including biology, psychology, economics, and finance. Knowing the correlations between variables is essential for analysis and decision-making. This paper aims to commence a novel type of correlation measure called Neutrosophic Micro vague Correlation Measure and Neutrosophic Micro Vague Weighted Correlation Measure. Further demonstrates the implementation of the Neutrosophic Micro Vague correlation measure in the MCDM Problem. By adopting …

Improved Estimator For Population Mean Utilizing Known Medians Of Two Auxiliary Variables Under Neutrosophic Framework, Rajesh Singh, Shobh Nath Tiwari

Neutrosophic Systems with Applications

In the context of classical statistics, the estimation of the population mean is done with determinate, precise, and crisp data when auxiliary information is available. However, there are instances where dealing with uncertain, indeterminate, and imprecise data in interval form is required. To overcome this issue, Florentin Smarandache introduced neutrosophic statistics as a novel approach. This paper introduces a neutrosophic modified ratio-cum-product log-type estimator for the estimation of the population mean using known medians of two auxiliary variables in the neutrosophic context. The bias and mean squared error (MSE) for the proposed estimators are computed to the first-order approximation. The …

Some Graph Parameters For Superhypertree-Width And Neutrosophictree-Width, Takaaki Fujita, Florentin Smarandache

Neutrosophic Systems with Applications

Graph characteristics are often studied through various parameters, with ongoing research dedicated to exploring these aspects. Among these, graph width parameters—such as treewidth—are particularly important due to their practical applications in algorithms and real-world problems. A hypergraph generalizes traditional graph theory by abstracting and extending its concepts [77]. More recently, the concept of a SuperHyperGraph has been introduced as a further generalization of the hypergraph. Neutrosophic logic [133], a mathematical framework, extends classical and fuzzy logic by allowing the simultaneous consideration of truth, indeterminacy, and falsity within an interval. In this paper, we explore Superhypertree-width, Neutrosophic treewidth, and t-Neutrosophic tree-width.

Enhancing Smart City Management With Ai: Analyzing Key Criteria And Their Interrelationships Using Dematel Under Neutrosophic Numbers And Mabac For Optimal Development, Asmaa Elsayed, Mai Mohamed

Neutrosophic Systems with Applications

Purpose: This paper explores the transformative role of AI across various domains of smart cities, including urban mobility, energy management, public safety, healthcare, environmental monitoring, economic development, and data management. It aims to develop a novel decision-making framework that integrates AI technologies with a hybrid approach to analyze the interrelationships among smart city components.

Methodology: This paper employs a hybrid decision-making framework that combines the Decision-Making Trial and Evaluation Laboratory (DEMATEL) method with single-valued trapezoidal neutrosophic numbers (STrNN). This approach is used to analyze the complex relationships among criteria and sub-criteria in smart city contexts, addressing uncertainty and incomplete information …

Mbj-Neutrosophic Structure Applied To Bp-Algebras: Bp-Subalgebras And Α-Ideals, Bavanari Satyanarayana, Shake Baji, Anjaneyulu Naik K.

Neutrosophic Systems with Applications

In this article, we introduce the concepts of MBJ-neutrosophic BP-subalgebras and MBJ-neutrosophic α-ideals in BP-algebra by applying MBJ-neutrosophic logic to algebraic structure BP-algebra. We prove that the intersection of two MBJ-neutrosophic α-ideals and the inverse image of an MBJ-neutrosophic α-ideal are also MBJ-neutrosophic α-ideals. Furthermore, we prove an MBJ-neutrosophic set is an MBJ-neutrosophic BP-subalgebra if and only if its level sets are BP-subalgebras.

