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Gauss Elimination Method For Solving The System Of Neutrosophic Linear Equations, Elsayed Badr, Shokry Nada, Saeed Ali, Aya Rabie

Neutrosophic Systems with Applications

This paper proposes a unified computational framework for solving linear systems under trapezoidal Neutrosophic uncertainty. The system is formulated as A( I )x = b( I ), where both the coefficient matrix and the right-hand side vector incorporate an indeterminacy parameter I, expressed as A( I ) = A₀ + IA₁ and b( I ) = b₀ + Ib₁. A decomposition strategy is developed to separate the model into deterministic and indeterminacy components, yielding a solution of the form x( I ) = x₀ + Ix₁. The deterministic component is obtained via …

Neutrosophic Hankel Transforms And Their Application To Cross-Domain Legislative Integration, Mona Gharib, Mehboob Ali, Ishtiaq Hussain

Neutrosophic Systems with Applications

This paper introduces the Neutrosophic Hankel Transform (NHT) as a novel mathematical framework for modeling systems with radial structure under uncertainty, indeterminacy, and inconsistency. Building upon classical Hankel transforms and neutrosophic logic, we define two complementary realizations: a componentwise transform (NHT–C) that transports uncertainty with the signal, and a kernel-weighted transform (NHT–K) that embeds neutrosophic weights into the integral kernel. We establish linearity, inversion, and Parseval-type relations, and derive operational rules that diagonalize the Bessel radial operator.

To demonstrate utility, we formulate a radial diffusion–reaction model for pollutant concentration in a radialized river cross-section and solve it in closed form …

A Visual Aid-Based Model For Constructing The Concept Of Probability For Students Aged 9 To 11, Validated Using Neutrosophic Plithogenic Statistics, Nela Del Rocío Sánchez López, Diana Carolina Pérez Duarte, Luis Fernando Pérez Duarte

Neutrosophic Sets and Systems

This article discusses a research endeavor whose intent was to further develop statistical reasoning by formulating probability notions for 9-11-year-old learners. The probability endeavor is formulated through a union of narrative, problem-solving and visual approaches. Action research allowed for formulation and implementation within a school setting, satisfactorily proving success in developing learners' abilities to think logically and critically. Results indicate a statistically significant probability of appropriating the notion of probability based on neutrosophic plithogenic statistics which assessed the degree of truth, indeterminacy, and falsity of student answers which ultimately promote rational decisions in uncertain situations. It's recommended that the union …

Technarrative Model (Ntm) For The Symbolic-Emotional Evaluation Of Architectural Space: A Neutrosophic Multiperspectivism Approach, Jesús Rafael Hechavarría-Hernández, Ana María Padrón-Medina, Erika Ascencio Jordán

Neutrosophic Sets and Systems

This research answers the need to evaluate an architectural space from a non-technical standpoint relative to its symbolism/emotion charge that is not taken into account by the design/planning of such public spaces. This research problem is sociologically relevant as today; architecture does not only dictate the layout of the physical world but also the group existence, sensitivity to experiences and modes of social appropriation. Yet the state-of- the-art literature provides purely professional and empirical avenues of investigation driven by economic/aesthetic value with no pathway for understanding appreciation of ambiguity and the multiple perspectives at play. Thus, a Neutrosophic Technarrative Model …

Neutrosophic Algebraic Structures For Precise Uncertainty Quantification In Outcome-Based Education Systems: A Rigorous Case Study Analysis, Mona Gharib, Imran Siddique, Miin Shen Yang

Neutrosophic Systems with Applications

Outcome-Based Education (OBE) emphasizes measurable learning results, yet the evaluation of professional talent training in physical education often involves uncertain, incomplete, or even contradictory indicators. Traditional assessment models are limited in capturing these indeterminacies. To address this challenge, we propose a novel neutrosophic algebraic framework that integrates neutrosophic probability, measure, and algebraic structures with OBE evaluation. This study introduces a neutrosophic evaluation framework that captures both determinate and indeterminate aspects of brand competitiveness. A case study on physical education professional training demonstrates how the proposed model captures hidden uncertainty and provides a more balanced assessment than classical methods. The results …

Neutrosophic Psychological Profiles In Habeas Corpus: An Analysis Of Judicial Indeterminacy, Esther Maricela Coello Avilés, Kevin Luis Flores Vega, Josselyn Bryggitte Vilela Verdezoto

