Digital Commons Network^™

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 …

Faim: Fuzzy‑Neutrosophic Academic Integrity Model For University Students, Elsy Rodriguez Revelo, Lorenzo Cevallos Torres

Neutrosophic Sets and Systems

The FAIM (Fuzzy-Neutrosophic Academic Integrity Model) is a novel approach developed to assess academic integrity among university students under conditions of uncertainty. This model emerged as a response to the challenges posed by the sudden shift from face-to-face to virtual education during the COVID-19 pandemic. This environment saw a notable increase in dishonest academic behavior. FAIM integrates fuzzy logic and neutrosophic reasoning to capture the complexity and indeterminacy of students’ conduct. Key variables associated with academic dishonesty—motivation, justification, and opportunities—were examined across three simulated scenarios. The results validated FAIM’s capacity to differentiate integrity levels within the student population effectively. Unlike …

Descriptive And Diagnostic Analysis Of Customer Complaints For Different Electric Companies Of Ecuador Using Neutrosophic Logic, Marco Arguello Arguello, Franklin Parrales Bravo, Roberto Tolozano Benites, Dayron Rumbaut Rangel

Neutrosophic Sets and Systems

This article presents a descriptive analysis of complaint and claim management by ARCONEL and Electricity Distribution Companies in Ecuador for the year 2023. The dataset includes information about complaint outcomes such as 'Procedentes' (resolved), 'No Procedentes' (dismissed), 'En Proceso' (pending), and 'Invalidado' (invalid). This analysis will examine the complaint dataset using neutrosophic logic, which extends traditional binary logic by incorporating indeterminacy. We apply Neutrosophic Logic to capture not only resolved and unresolved complaints, but also uncertainty in complaint status. Key findings reveal high median resolution rates (99.98%), yet notable disparities exist: Sierra region companies outperform those in Costa, and private …

Neutrosophic Evaluation Of Sentiments Through Neutroalgebra Applied To The Use Of The Mediation Record As A Means For Lifting Precautionary Measures In Child Support Proceedings, Marcelo Raúl Dávila Castillo, Jessica Johanna Santander Moreno, Rosa Evelyn Chugá Quemac

Neutrosophic Sets and Systems

This is a study of perception and effectiveness of mediation to remove cautionary measures in child support proceedings. This is based on an assessed need within family law. This was an attempt to assess the mechanism via those who know law and mediation and justice to an extent as the predictions do not rely upon prior assessments. This assesses whether the mediation is ethical/legal/social for conflict resolution wherein it's not just warring adults; minors are at stake. Why is this topical? More and more people want this natural approach to attract judicial efficiency while simultaneously, de facto wellbeing. In this …

Neutrosophic Assessment Of Evidence In Cases Of Divorce Due To Adultery: An Application Of The Owa-Topsis Model To The Evidentiary Obstacle In The Ecuadorian Legal System, Jason Humberto Ruiz Silva, Esther Maricela Coello Avilés, Vanessa Josefa Hernández Alvarado

Neutrosophic Sets and Systems

The current research resolves an internal issue of the Ecuadorian legal system: the assessment of evidence for divorce by adultery, an unjust approach since it cannot always be evidenced properly. Thus, when judges have the power to rule, their authority is compromised since one of the most crucial elements of adjudicatory due process is equity, and equity stems from objectivity. Unfortunately, we see subjectivity here stemming from the uncertainty and indeterminacy relative to such evidence. While much literature exists relative to the analysis of judicial determination, little evolution occurs relative to a solid approach that incorporates such uncertainty and indeterminacy …

Current Situation Of The Integration Of Neutrosophy In Requirements Engineering, Franklin Parrales-Bravo, Roberto Tolozano-Benites, Leonel Vasquez-Cevallos, Leili Lopezdominguez-Rivas

Neutrosophic Sets and Systems

This study conducts a comprehensive literature review to explore the integration of neutrosophic logic in Requirements Engineering (RE), addressing challenges such as uncertainty, ambiguity, and conflicting stakeholder perspectives. By systematically analyzing peer-reviewed studies from 2015 to 2024, the research synthesizes existing neutrosophic techniques—including Type-2 Neutrosophic Numbers (T2NNs), Neutrosophic Cognitive Maps (NCMs), and Single-Valued Neutrosophic Sets (SVNS)—and categorizes their applications into uncertainty handling, conflict resolution, and requirement prioritization. The study highlights neutrosophy’s transformative potential in enhancing RE practices, offering robust solutions beyond traditional methods. Additionally, it identifies underexplored techniques like Bipolar Neutrosophic Sets (BNS) and Neutrosophic Rough Sets (NRS) for future …