Solving N-Players Continuous Differential Games Under Neutrosophic Environment, M. G. Brikaa

Neutrosophic Systems with Applications

Uncertainty plays a crucial role in decision-making problems, particularly in game theory. Various forms of uncertainty have been explored in the literature, including fuzzy, soft, rough, and interval-based approaches. Game theory has been extensively studied under these uncertainty models, with researchers addressing vagueness, and imprecision from multiple perspectives. More recently, neutrosophic sets have emerged as an alternative framework for handling uncertainty. Neutrosophic numbers effectively incorporate indeterminacy in decision-making by considering factors such as intuition, assumptions, judgment, behavior, evaluation, and preferences of decision-makers. This paper presents a novel approach to solving a new class of n-player continuous differential games within a …

Einstein Aggregate Operators Under Q-Rung Orthopair Fuzzy Hypersoft Sets With Machine Learning, Muhammad Gulistan, Muhammad Abid

Neutrosophic Systems with Applications

Thailand with its impressive 15.5% global share of renewable energy production, has a small 1% share of bitcoin mining. At the same time, the country is dealing with the severe effects of climate change, which emphasizes the necessity of taking proactive steps to solve environmental issues. This research integrates machine learning techniques and Einstein Aggregate Operators under q-rung orthopair fuzzy hypersoft set (q-ROFHS)-based multi-criteria decision-making technique to present a new method for analyzing CO₂ impacts and mitigation solutions in Thailand. We evaluate the environmental impacts of bitcoin mining and the incorporation of renewable energy sources using an interdisciplinary framework, …

Neutrosophic Automata And Its Algebraic Properties, Anil Kr. Ram, Anupam K. Singh

Neutrosophic Systems with Applications

This research endeavors to elucidate the interrelationships among various classes of operators, including neutrosophic successor/neutrosophic source/neutrosophic core operators of neutrosophic automata based on neutrosophic resituated lattices. Furthermore, it delves into the characterization of algebraic properties such as neutrosophic subsystem, neutrosophic connectivity, and neutrosophic separability of a neutrosophic automaton using these operators. Finally, we study the concepts of neutrosophic primaries of the given neutrosophic automata using neutrosophic core operators.

An Approach For Hybridizing N-Subalgebra With Quantified Neutrosophic Set Using G-Algebra, Neha Andaleeb Khalid, Muhammad Saeed

Neutrosophic Systems with Applications

Neutrosophic sets are a generalized form of fuzzy sets as well as intuitionistic fuzzy sets, as they address the uncertainty factor as an independent component along with truthfulness and falsity. However, traditional neutrosophic approaches often struggle with effectively managing and quantifying indeterminate elements in complex algebraic structures. To address this limitation, this paper employs an expanded version of the neutrosophic set, incorporating a subalgebra. The proposed research is multifaceted: firstly, the new concept of N-Subalgebra (NSU) is proposed. This is the modified setting in the family of subalgebras whose proposed name is the representation of the author's initial name. Secondly, …

A Reconsideration Of Advanced Concepts In Neutrosophic Graphs: Smart, Zero Divisor, Layered, Weak, Semi, And Chemical Graphs, Takaaki Fujita, Florentin Smarandache

Neutrosophic Systems with Applications

One of the most powerful tools in graph theory is the classification of graphs into distinct classes based on shared properties or structural features. Over time, many graph classes have been introduced, each aimed at capturing specific behaviors or characteristics of a graph. Neutrosophic Set Theory, a method for handling uncertainty, extends fuzzy logic by incorporating degrees of truth, indeterminacy, and falsity. Building on this framework, Neutrosophic Graphs [9, 84, 135] have emerged as significant generalizations of fuzzy graphs. In this paper, we extend several classes of fuzzy graphs to Neutrosophic graphs and analyze their properties.

A Concise Formalization Of Hyperrealism-Antirealism In Physics Using Neutrosophic Logic, Takaaki Fujita, Florentin Smarandache, Victor Christianto

Neutrosophic Sets and Systems

In [6], the relationship between hyperrealism and antirealism in physics is proposed. Hyperrealism Antirealism describes a spectrum where theories transition from being empirically grounded (realist) to speculative frameworks dominated by untestable assumptions, thereby detaching from observable reality. This paper presents a concise mathematical formalization of the spectrum of hyperrealism-antirealism in theoretical physics and the philosophy of science. We propose a method to quantify the extent to which a theory is “hyperreal” or “antirealist” using a ratio of testable to untestable statements. Additionally, we provide several theorems that outline the conditions under which theories shift into hyperreal or antirealist domains. Finally, …

