Digital Commons Network^™

Plithogenic Duplets And Plithogenic Triplets, Takaaki Fujita, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

A Neutrosophic Set is a mathematical framework that represents degrees of truth, indeterminacy, and falsehood to address uncertainty in membership values [41, 42]. In contrast, a Plithogenic Set extends this concept by incorporating attributes, their possible values, and the corresponding degrees of appurtenance and contradiction [50]. Among the related concepts of Neutrosophic Sets, Neutrosophic Duplets and Neutrosophic Triplets are well-known. This paper defines Plithogenic Duplets and Plithogenic Triplets as extensions of these concepts using the Plithogenic Set framework and briefly examines their relationship with existing concepts.

Some Types Of Hyperneutrosophic Set (2): Complex, Single-Valued Triangular, Fermatean, And Linguistic Sets, Takaaki Fujita, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

This paper is a continuation of the work presented in [35]. The Neutrosophic Set provides a mathematical framework for managing uncertainty, characterized by three membership functions: truth, indeterminacy, and falsity. Recent advancements have introduced extensions such as the Hyperneutrosophic Set and SuperHyperneutrosophic Set to address more complex and multidimensional challenges. In this study, we extend the Complex Neutrosophic Set, Single-Valued Triangular Neutrosophic Set, Fermatean Neutrosophic Set, and Linguistic Neutrosophic Set within the frameworks of Hyperneutrosophic Sets and SuperHyperneutrosophic Sets. Furthermore, we investigate their mathematical structures and analyze their connections with other set-theoretic concepts.

Soft Directed N-Superhypergraphs With Some Real-World Applications, Takaaki Fujita, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

This paper introduces the Directed Soft Super Hyper Graph, a unified framework for modeling complex, multi-layered directed networks. It combines directionality, recursive hyperstructure, and soft-set parameterization to address the integration of Soft Super HyperGraphs and Directed SuperHyperGraphs, which remains largely unexplored. The paper provides formal definitions, core operations, and real-world examples, such as urban infrastructure and transportation networks, to demonstrate the framework's effectiveness in managing deep hierarchies and uncertain relationships simultaneously.

Beyond Dialectics, Paradoxes, And Binary Logic, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

Philosophy, long defined by its pursuit of truth, has historically been a battleground for dichotomies: truth vs. falsehood, materialism vs. idealism, reason vs. emotion. These oppositions often provide a framework for understanding philosophical discourse, but they fail to capture the full nuances of reality. To challenge these binary oppositions, I introduced the neutrosophic perspective in philosophy, rooted in Mathematics, and Many-Valued Logics.1 By emphasizing the interrelation of affirmation, negation, and neutrality, neutrosophy allows for the reconciliation of seemingly irreconcilable viewpoints, providing a new lens through which to reinterpret age-old philosophical questions.

A New Simulation Framework For Analyzing Neutrosophic Data In Experimental Design, Muhammad Aslam, Nasrullah Khan, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

A recent simulation-based classical analysis has been developed for interval data. However, a review of the literature indicates that these existing simulations have notable limitations and fail to conform to the neutrosophic statistical framework. In this paper, we propose a novel simulation process designed to analyze neutrosophic data within an appropriate and rigorous neutrosophic framework. We demonstrate that the proposed simulation is more comprehensive and aligns closely with the principles of neutrosophic theory. The results will be obtained through simulation and compared with those of existing methods, with the expectation that the proposed approach provides substantial improvements and is better …

A Plausible Formal Correspondence Between Tetrahedral Condensates/Tsc And Pt-Symmetric Crystals Model Of Cmns (Aka. Low-Energy Nuclear Reactions), Victor Christianto, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

Akito Takahashi's Tetrahedral Symmetric Condensate (TSC) model, detailed in several of his earlier works1 proposes a mechanism for condensed matter nuclear science (CMNS) aka. low-energy nuclear reactions (LENR) within palladium lattices. The model centres on the formation of a tetrahedral cluster of deuterons, enhancing the probability of nuclear fusion. Here, we explore the possibility of extending this framework by considering the TSC within a more general crystalline solid with tetrahedral symmetry, and by approximating the screening potential experienced by the deuterons using PT-symmetric potentials.