Design Thinking Model Based On Plithogenic Logic For The Management Of Entrepreneurship And Innovation In Higher University Education In Peru, Wilmer Ortega Chávez, Eudosio Paucar Rojas, Daniel Alberto Oswaldo Valenzuela Narváez, Carlos Máximo Gonzales Añorga, Herbert Víctor Huaranga Rivera, Enoc López Navarro, Aníbal Campos Barreto, Hugo Aysanoa Calixto

Neutrosophic Sets and Systems

Design Thinking is a methodology that has been gaining popularity in the business world and also in higher education management. This methodology proposes a set of steps to follow, with the client and the human being at the center of attention. It encourages the search for creative and collaborative solutions to problems. The role of Design Thinking in entrepreneurship and entrepreneurship management for higher education lies in its contribution to innovation in business management within this field. The development of skills in Design Thinking fosters creativity, innovation, and critical thinking in students, improving their problem-solving and project development skills. The …

Intercultural Dialogue In The Meeting On Neutrosophy And Latin American Worldviews: A Perspective From The Náhuat Indigenous Chair Of The Technological University Of El Salvador, Morena Guadalupe Magaña

Neutrosophic Sets and Systems

This article presents a reflective analysis of the intercultural forum held during the Meeting on Neutrosophy and Latin American Worldviews, focusing on the contribution of the Náhuat Indigenous Chair at the Technological University of El Salvador. Drawing on philosophical and decolonial frameworks, it explores how the revitalization of the Náhuat language serves as both an act of cultural resistance and an epistemological statement. The Chair's initiatives—including teacher training, language certification, and community-based educational projects—are examined as concrete expressions of intercultural commitment. These efforts are contextualized within a broader critique of historical erasure, media manipulation, and social forgetting that have affected …

Thinking About Complexity In Latin America: Contributions Of Neutrosophy In Dialogue With Edgar Morin, Noel Batista-Hernández, Maikel Yelandi Leyva-Vázquez, Alenna Rosa Batista-Barallobre

Neutrosophic Sets and Systems

Smarandache’s neutrosophic logic—and its broader philosophical umbrella of MultiAlism, which insists that any assertion must be considered together with its neutral and anti-assertive counterparts—offers powerful methodological tools to operationalize Edgar Morin’s complexity thinking. While Morin contributes the principles of dialogic, recursiveness and the hologrammatic approach, his continental framework can be difficult to apply empirically. Neutrosophy and MultiAlism formalize contradiction, uncertainty and multidimensionality, thereby bridging theory and practice. In Latin America, where complexity thinking is widely adopted to address realities marked by inequality and instability, this integration enables rigorous modelling of non-linear phenomena. Applications such as Neutrosophic QCA (NsQCA), Neutrosophic Cognitive …

Exploring Emotional Dimensions In Educational Data: A Neutrosophic Sentiment Analysis Approach., Joffre Paladines Rodríguez, Adrián Del Pozo Biscarra, Felix Tamayo

Neutrosophic Sets and Systems

This study contributes to the literature by trying to understand which emotions translate to transcription in the classroom from the perspective of emotional impact on academic achievement in digital environments. This is specific to the chosen sample population from Instituto Superior Tecnológico Guayaquil, which operates within the Google Classroom environment. The importance of such a study is essential in twenty-first-century life be-cause relative emotions—positive or negative, from constructs like motivation, anxiety, or frustration—are in-tegral to positioning and learning processes in digital teaching environments which excessively appear in to-day's higher education curriculum. Yet the state-of-the-art does not highlight such a systematic …

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 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.

Application Of Neutrosophic Multi-Criteria Decision-Making Tech-Niques For Assessing Violations Of Child Support Rights, Vanessa Lisseth Montenegro Altamirano, Jaime Rodrigo Cadena Morillo, Carmen Marina Méndez Cabrita, Ricardo Sánchez Casanova

Neutrosophic Sets and Systems

The study addresses a crucial challenge in the analysis of rights violations by applying neutrosophic methods. Specifically, it investigates how multi-criteria assessment tools can provide a more precise and nuanced approach to addressing rights violations, a topic that remains of global relevance, given the complexity and diversity of situations that occur in different contexts. The existing literature, although abundant in human rights studies, of-ten lacks approaches that integrate the uncertainty and ambiguity inherent in these cases, limiting the effective-ness of conventional analyses. This work fills that gap by implementing a neutrosophic approach that captures these dynamics more effectively and adequately. …