Neutrosophic Sets And Systems, Vol. 81,2025, Florentin Smarandache, Mohamed Abdel-Basset, Maikel. Leyva Vazquez

Neutrosophic Sets and Systems

the whole of the volume

From Di-Alectics To N-Alectics: Indigenous Cultures And Ancestral Philosophies In Latin America, Florentin Smarandache, Maikel Y. Leyva Vázquez

Neutrosophic Sets and Systems

This paper explores the n-alectic framework, which extends traditional di-alectic and tri-alectic models by integrating multiple subcomponents through refined neutrosophic logic. Drawing from pre Columbian philosophies, particularly Mesoamerican, Andean, and Amazonian traditions, the study demonstrates how indigenous worldviews align with n-alectic structures. The figure of Quetzalcóatl/Kukulkán illustrates a triadic balance of sky, earth, and underworld, while Andean Yanantin and Pachakuti reflect complementary duality and transformation. Shuar cosmology further exemplifies a complex n-alectic system, where multiple spiritual and natural forces interact dynamically. The ethical decision-making model, applied to resource extraction and Pachamama principles, utilizes weighted metrics and neutrosophic distance calculations to …

Global Gender Inequality In Industry: A Systematic Review With Neutrosophic Analysis, Jimmy Hurtado Paspuel, Raquel Vera-Ortega, Angel M. Plaza, Bernardo Hubert Ovalle Correa

Neutrosophic Sets and Systems

This study examines gender inequalities in the worldwide sector via a systematic review employing a neutrosophic approach, focusing on income discrepancies, workplace harassment, preventative strategies, professional hurdles, and leadership representation. The neutrosophic methodology categorizes findings into components of truth, falsehood, and indeterminacy, assessing evidence via four metrics: neutrosophic score, reliability index, certainty level, and information quality index. In accordance with PRISMA 2020 standards, 282 studies published from 2020 to 2024 were examined. The findings indicate that workplace harassment exhibits the most substantial evidence (reliability=0.828, IQI=0.496), succeeded by wage disparities (reliability=0.813, IQI=0.400), whereas prevention policies reveal the greatest uncertainty (reliability=0.696). Robust …

Interval-Valued Neutrosophic Framework For Improving The Decision-Making On The Quality Evaluation Of English Classics Translation, Ying Du

Neutrosophic Sets and Systems

English translations of literary classics are a subject of interest for many scholars and evaluators. However, the evaluation of the translations is a complex and multifaceted task, which necessitates a balance between linguistic accuracy, cultural fidelity, and readability. This makes traditional methods often fall short of catching the uncertainties, ambiguities, and subjective judgments. In an attempt to bridge these gaps between computational linguistics and translation studies, we introduce a mathematically grounded IVNS approach to evaluate the translation of English classics by flexible modeling of the ambiguities inherent in translation decisions. Then, we introduced an extended version of the MULTIMOORA method, …

Neutrosophic Linguistic Rhotrix In Managerial Decision Making, R. Priya, Nivetha Martin, Florentine Smarandache

Neutrosophic Sets and Systems

The developments in rhotrix theory and their applications are unveiled at recent times. This research work proposes the notion of linguistic rhotrix conjoining the theories of linguistic matrix and rhotrix. The theory of linguistic rhotrix comprising fundamental definitions, operators and classifications is presented in this study. The algorithmic framework of applying linguistic rhotrix to decisioning problem is presented in this work. A managerial decision-making illustration is putforth to validate the proposed decisioning framework based on neutrosophic quantifications of linguistic rhotrix. The results obtained are compared with fuzzy and intuitionistic fuzzy quantifications to demonstrate the efficacy of neutrosophic quantifications of linguistic …

Classification Of Organizational Behavior At The National Agrarian University Of La Selva Based On Plithogenic Sets, Ketty Marilú Moscoso-Paucarchuco, Lucila Maribel Justiniano-Advincula, Monica Gisela Justiniano-Advincula, Manuel Michael Beraún-Espíritu, Inocente Feliciano Salazar-Rojas, Carlos Walter Mayta-Molina, Juan Dionicio Paz-Soldán Chávez

