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Local-Neutrosophic Logic And Local-Neutrosophic Sets: Incorporating Locality With Applications, Florentin Smarandache, Takaaki Fujita

Branch Mathematics and Statistics Faculty and Staff Publications

The study of uncertainty has been a significant area of research, with concepts such as fuzzy sets [87], fuzzy graphs [51], and neutrosophic sets [58] receiving extensive attention. In Neutrosophic Logic, indeterminacy often arises from real-world complexities. This paper explores the concept of locality as a key factor in determining indeterminacy, building upon the framework introduced by F. Smarandache in [73]. Locality refers to processes constrained within a specific region, where an object or system is directly influenced by its immediate surroundings. In contrast, nonlocality involves effects that transcend spatial or temporal boundaries, where changes in one location have direct …

Some Types Of Hyperneutrosophic Set (1): Bipolar, Pythagorean, Double-Valued, Interval-Valued Set, Takaaki Fujita, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

The Neutrosophic Set is a mathematical framework designed to manage uncertainty, characterized by three membership functions: truth (T), indeterminacy (I), and falsity (F). In recent years, extensions such as the Hyperneutrosophic Set and SuperHyperneutrosophic Set have been introduced to address more complex scenarios. This paper proposes new concepts by extending Bipolar Neutrosophic Sets, Interval-Valued Neutrosophic Sets, Pythagorean Neutrosophic Sets, and Double-Valued Neutrosophic Sets using the frameworks of Hyperneutrosophic and SuperHyperneutrosophic Sets. Additionally, a brief analysis of these extended concepts is presented.

Some Types Of Hyperneutrosophic Set (7): Type-M, Nonstationary, Subset-Valued, And Complex Refined, Takaaki Fujita, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

This paper builds upon the foundational advancements introduced in [26,39–43]. TheNeutrosophic Set provides a versatile mathematical framework for addressing uncertainty through its three membership functions: truth, indeterminacy, and falsity [84]. Extensions such as the Hyperneutrosophic Set and the SuperHyperneutrosophic Set have been recently proposed to address increasingly complex and multidimensional problems. Detailed formal definitions of these concepts can be found in [33]. In this paper, we extend the Type-𝑚, Nonstationary, Subset-Valued, and Complex Refined Neutrosophic Sets using the Hyperneutrosophic Set and the SuperHyperneutrosophic Set frameworks.

Some Types Of Hyperneutrosophic Set (6): Multineutrosophic Set And Refined Neutrosophic Set, Takaaki Fujita, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

This paper builds on the foundational advancements introduced in [22, 29–32]. The Neutrosophic Set pro-vides a flexible mathematical framework for managing uncertainty by utilizing three membership functions: truth, indeterminacy, and falsity. Recent extensions, such as the HyperNeutrosophic Set and the SuperHy-perNeutrosophic Set, have been developed to address increasingly complex and multidimensional challenges. Comprehensive formal definitions of these concepts are provided in [26]. In this paper, we further extend various specialized classes of Neutrosophic Sets. Specifically, we explore extensions of the MultiNeutrosophic Set and the Refined Neutrosophic Set using HyperNeutrosophic Sets and 𝑛-SuperHyperNeutrosophic Sets, providing detailed analysis and examples.

Some Types Of Hyperneutrosophic Set (5): Support, Paraconsistent, Faillibilist, And Others, Takaaki Fujita, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

This paper builds upon the foundational advancements introduced in [14, 25–27]. The Neutrosophic Set offers a versatile mathematical framework for addressing uncertainty through its three membership functions: truth, indeterminacy, and falsity. Extensions such as the Hyperneutrosophic Set and the SuperHyperneutrosophic Set have been recently proposed to tackle increasingly sophisticated and multidimensional problems. Detailed formal definitions of these concepts can be found in [20]. In this paper, we extend various specialized classes of Neutrosophic Sets—namely, the Support Neutrosophic Set, Neutrosophic Intuitionistic Set (distinct from the Intuitionistic Fuzzy Set), Neutrosophic Paraconsistent Set, Neutrosophic Faillibilist Set, Neutrosophic Paradoxist Set, Neutrosophic Pseudo-Paradoxist Set, Neutrosophic …

Neutrosophic Treesoft Expert Set And Forestsoft Set, Takaaki Fujita, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

Concepts such as Fuzzy Sets [28,57],Neutrosophic Sets [42,44], and Plithogenic Sets [48] have been extensively studied to address uncertainty, finding diverse applications across various fields. The Soft Set provides a framework that associates each parameter with subsets of a universal set, enabling flexible approximations [31]. The TreeSoft Set extends the Soft Set by introducing hierarchical, tree-structured parameters, allowing for multi-level data representation [53]. In this paper, we revisit the concept of the Neutrosophic TreeSoft Set, which has been discussed in other studies [8, 34]. Additionally, we propose and examine the Neutrosophic TreeSoft Expert Set by incorporating the framework of the …

A Critical Evaluation Of The Criticisms Against Neutrosophic Statistical Methods, Muhammad Aslam, Abdulrahman Alaita, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