Neutrosophic Sets and Systems

This study investigates the psychological influences, particularly indeterminacy, on judges' and lawyers' decisions regarding habeas corpus, an area underexplored in legal psychology which traditionally focuses on cognitive bias and emotional processing. Employing Neutrosophic Psychology, the research utilized semi-structured interviews and neutrosophic questionnaires with 60 legal practitioners to analyze their levels of acceptance, rejection, and indeterminacy. The findings reveal significant indeterminacy in granting or denying habeas corpus, fueled by a persistent tension between sympathetic and conservative leanings. Key impactful variables identified include existential factors, social pressures, and personal values. Ultimately, the study validates Neutrosophic Psychology as an applicable framework in the …

Nahp: Neutrosophic Hierarchical Analysis For Pest Prioritization In Plantain Cultivation, Marely Del Rosario Cruz Felipe, Víctor Noe Sánchez Carreno, Lorenzo Cevallos-Torres

Neutrosophic Sets and Systems

The following study addresses the impact of pests on plantain cultivation, recognizing them as a critical factor for both sustainability and productivity. Traditionally, decision-making in this context relies heavily on subjective and unstructured criteria, often leading to inaccurate prioritization of pest- and disease-related risks. This issue becomes even more pressing considering the growing global demand for plantains and the need to manage resources effectively, which calls for clear identification of intervention priorities. However, agricultural systems—characterized by ecological and social variability—often present incomplete, ambiguous, or contradictory information, making conventional multicriteria analysis insufficient. To address this challenge, this research introduces the Neutrosophic …

A Neutrosophic Approach To Social Phenomena, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

Sociology has long sought to understand human societies and the social behaviors within them. It explores the organization, structure, dynamics, and transformations of society over time. However, traditional sociological methods face significant challenges in addressing the complexity and indeterminacy inherent in social data—data that is often ambiguous, incomplete, and contradictory. The Neutrosociology offers a novel approach to studying and modeling social phenomena by employing mathematical and philosophical tools that can accommodate uncertainty.

Applying Neutrosophic Natural Language Processing To Analyze Complex Phenomena In Interdisciplinary Contexts, Diego Fernando Coka Flores, Ignacio Fernando Barcos Arias, María Elena Infante Miranda, Omar Mar Cornelio

Neutrosophic Sets and Systems

The paper addresses the challenge of integrating natural language processing (NLP) with neutrosophic logic to solve problems where uncertainty, ambiguity, and indeterminacy play a critical role. This approach becomes particularly relevant in an increasingly digitalized world, where human-machine interaction requires a deeper understanding of linguistic and contextual nuances. Despite advances in conventional NLP, many existing methodologies lack tools to effectively manage undefined or contradictory elements present in real data. In this context, neutrosophic logic offers an innovative framework to model and analyze complex and multifaceted human perceptions. The study applies a methodology that combines advanced NLP techniques with neutrosophic analytical …

Application Of The Plithogenic Iadov Approach To Evaluate Satisfaction With The Implementation Of Indigenous Rights, Gıovanna Fernanda Vınueza Arroyo, Tanya Tupamara Camargo Martinez, Manuel Augusto Suarez Albıñol, Joffre R. Paladines Rodriguez

Neutrosophic Sets and Systems

The present study addresses a crucial challenge in the evaluation of complex systems: the need to incorporate a holistic view that contemplates not only defined elements but also those that are intrinsically ambiguous or uncertain. The research focuses on the application of the Plithogenic IADOV approach, a model based on neutrosophic logic, to overcome the limitations of traditional methodologies that often fall short when addressing phenomena containing contradictory or unknown dimensions. In the existing literature, despite the wealth of approaches used for the evaluation of systems, there is a perceived lack of methodologies that effectively manage the indeterminacy inherent in …

Use Of Neutrosophic Cognitive Maps For A More Complex Representation Of Human Perceptions, Juan Alberto Rojas Cardenas, Nelson Francisco Freire Sanchez, Alipio Absalon Cadena Pozo, Karina Perez Teruel

Neutrosophic Sets and Systems

The research addresses a central problem in the modeling and analysis of human perceptions: the need for tools that capture more richly and accurately the complexity inherent in opinions, especially in contexts of high uncertainty and contradiction. In a scenario where traditional methodologies such as conventional cognitive maps lack the flexibility to represent nuances such as ambiguity or non-linear relationships, a key opportunity arises to explore innovative approaches. This methodological gap raises the question of how to integrate neutrosophic logic into analytical tools to improve the representation and analysis of complex perceptions in diverse environments. The study proposes and validates …