When Emotions Flare: Solar Rhythms, Emotions And Cycles Of Political Revolution, Andreas Hernandez, Carolina Zilli Vieira, Alexandra Smith, Rebecca Olson

Geography and Environmental Studies Faculty Publications

Revolutions are among the most transformative events in human history. Analyzing 395 revolutionary episodes from 1900 to 2014, we find that major waves cluster around solar maxima - periods of intensified geomagnetic activity. Drawing on biomedical research linking geomagnetic disturbances to cardiovascular and stress regulation, and thus to emotional states, we propose that solar cycles modulate the affective ecologies within which revolutions arise. Solar activity may accelerate, shape, and amplify revolutionary cycles by heightening emotional climates and tipping fragile systems toward mass mobilization. This reframes revolutions as planetary events - entanglements of political conflict, embodied emotion, and cosmic …

A Python Framework Enhancement For Neutrosophic Topologies, Giorgio Nordo, Saeid Jafari, Maikel Yelandi Leyva V Azquez

Neutrosophic Sets and Systems

This paper introduces an extension to the Python Neutrosophic Sets (PYNS) framework, originally detailed in [13], with the addition of the NSfamily class for constructing and manipulating neutrosophic topologies. Building on existing classes like NSuniverse and NSset, the NSfamily class enables the definition and testing of neutrosophic families as basis and sub-basis for neutrosophic topological spaces. This extension provides tools for verifying closure properties under union and intersection, and for determining whether a given family constitutes a neutrosophic topology. Through implemented algorithms, the framework automates the generation of topologies from families of neutrosophic sets, offering an efficient tool for advancing …

A Neutrosophic Fixed Charge Multi-Objective 4 Dimensional Multi-Item Transportation Problem With Carbon Emission And Budget Constraints, A.N. Revathi, S. Mohanaselvi

Neutrosophic Sets and Systems

This paper seeks to address 4-dimensional transportation challenges by integrating budget con straints, vehicle speed, carbon emissions, and optimizing for maximum profit and minimum time. The rising number of vehicles, varying road conditions, and diverse vehicle types used to meet daily needs have exacerbated issues like global warming and greenhouse gas (GHG) emissions. Our goal is to reduce carbon emissions for a cleaner environment. Single-objective, single-item transportation systems are often insufficient for scenarios with multiple criteria. Thus, we adopt a multi-objective, multi-item decision-making approach to tackle real-life transportation problems. Practical challenges frequently involve uncertainties stemming from time pressures, insufficient data, …

Neutrosophic Circular-Arc Graphs And Proper Circular-Arc Graphs, Takaaki Fujita, Florentin Smarandache

Neutrosophic Sets and Systems

Graph theory is a fundamental branch of mathematics that studies networks made up of nodes (vertices) and connections (edges). A key concept in graph theory is the intersection graph, where vertices represent sets, and edges are drawn between vertices if their corresponding sets intersect. A circular-arc graph specifically models the intersections of arcs on a circle, with vertices corresponding to the arcs and edges existing between intersecting arcs. This paper delves into the study of circular-arc graphs within the frameworks of fuzzy, intuitionistic fuzzy, neutrosophic, and Turiyam Neutrosophic graphs, all of which incorporate uncertainty into graph structures. Additionally, we examine …

Modified Waspas Technique For Triangular Fuzzy Neutrosophic Number Multiple-Attribute Decision-Making To Safe Operation Risk Assessment Of Batteries In Energy Storage Power Stations, Lunsen Zou, Zhiqiang Wang, Jin Wang, Linwei Wang, Liangrui Zhou

Neutrosophic Sets and Systems

With the proposal of China's "dual carbon" goals and the rapid development of the energy storage industry, in recent years, there have been more and more reports on safety accidents of energy storage power stations in the application of the energy storage industry. It can be seen that the pressure and safety hazards of the safe operation of energy storage power stations have significantly increased, and safety issues have become the main bottleneck restricting the good development of the energy storage industry. The safe operation risk assessment of batteries in energy storage power stations could be considered (MADM). Recently, the …

Correlation And Regression Coefficients Of Neutrosophic Graph Products Using Minimum Spanning Tree For Enhancing Healthcare Strategies, A. Meenakshi, Shivangi Mishra J

Neutrosophic Sets and Systems

This paper investigates the correlation and regression coefficients (CRCs) of single-valued neutro sophic graph products (SVNGPs) with a focus on the minimum spanning tree (MST) and their applications in enhancing healthcare strategies. Single-valued neutrosophic Graph (SVNG) is an extension of traditional graph theory that uses neutrosophic logic to solve uncertainties and indeterminacy. We have introduced the modular and strong products of SVNGs and calculated the CRCs with and without using MST to evaluate the relationships within healthcare networks. A comparative analysis has been done for CRCs with and without MST which helps to increase the accuracy and efficiency of CRCs. …

, Superhypersoft-Driven Evaluation Of Smart Transportation In Centroidous-Moosra: Real-World Insights For The Uav Era, Mona Mohamed, Ahmed M. Abdelmouty, Khalid Mohamed, Florentin Smarandache