Neutrosophic Sets and Systems

In human organizations, there are group ways of conducting themselves, the interaction between members, and internal dynamics, among others that make the organization maintain a specific behavior as if it were an individual. This is the so-called Organizational Behavior, which is important to identify within a particular organization to improve the performance and efficiency of the entity. There are four types of organizational behavior models, namely, autocratic, custodial, supportive, and collegial. This paper aims to classify the organization that belongs to the office of the Academic Vice-Rector of the National Agrarian University of La Selva in Peru. To do this …

Neutrosophic Sets And Systems: A Decade Of Scientific Contribution And Growth, Muhammad Saqlain, José M. Merigó, Poom Kumam

Neutrosophic Sets and Systems

Neutrosophic Sets and Systems (NSS) has become an important Journal for neutrosophic theory and its applications in uncertainty modeling and decision sciences. In 2023, NSS celebrated its 10th anniversary, marking a decade of contributions to scientific literature. Motivated by this event, this paper provides a critical bibliometric analysis of NSS’s evolution as a leading academic journal in neutrosophy. This study explores the publication trends, citation impact, most productive authors, institutions, and global collaboration networks of NSS. The study maps bibliographic coupling, keyword co-occurrence and co-citation analysis using data from the Scopus database, secondary search using NSS webpage, and visualization tools …

Convolutional Interval-Valued Neutrosophic Network For Intelligent Evaluation Of Smart Clothing Design Choices, Fengfang Wu

Neutrosophic Sets and Systems

Smart clothing design turned out to be a set of complex decision-making processes requiring complementary aesthetics, functionality, as well as customer preferences. This, in turn, makes the traditional evaluation methods struggle to deal with uncertainty and subjectivity in customer feedback about smart clothing design. In an attempt to address this challenge, this research article proposes a novel Neutrosophic approach that integrates Interval-Valued Neutrosophic (IVN) with Convolutional Network to build an intelligent tool for the evaluation of smart clothing design choices. The Neutrosophic representation enables modeling uncertainty, inconsistency, and hesitancy in decision-making by assigning interval-ed membership degrees for different views of …

A Comparison Between Euler's Method And 4-Th Order Runge- Kutta Method For Numerical Solutions Of Neutrosophic And Dual Differential Problems, Ahmed Salem Heilat

Neutrosophic Sets and Systems

This paper is dedicated to study some numerical solutions of neutrosophic and dual differential problems through a numerical comparison between neutrosophic Euler's method and 4-th order Runge-Kutta neutrosophic and dual method, where we apply both methods on the same problems and compare the numerical results of solutions and numerical estimations of errors by using numerical tables.

An Analysis Of Bipolar Trapezoidal Neutrosophic Sets (Btnss) For Examining The Income-Increasing And Poverty-Reduction Effects Of Ecological Compensation In The Huai River Basin Of Anhui Province: A Comprehensive Study, Yuwei Wang, Shengnan Zhang

Neutrosophic Sets and Systems

This study proposes the decision-making approach for evaluation of ecological compensation in the Huai river basin of Anhui province. We used the neutrosophic sets to deal with the uncertainty information. In both the trapezoidal and bipolar neutrosophic environments, decision makers supply all the information needed to make decisions in complex multicriteria decision-making problems. This work suggests a novel, efficient method to handle these situations. We used two methods to evaluate the criteria and alternatives such as LMAW and MARCOS. We used the LMAW method to compute the criteria weights and the MARCOS method to rank the alternatives. Nine criteria and …

Enhancing Medical X-Ray Image Classification With Neutrosophic Set Theory And Advanced Deep Learning Models, Walid Abdullah