Using The Neutrosophic N-Ahp Method To Prioritize Variables And Expert Analysis, Oswaldo Lıber Andrade Salazar, Lenı Cecılıa Campaña Muñoz, Second Huacón Farm, Angel Braulio Martinez Vasquez

Neutrosophic Sets and Systems

The study focuses on addressing a growing challenge in complex decision-making: how to prioritize key variables in an environment of inherent uncertainty and contradiction. In this context, the research explores the implementation of the neutrosophic N-AHP method, a variant of Hierarchical Process Analysis (HPA) that incorporates neutrosophic logic to handle ambiguity and indeterminacy in the evaluation of critical variables. Although traditional HPA has been widely used to prioritize options, it has been limited in contexts where expert perceptions are not clear-cut or are marked by high levels of uncertainty. This work seeks to overcome those limitations, proposing a more flexible …

Neutrogeometry And Fractal Geometry, Erick González-Caballero, Maikel Y. Leyva-Vázquez, Noel Batista-Hernández, Florentin Smarandache

Neutrosophic Sets and Systems

Geometries are structures with certain elements like points, lines, planes, and spaces, among others, that satisfy certain definitions, axioms, properties, and theorems for the total of the elements. NeutroGeometries are geometric structures that meet at least one of these concepts only partially, never for 100% or 0% of the elements. Until now, NeutroGeometries have been developed from the ideas of classical geometries such as Euclidean, Hyperbolic, Elliptic, Mixed (Smarandache) geometries, among others where axiomatization is the basis of their construction. This paper aims to discuss some ideas about the relationship between NeutroGeometries and fractal geometry. This relation is not necessarily …

Uncertainty Analysis In Prediction Intervals Using Neutrosophic Numbers, Héctor Félix Cerna Maguiña, Domingo Guzmán Chumpitaz Ramos, Ada Lucía Gallegos Ruiz Conejo, Nancy Isabel Pool Painted, Jesús Isabel Baltazar Ángeles

Neutrosophic Sets and Systems

This study analyzes uncertainty in prediction intervals by applying neutrosophic numbers to quality of life forecasts based on characteristics such as compensation, job hours, years of experience, and academic level. Three examples were studied, with indeterminacy values ranging from 0.589 to 0.628. These statistics show that between 58.9% and 62.8% of the prediction intervals are affected by uncertainty. Higher indeterminacy levels reflect a stronger effect of external influences or unpredictability within the data. The analysis demonstrates that as variables like compensation and labor hours grow, so does the level of uncertainty in the projections. Neutrosophic numbers provide a valuable framework …

Nidus Idearum. Scilogs, Xiii: Structure / Neutrostructure / Antistructure, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

In this thirteenth book of scilogs – one may find topics on Neutrosophy, Plithogeny, Physics, Mathematics, Philosophy – email messages to research colleagues, or replies, notes, comments, remarks about authors, articles, or books, spontaneous ideas, and so on. It presents new types of soft sets and new types of topologies.

Exchanging ideas with Mohammad Abobala, Ishfaq Ahmad, Ibrahim M. Almanjahie, Fatimah Alshahrani, Nizar Altounji, Muhammad Aslam, Said Broumi, Victor Christianto, R. Diksh, Feng Liu, Frank Julian Gelli, Erick Gonzalez Caballero, Riad Hamido, Yaser Al-Hasan, Ahmed Hatip, Yasin Karmouta, Nivetha Martin, Preda Mihăilescu, V. Lakshmana Gomathi Nayagam, Ze Carlos Tiago de …

Neutrosophic Statistical Analysis Of Temperatures Of Cities In The Southeastern Anatolia Region Of Turkey, Hacer Şengül Kandemir, Nazlım Deniz Aral, Murat Karakaş, Mikail Et

Neutrosophic Systems with Applications

In the paper, neutrosophic statistical analysis of temperature data of different cities in the southeastern Anatolia region of Turkey is given. The neutrosophic mean and neutrosophic coefficient of variation are computed using the temperature data. From the analysis, it is concluded that the temperatures of Mardin and Şanlıurfa cities are more consistent than the other cities in Turkey. In addition, the neutrosophic results are compared with results under classical statistics. Based on the comparative study, it can be concluded that neutrosophic statistical results are more adequate, flexible, and more informative than classical statistics.