Neutrosophic statistical analysis has gained attention for incorporating the degree of indeterminacy when analyzing imprecise and interval data under uncertainty—an aspect often overlooked by classical statistics, fuzzy statistical analysis, and interval statistics. Recently, critical discussions have emerged regarding the use and applications of neutrosophic statistics, with some questioning its usefulness and validity. In this paper, we present a critical assessment of the existing literature, focusing on areas where misunderstandings and misinterpretations of neutrosophic statistical methods have occurred. We also examine flawed comparisons made between the results of neutrosophic statistics and interval statistics. Furthermore, substantial issues have been identified in the …

Neutrosophic Stance Detection And Fsqca-Based Necessary Condition Analysis For Causal Hypothesis Assessment In Ai-Enhanced Learning, Jesús Rafael Hechavarría-Hernández, Maikel Y. Leyva Vazquez, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

This study addresses the ambiguities in empirical findings on artificial intelligence (AI) in education by proposing a new methodological framework that combines neutrosophic stance detection and Fuzzy Set Qualitative Comparative Analysis (fsQCA). This approach explicitly models truth, indeterminacy, and falsity, allowing for the synthesis of contradictory research. The authors evaluated four causal hypotheses related to AI-based learning, using a survey of 24 university participants to explore the necessary conditions for perceived learning improvements. The results indicate that the digital divide is a perfectly necessary condition for effective AI-enhanced learning. The findings also reveal that AI feedback and AI platform use …

Neutrosophic Twofold Superhyperalgebra And Anti Superhyperalgebra, Takaaki Fujita, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

Neutrosophic Sets are conceptual frameworks designed to address uncertainty. A Neutrosophic TwoFold Algebra is a hybrid algebraic structure defined over a neutrosophic set, combining classical algebraic operations with neutrosophic components. Concepts such as Hyperalgebra and Superhyperalgebra extend classical Algebra using Power Sets and 𝑛-th powersets. Additionally, structures such as NeutroAlgebra and AntiAlgebra have been defined in recent y ears. This paper explores several related concepts, including TwoFold SuperhyperAlgebra and Anti SuperhyperAlgebra.

Enhanced Madm Strategy With Heptapartitioned Neutrosophic Distance Metrics, Mohamed Eassa, M. Myvizhi, Mohamed Elkholy, Ahmed Abdelhafeez, Hussam Elbehiery

Neutrosophic Sets and Systems

In this work, a novel methodological approach to multi-attribute decision-making problems is developed and the notion of Heptapartitioned Neutrosophic Set Distance Measures (HNSDM) is introduced. By averaging the Penta-Partitioned Neutrosophic Distance Measures under particular conditional criteria, the suggested technique ranks the options. Additionally, we explore the fundamental characteristics of HNSDM and provide several illustrative theorems. The Heptapartitioned Neutrosophic Set Distance Measures are formulated based on the Hepta Neutrosophic Set. Lastly, a practical numerical example is provided to illustrate the efficacy of the suggested methodology.

A Cross-Entropy-Based Framework Using Hypersoft Type-2 Neutrosophic Numbers For Innovation Capability Evaluation In Central Cities Of Emerging Economies, Xiangke Zhang, Shoukui He, Xu Chen

Neutrosophic Sets and Systems

The comprehensive evaluation of innovation capabilities in central cities of emerging countries is essential for promoting regional economic growth. This evaluation examines various factors, such as scientific activities, innovation infrastructure, talent resources, and policy environments, offering insights into the current innovation landscape and future potential. By guiding the allocation of resources and optimizing innovation policies, it fosters the transformation of technological achievements and accelerates urban economic transformation and sustainable development. Moreover, it helps cities attract investment and skilled talent, enhancing their competitiveness and influence. This evaluation is a multi-attribute decision-making (MADM) challenge, for which the cross-entropy method has been recently …

Utilizing Cocoso And Interval Neutrosophic Magdm With Superhypersoft For Competitiveness Assessment In Rural Tourism Of Surrounding Cities, Aiping Cui, Zhiyao Liu

Neutrosophic Sets and Systems

With rising living standards, rural tourism near cities has rapidly developed, playing a key role in the sustainable development of urban economies and societies. Factors like ecological environment, historical and cultural resources, and landscape significantly influence the competitiveness of rural tourism. However, current research on this topic is still in its early stages, with a focus on tourism benefits to cities, often overlooking other impacts. Rural tourism boosts employment, promotes rural industries, and increases farmers' incomes, accelerating rural urbanization and economic growth. Therefore, evaluating the competitiveness of rural tourism near cities is essential for its development. The evaluation of rural …

Uncertain Labeling Graphs And Uncertain Graph Classes (With Survey For Various Uncertain Sets), Takaaki Fujita, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

Graph theory, a branch of mathematics, studies the relationships between entities using vertices and edges. Uncertain Graph Theory has emerged within this field to model the uncertainties present in real-world networks. Graph labeling involves assigning labels, typically integers, to the vertices or edges of a graph according to specific rules or constraints. This paper introduces the concept of the Turiyam Neutrosophic Labeling Graph, which extends the traditional graph framework by incorporating four membership values—truth, indeterminacy, falsity, and a liberal state—at each vertex and edge. This approach enables a more nuanced representation of complex relationships. Additionally, we discuss the Single-Valued Pentapartitioned …