Neutrosophic Sets and Systems

Over recent decades unmanned aerial vehicles (UAVs) have significantly impacted many areas and applications that affect our daily lives. Such as transportation, healthcare, and agricultural surveillance and management. Along with intelligently digitizing these sectors. Hence, this study focuses on exhibiting UAVs' contributions to transportation systems to be smart. An intelligent decision-maker framework is constructed to evaluate smart transportation systems (STSs) that leverage UAVSs in their operations. Preferencing candidates of STSs conduct the evaluation process based on a set of criteria and attributes. Moreover, the new multi-criteria decision-making (MCDM) of centroidous to obtain criteria attribute weights. As well as Multi-objective optimization …

Enhancing Neutrosophic Data Analysis: A Review Of Neutrosophic Measures And Applications With Neutrostat, Zahid Khan, Katrina Lane Krebs

Neutrosophic Sets and Systems

Neutrosophic statistical measures analyze data that is not fully determined, often due to imprecise observations. This type of data presents a major concern in neutrosophic statistics. The existing literature cat egorizes neutrosophic measures into two types: descriptive and inferential, aiming to broaden the categorization of statistics in these two major areas. Every statistical measure can be contextualized within the neutrosophic framework by acknowledging the inherent imprecision, vagueness, or not fully defined. In this study, the major focus is on reviewing existing neutrosophic measures rather than proposing new ones. The aim is to enhance current neutrosophic structures to make them more …

A Novel Approach To Assessing Art Education Teaching Quality In Vocational Colleges Based On Double-Valued Neutrosophic Numbers And Multi-Attribute Decision-Making With Tree Soft Sets, Heng He

Neutrosophic Sets and Systems

To promote stable and sustainable growth in vocational education, it is crucial to innovate and adapt the teaching methods of art education to align with modern educational trends. A comprehensive analysis of the art education curriculum is necessary to drive reform and modernize teaching methodologies, ensuring the continued relevance and effectiveness of art instruction. By updating art education, students can enhance their aesthetic appreciation, develop a refined understanding of high-quality artworks, and experience consistent growth in their artistic development. Moving beyond traditional teaching models is essential for the ongoing advancement of art education in vocational colleges. The evaluation of teaching …

A Novel Analysis On The Perception Of Physical Environmental Quality: An In-Depth Study Comparing The Neutrosophic Likert Scale With Score Function And The Classic Likert Scale - Statistical Analysis Of Data From A Restaurant Survey, Seher Bodur, Serpil Kaya, Selçuk Topal

Neutrosophic Sets and Systems

There are studies examining the quality of the physical environment in the restaurant industry. However, these studies have only been conducted using Likert scale. Since the neutrosophic scale has not been used in the restaurant industry before, it is considered to be an important gap. For this reason, it is aimed to investigate the perceptions of physical environmental quality in restaurants by using Likert and neutrosophic scales for the first time. By applying Exploratory Factor Analysis, evidence is presented that a single factor adequately incorporates both scales, thus optimising the assessment procedure. Their consistency and reliability in assessing environmental perceptions …

A Refined Dual-Valued Neutrosophic Copras-Based Approach For Holistic Evaluation Of English Teaching Standards, Peng Tong, Bin Xie

Neutrosophic Sets and Systems

The evaluation of college English teaching (CET) quality helps to improve teaching standards, ensure the achievement of teaching objectives, and enhance students' language skills and overall competence. Through feedback from evaluations, teachers can refine their teaching methods, optimize course design, and meet students' needs. Additionally, teaching quality evaluation promotes the professional development of teachers, facilitates the rational allocation of educational resources, and ensures effective teaching outcomes. The evaluation of CET quality in vocational colleges in the new era involves the multiple-attribute decision-making (MADM) process. Currently, COPRAS methods are employed to address Multi-Attribute Decision-Making (MADM) challenges. To handle uncertain data in …

A Triangular Fuzzy Neutrosophic Model For Assessing And Optimizing Educational Quality In University Badminton Initiatives: A Comprehensive Study, Yi Zheng, Jun Chen

Neutrosophic Sets and Systems

The evaluation of teaching quality in public badminton classes at general universities primarily considers students' learning outcomes, teachers' teaching abilities, class organization, and the appropriateness of the teaching content. Evaluation criteria include students' mastery of skills, participation, interest development, and teachers' teaching methods, classroom management, and interaction effectiveness. By combining quantitative and qualitative approaches, the evaluation aims to assess teaching quality, promote improvements, enhance students' physical fitness and sports skills, and support teachers' professional development and improvement of teaching standards. The teaching quality evaluation of public badminton classes at general universities is a multi-attribute decision-making (MADM). In this paper, a …