Logical Pluralism And Neutrosophy: Reflections On The Nature Of Truth, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

The article explores the shift from classical binary logic (true and false) to a more complex landscape of logical frameworks. It introduces logical pluralism, which suggests that no single, universally accepted system of logic exists. The paper connects this idea to neutrosophy, a framework that extends fuzzy logic by incorporating a third value: indeterminacy. This triadic approach, where every proposition has a degree of truth (T), falsity (F), and indeterminacy (I), is particularly useful for managing incomplete or contradictory information. The author argues that different logical systems, like different tools, are suited for different problems, and that the …

Análisis Neutrosófico De Las Actitudes Hacia La Máquina De Experiencia De Nozick, Maikel Yelandi Leyva Vázquez, Jesús Estupiñán Ricardo, Noel Batista Hernández, Ricardo Sánchez Casanova, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

This paper presents a neutrosophic study on attitudes towards virtual technology, with a special focus on the "Experience Machine". Employing a methodology that incorporates the theory of indecision and neutrality into response analysis, the perceptions of 50 university students were investigated. Opinions and feelings were transformed into neutrosophic numbers to calculate contradiction and conduct a detailed analysis. The results indicate a predisposition towards agreement with virtual technology, although notable indecision and a significant presence of neutral attitudes were detected. The correlations and clustering methods applied reveal a complex dynamic of attitudes, challenging binary interpretations and highlighting the need for more …

Nidus Idearum. Scilogs, Xii: Seed & Heed, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

In this twelfth book of scilogs – called seed & heed –, one may find topics on Neutrosophy, Superluminal Physics, Mathematics, Information Fusion, Philosophy, or Sociology – email messages to research colleagues, or replies, notes, comments, remarks about authors, articles, or books, spontaneous ideas, and so on.

Management Of Indeterminacy In The Analysis Of Knowledge About Reproductive Tract Infections In Women, Julio Morillo Cano, Melba Esperanza Narváez Montenegro, Adisnay Rodríguez Placencia, Olger Efraín Velastegui Naranjo

Neutrosophic Sets and Systems

The research aims to assess the level of knowledge about reproductive tract infections among women to apply statistical analysis of the probability of indeterminacy. The main methods and techniques used were: theoretical, analytical-synthetic, and inductive-deductive, while within the empirical are the survey, measurement, and statistical-mathematical. The sample was calculated using neutrosophic statistics and python interval arithmetic library. The results achieved are evaluated quantitatively and qualitatively, where the validity of the same was demonstrated since there was a level of significance equal to or less than p 0.05.

True-False Set Is A Particular Case Of The Refined Neutrosophic Set, Florentin Smarandache, Said Broumi

Branch Mathematics and Statistics Faculty and Staff Publications

Borzooei, Mohseni Takallo, and Jun recently proposed a new type of set, called True-False Set [1], and they claimed it is a generalization of Neutrosophic Set [2]. We prove that this assertion is untrue. Actually it’s the opposite, the True-False Set is a particular case of the Refined Neutrosophic Set.

Octagonal Neutrosophic Number: Its Different Representations, Properties, Graphs And De-Neutrosophication With The Application Of Personnel Selection, Muhammad Saqlain, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

To deal with fluctations in decision-making, fuzzy / neutrosophic numbers are used. The problem having more fluctuations are difficult to sovle. Thus it is a dire need to define higher order number, also It is a very curious question by researchers all around the world that how octagonal neutrosophic number can be represented and how to be graphed? In this research article, the primarily focused on the representation and graphs of octagonal neutrosophic number. at last, a case study is done using VIKOR method based on octagonal neutrosophic number. These representations will be helpful in multi-criteria decision making problems in …

Introduction To Neutrosophic Statistics, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

Neutrosophic Statistics means statistical analysis of population or sample that has indeterminate (imprecise, ambiguous, vague, incomplete, unknown) data. For example, the population or sample size might not be exactly determinate because of some individuals that partially belong to the population or sample, and partially they do not belong, or individuals whose appurtenance is completely unknown. Also, there are population or sample individuals whose data could be indeterminate.

In this book, we develop the 1995 notion of neutrosophic statistics. We present various practical examples. It is possible to define the neutrosophic statistics in many ways, because there are various types of …