Neutrosophic Sets and Systems

The classification of medical images presents significant challenges due to the presence of noise, uncertainty, and indeterminate information. Traditional deep learning models often struggle to manage this, leading to reduced diagnostic accuracy, especially when dealing with low-quality or ambiguous conditions. This paper proposes a hybrid approach that integrates Neutrosophic Set (NS) theory with deep learning models to enhance X-ray image classification under uncertain conditions. NS theory introduces three domains: True (T), Indeterminate (I), and False (F) to manage image uncertainty and noise, allowing deep learning models to better interpret complex, ambiguous visual information. To evaluate the approach, five state-of-the-art deep …

New Energy Vehicle Industry Chain Evaluation By Developing Decision-Making Methodology With Hypersoft Set And Neutrosophic Sets, Lulu Shi

Neutrosophic Sets and Systems

The New Energy Vehicle (NEV) industry has emerged as a crucial sector in the global transition toward sustainable transportation. This study proposed a decision-making methodology for NEV industry chain evaluation. We used two decision making methods, such as SWARA method to compute the criteria weights and the MAIRCA method to rank the alternatives. These methods are used under the neutrosophic sets to deal with uncertainty data. Then we used the HyperSoft Set to show the relationship between the criteria and their values. This study proves the validation of the proposed approach by applying the proposed approach in case study. Four …

Neutrosophic Hypersoft Set (Nhss) For Teaching Quality Assessment In University Interior Design Courses, Ruijuan Zhang

Neutrosophic Sets and Systems

Teaching quality evaluation in university interior design courses have different criteria and values. So, we used the multi-criteria decision making (MCDM) approach to deal with various criteria. Two MCDM methods are used such as Entropy to compute the criteria weights and RAFSI method to rank the alternatives. Two MCDM methods are used under the neutrosophic-Z number (NZN) to deal with uncertain and vague information. This study uses the neutrosophic HyperSoft set (NHSS) to find the relationship between different criteria. Seven criteria and eight alternatives are used in this study. An empirical application is applied to show the validation of the …

Prioritization Of Higher Education Management Strategies Based On The Neutrosophic Uncertainty Model For Sustainability, Xinxiu Yang

Neutrosophic Sets and Systems

This study proposes the multi-criteria decision-making methodology (MCDM) to rank the strategies of higher education management. We used the neutrosophic sets to deal with uncertain information in the MCDM solutions. We used two MCDM methods in this study such as CRiteria Importance Through Intercriteria Correlation (CRITIC) and alternative ranking order method accounting for two-step normalization (AROMAN). The CRITIC method is used to compute the criteria weights and the AROMAN method is used to rank the alternatives. We use the Trapezoidal Neutrosophic Z-Number (TNZN) which is an extension of the neutrosophic set to deal with vague data. This study uses nine …

Neutrosophic Normal Vague Set Fitting To Trigonometric Concept Via Aggregation Operators And Its Augmentation, M. Palanikumar, Nasreen Kausar, Tonguc Cagin

Neutrosophic Sets and Systems

Using a cotangent trigonometric neutrosophic normal vague set (CotNNVS), we begin this communication article with several novel techniques. Some trigonometric neutrosophic sets and imprecise neutrosophic sets are extended by the novel idea of CotNNVS. We will discuss the various aggregating processes that interpret Cotangent trigonometric neutrosophic normal vague weighted averaging (CotNNVWA), cotangent trigonometric neutrosophic normal vague weighted geometric (CotNNVWG), cotangent trigonometric generalized neutrosophic normal vague weighted averaging (CotGNNVWA), and cotangent trigonometric generalized neutrosophic normal vague weighted geometric (CotGNNVWG) are the new topics covered in this paper

Adaptability Evaluation Of Vocational Education And Economic Development Under The Bipolar Neutrosophic Sets, Chen Yuan, Yongye Chen

Neutrosophic Sets and Systems

This study suggests a decision-making methodology to evaluate the risks in vocational education and economic development. This problem has different criteria and alternatives which must be evaluated. This evaluation can include uncertainty in the evaluation process. So, we use the bipolar neutrosophic sets (BNSs) to deal with uncertainty and vague data. The BNSs are extensions of the neutrosophic sets. We used two decision-making methods for the evaluation of risks in vocational education and economic development such as BWM to compute the criteria weights and the COPRAS method to rank the alternatives based on a set of criteria. This study uses …