Some Types Of Hyperneutrosophic Set (4): Cubic, Trapozoidal, Q-Rung Orthopair, Overset, Underset, And Offset, Florentin Smarandache, Takaaki Fujita

Branch Mathematics and Statistics Faculty and Staff Publications

This paper builds upon the foundational work presented in [38–40]. The Neutrosophic Set provides a comprehensive mathematical framework for managing uncertainty, defined by three membership functions: truth, indeterminacy, and falsity. Recent advancements have introduced extensions such as the Hyperneutrosophic Set and the SuperHyperneutrosophic Set, which are specifically designed to address increasingly complex and multidimensional problems. The formal definitions of these sets are available in [30]. In this paper, we extend the Neutrosophic Cubic Set, Trapezoidal Neutrosophic Set, q-Rung Orthopair Neutrosophic Set, Neutrosophic Overset, Neutrosophic Underset, and Neutrosophic Offset using the frameworks of the Hyperneutrosophic Set and the SuperHyperneutrosophic Set. Furthermore, …

Some Types Of Hyperneutrosophic Set (3): Dynamic, Quadripartitioned, Pentapartitioned, Heptapartitioned, M-Polar, Takaaki Fujita, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

This paper builds upon the foundation established in [50, 51]. The Neutrosophic Set provides a robust mathematical framework for handling uncertainty, defined by three membership functions: truth, indeterminacy, and falsity. Recent developments have introduced extensions such as the Hyperneutrosophic Set and SuperHyperneutrosophic Set to tackle increasingly complex and multidimensional problems. In this study, we explore further extensions, including the Dynamic Neutrosophic Set, Quadripartitioned Neutrosophic Set, Pentapartitioned Neutrosophic Set, Heptapartitioned Neutrosophic Set, and m-Polar Neutrosophic Set, to address advanced challenges and applications.

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.

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.

Healthy Here Family Healthy Weight Program Year 1 Summary, Camille R. Velarde, Courtney A. Fitzgerald, Theresa H. Cruz

Reports & Documents

No abstract provided.

Lagrange-Integrated Gra Model For Urban Landscape Sculpture Site Selection With Neutrosophic Decision-Making, Qiwei Liu, Jiayin Li, Chang Liu

Neutrosophic Sets and Systems

Urban landscape sculpture plays a crucial role in preserving cultural heritage, enhancing city vitality, and reflecting the lives of urban citizens. With the continued development of landscape sculpture in modern urban environments, the process of site selection has become increasingly important. A well-chosen location can establish a positive interaction between sculptures and urban activities. Traditionally, site selection methods have been largely theoretical, lacking quantitative foundations, which made practical application challenging for designers. To address this, site selection for urban landscape sculptures can be approached as a multiple-attribute decision-making (MADM) problem. Grey Relational Analysis (GRA) is an effective method for handling …

, 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 …

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 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 …

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, …

An Efficient Neutrosophic Weighted Sum Approach With Insights Into Engineering Project Management Performance Assessment, Rong Yan, Yongguang Han, Liqing Hao

Neutrosophic Sets and Systems

Project engineering management performance evaluation is a systematic assessment of various tasks in the project management process to measure performance in areas such as efficiency, quality, schedule, and cost control. Through evaluation, strengths and weaknesses in management can be identified, ensuring the achievement of project objectives and optimizing resource allocation. This evaluation not only helps improve the overall management level of engineering projects but also provides valuable experience and insights for future projects, thereby facilitating smooth implementation and successful delivery. The project engineering management performance evaluation is multiple-attribute decision-making (MADM). Recently, the weighted sum method (WSM) method has been established …

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 …

Family Roots And Research Journal Unm Emeritus Professor José A. Rivera, José A. Rivera Ph.D

Faculty Publications

This article is an abbreviated life narrative of UNM Emeritus Professor of Community and Regional Planning, José A. Rivera. It begins with highlights of his family ancestry and continues with an account of his educational experiences K-12 and into a decade of university life as a student while earning a bachelor’s, two master’s and a doctorate. He taught at UNM for 35 years while also conducting research in his areas of interest, mostly in community irrigation studies, mutual aid societies, and rural development. The main body in the article focuses on positions he held at UNM and on publications that …

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 …

Language Use Of Emergent Bilingual Latino/A Students In A Music Class Setting, Karen G. Granados Dumais

Language, Literacy, and Sociocultural Studies ETDs

This study investigated the way in which emergent bilingual students utilize their linguistic repertoire in order to achieve new learning. Previous research has suggested that bilingual students learn differently than their monolingual counterparts due to their varying linguistic repertoires. Research has also suggested that translanguaging and culturally relevant teaching are valuable frameworks to adopt in the classroom, as they result in a better academic experience for all students.

I took an ethnographic approach while conducting a case study. I collected data in my elementary music classroom in the form of observations, audio recordings, and document analysis in order to help …