On Schur Complement In K-Kernel Symmetric Block Quadri Partitioned Neutrosophic Fuzzy Matrices, K. Radhika, T. Harikrishnan, R. Ambrose Prabhu, P. Tharaniya, M.John Peter, M. Anandhkumar

Neutrosophic Sets and Systems

In this paper, we present equivalent characterizations of k-kernel symmetric (k-KS) Quadri Partitioned Neutrosophic Fuzzy Matrices (QPNFMs). Additionally, we establish the necessary and sufficient conditions for the Schur complement (SC) within a k-KS QPNFM to be k-symmetric. The study also offers equivalent characterizations of both KS and k-KS QPNFMs. A few fundamental examples of KS QPNFMs are provided to clarify these concepts. It is shown that although k-symmetry implies k-KS, the converse does not necessarily hold. Several fundamental properties of k-KS QPNFMs are also derived. Finally, decision-making model utilizing QPNSMs has been successfully developed and validated through its application to …

A Study On Continuity Functions In Neutro-Topological Spaces, Bhimraj Basumatary, Jeevan Krishna Khaklary

Neutrosophic Sets and Systems

The specific purpose of this study is to define continuity of mappings in neutro-topological spaces using neutro-open and neutro-closed sets and analyze the properties of continuous functions that are true in classical topological spaces in the neutro-topological space. Neutro-interior and neutro-closure in neutro-topological spaces have some properties that are somewhat different from those in classical topological spaces. However, with the definition of a new form of continuity, termed as weakly neutro-continuity, much of the properties of continuous functions could be established in neutro-topological spaces. Neutro-open map and neutro-closed maps are also defined on the basis of neutro-open and neutro-closed sets. …

Solving The Shortest Path Based On The Traveling Salesman Problem With A Genetic Algorithm In A Fermatean Neutrosophic Environment, Prasanta Kumar Raut, Surapati Pramanik, Deepak Kumar Mohapatra, Srikanta Kumar Sahoo

Neutrosophic Sets and Systems

The Traveling Salesman Problem (TSP) is one of the most significant and well-known optimization problem that is frequently limited by uncertainty in edge lengths. Existing methods fail to effectively model and solve such problems in uncertain environments. To address this gap, we propose a novel approach that combines a genetic algorithm (GA) with Fermatean neutrosophic numbers to provide a more robust representation of uncertainty. This work presents a comprehensive framework for evaluating the shortest path in a given network by precisely characterizing uncertain edge lengths. The proposed methodology is tested on various TSP scenarios of varying complexities, demonstrating its ability …

Elevating Service Quality In Mass Sports Events Through Trapezoidal Neutrosophic Weighted Product Models, Yifang Zhao

Neutrosophic Sets and Systems

The evaluation of service quality in mass sports events is a structured process assessing aspects such as event organization, venue facilities, safety measures, staff services, and information dissemination. This evaluation assists organizers in identifying strengths and weaknesses, enabling optimization of services to enhance participant and spectator satisfaction. This study applies to the Weighted Product Method (WPM) integrated with Trapezoidal Neutrosophic Numbers (TNN) to address uncertainties inherent in multi-attribute decision-making. By presenting numerical examples and comparative analyses, the study demonstrates the effectiveness of the TNN-WPM technique. The findings provide a reliable framework for systematically evaluating service quality in mass sports events, …

A Statistical Comparison Study Of A Real-Life Survey Data On Procedural Justice Via Neutrosophic Likert Scale With Score Function And Classical Likert Scale, Seher Bodur, Selçuk Topal, Hacı Gürkan

Neutrosophic Sets and Systems

The present study aims to examine the distinctions between Likert and Neutrosophic scales in their ability to measure organizational behaviors and the many dimensions of organizational justice. To evaluate procedural justice, 6 questions measuring procedural justice from the Learning Environment Questionnaire were used. Compared to the Likert scale, the Neutrosophic scale exhibited greater decision weights and a more distinct expression of participants' ideas due to its ability to capture more complex replies. The reliability of both scales was found to be high, as indicated by satisfactory Cronbach's alpha coefficients. The results of the exploratory factor analysis indicated that both scales …

Regime Framework For Performance Ability Evaluation Of Excellent Football Players With Probabilistic Simplified Neutrosophic Sets, Dongdong Liu

Neutrosophic Sets and Systems

The evaluation of an excellent football player's performance abilities involves assessing their overall capabilities based on in-game performance. Key evaluation dimensions include technical skills (such as passing, shooting, dribbling, etc.), tactical awareness, physical fitness, mental resilience, and teamwork. Through data analysis, video review, and coach feedback, the player's impact and contribution to the game are comprehensively evaluated, helping to determine their actual level in matches and provide guidance for future development. The performance ability evaluation of excellent football players is multiple attribute decision-making (MADM). The REGIME proves to be an effective method for tackling MADM challenges. The Probabilistic Simplified Neutrosophic …

Interval Valued Secondary K-Range Symmetric Quadri Partitioned Neutrosophic Fuzzy Matrices With Decision Making, K. Radhika, S. Senthil, N. Kavitha, R. Jegan, M. Anandhkumar, A. Bobin

Neutrosophic Sets and Systems

The objective of this study is to establish the results concerning Interval-Valued (IV) Secondary k-Range Symmetric (RS) Quadri Partitioned Neutrosophic Fuzzy Matrices (QPNFM). We have applied the RS condition within the neutrosophic environment to explore the relationships between IVQP s−k- RS, s-RS, IVQP k-RS, and IVQP RS matrices. This analysis has yielded significant insights into how these various matrix types interrelate and their structural properties. We have established the necessary and sufficient criteria for IVQP s−k-RS IVQPNFM, along with various generalized inverses of an IVQP s−ks- RS fuzzy matrix to maintain its classification as an IVQP s−k- RS matrix. Furthermore, …

A Methodological Approach To Decision-Making Using Interval-Valued Neutrosophic Framework For Enhancing And Evaluating English Blended Teaching Quality, Ying Du

Neutrosophic Sets and Systems

The future of blended English instruction in universities is promising, driven by ongoing technological advancements and the increasing diversity of educational needs. This teaching model is expected to better integrate the strengths of both online and in-person learning, providing students with more flexible and personalized learning experiences. By combining these two modalities, blended instruction can improve student motivation and engagement while allowing educators to continuously refine their teaching methods and materials based on real-time data and feedback. As a result, blended learning is projected to become a more widespread and preferred method of instruction in higher education. In terms of …

Neutrosophic Sets And Systems, Vol. 78,2025, Florentin Smarandache, Mohamed Abdel-Basset, Maikel. Leyva Vazquez

Neutrosophic Sets and Systems

the whole volume

Innovations In Educational Research: Developing An Original Questionnaire To Measure New Mexico’S Teacher Practices And Beliefs Related To Project-Based Learning And Culturally And Linguistically Responsive Teaching, Zachary R. Ramsey

Teacher Education, Educational Leadership & Policy ETDs

This dissertation investigates teacher practices and beliefs related to project-based learning (PBL) and culturally and linguistically responsive teaching (CLRT), central to New Mexico’s educational reform efforts following Martinez & Yazzie v. New Mexico (2018). The study also explored teachers’ professional learning needs and their awareness of the state’s reform initiatives. I collected responses from 37 participants using an original questionnaire instrument. While the findings are not generalizable, they reveal that teachers practiced elements of PBL and CLRT with moderate frequency and generally believed in their efficacy for improving educational outcomes for diverse student groups. The results also highlighted varying levels …

Modelling V-Band Atmospheric Loss With Deep Learning, Ralph Lyndon Gesner

Electrical and Computer Engineering ETDs

Modelling atmospheric loss is fundamental to implementation of future mm-wave terrestrial and earth space communication links. Atmospheric losses have traditionally been estimated by calculating the contributions of individual weather phenomena through in-situ meteorological measurements and statistically derived models for estimating localized atmospheric water content. Collecting data for all points along the propagation path and calculating the physical effects of gases, clouds, and precipitation individually is both time consuming and impractical for large-scale use cases.

In response to these present limitations, this work proposes the use of novel deep learning models for estimating atmospheric losses from tabular meteorological sensor data and …

Operations On Submodules With The Multiplicative And Quotient Properties, Jiekai Pang

Mathematics & Statistics ETDs

Inspired by the works of Petro, Epstein, Vassilev, and Morre, this thesis aims to study the generalized definitions of the semiprime operation, weakly prime operation, and standard closure operation on rings, that is, the multiplicative operation, weakly multiplicative operation, and standardly multiplicative operation on submodules. Then, we will use Matlis duality to induce the dual notions of these definitions on submodules of Matlis-dualizable Artinian modules. In order to understand the dual notion of the standardly multiplicative operation, that is, the standardly quotient operation, we will classify the operations on the injective hull of residue field of the ring K[[x,y]]/(xy) which …