Analyzing Internal And External Factors For Ecological Preservation In San Juan De Pastocalle: A Combined Swot And Neutrosophic Ahp Approach, Magaly Lucia Benalcázar Luna, Ana Lucía Naranjo, Luis Fernando Muisin Salazar

Neutrosophic Sets and Systems

This study aimed to analyze the role of Community Circles in preserving the ecological link in the rural parish of San Juan de Pastocalle, identifying both the factors that enhance and those that limit this process. The SWOT analysis combined with the neutrosophic AHP method was applied to evaluate the key elements that affect eco-logical sustainability in the community. The results revealed that the main weaknesses were the lack of training in adequate recycling and the poor infrastructure for waste management. Strategic actions focused on strengthen-ing local capacities and ensuring economic support were proposed. The use of decision-making methods apply-ing …

Insertion And Use Of Multicriteria Methods For Neutrosophic Judicial Evaluation, Roberto Carlos Jiménez Martinez, María José Calderón Velásquez, Manuel Augusto Suarez Albiñol, Yusleidy Marlie Gordo Gómez

Neutrosophic Sets and Systems

This study addresses the growing need to integrate multicriteria methods into judicial evaluation, specifically through a neutrosophic approach, to improve the accuracy and reliability of legal decision-making. Today, the judicial system faces critical challenges related to the interpretation of evidence, the consideration of multiple factors, and the uncertainty inherent in complex cases. Although various approaches have been used in judicial evaluation, few effectively address the ambiguity and indeterminacy present in the opinions of judges and experts, leading to fragmented or biased analysis. This study seeks to close that gap by applying neutrosophic multicriteria methods, which allow for a more balanced …

Ncc: Neutrosophic Control Charts, A Didactic Way To Detect Cardiac Arrhythmias From Reading Electrocardiograms, Lorenzo Cevallos-Torres, Jefferson Núñez-Gaibor, Maikel Leyva-Vasquez, Víctor Gómez-Rodríguez, Franklin Parrales-Bravo, Jesús Hechavarría-Hernández

Neutrosophic Sets and Systems

Cardiac arrhythmias are cardiovascular conditions caused by irregularities in the formation or transmission of electrical impulses. To identify these arrhythmias and determine their origin, an electrocardiogram (ECG) is used, which graphically records the electrical activity responsible for each heartbeat over a short period. This analysis can reveal stochastic changes, introducing a degree of uncertainty. To detect these changes, neutrosophic control charts provide an appropriate statistical tool to assess the stability of the ECG, anticipate potential heart failures, reduce variability in measurements, and, in some cases, make predictions. The results indicate that the proposed model is highly accurate in detecting and …

A Neutrosophic Model For Measuring Evolution, Involution, And Indeterminacy In Species: Integrating Common And Uncommon Traits In Environmental Adaptation, Antonios Paraskevas, Michael Madas

Neutrosophic Systems with Applications

In 2017, Professor F. Smarandache introduced the Neutrosophic Theory of Evolution, Involution, and Indeterminacy (or Neutrality) (NToEIaI). He concluded that every theory of evolution is characterized by a certain degree of truth, indeterminacy, and untruth, as in neutrosophic logic. In this perspective, he raised several open questions on evolution, neutrality, and involution that required further research effort. Very recently, in 2024, Smarandache conducted research, from a soft sciences/philosophical viewpoint, on identifying and studying common parts in uncommon things and uncommon parts in common things emphasizing the complexity and interconnectedness of concepts within the context of neutrosophy. In this article, we …

Study Of Knowledge And Preservation Of Traditional Stories Of The Shipibo-Konibo Culture In Primary School Students Based On Neutrosophic Logic, Hulda Cahuaza Ochavano, Beker Maraza Vilcanqui, Elizabeth Norma Calixto Arias, Aniceto Elías Aguilar Polo, Iris Katheryne Mori Cairuna, Walter Arturo Quispe Cutipa, Maritza Soria Ramírez, Roció Del Águila Sandoval

Neutrosophic Sets and Systems

This paper aims to determine the knowledge and preservation of traditional stories of the Shipibo-Konibo culture in students of the Primary Educational Institution No. 64161-Bilingue Nuevo Nazareth de Iparia, Peru in 2023. A population of 119 students from the educational institution was considered, whom we interviewed personally after filling out a questionnaire to collect information regarding their knowledge of traditional stories of the Shipibo-Konibo culture. The opinions of the children surveyed are given in the form of linguistic values associated with Single-Valued Neutrosophic Numbers. The data is processed with the help of some propositions according to the neutrosophic logic. The …

Cognitive Mapping In The Study Of Agricultural Orality In The Apagua Community, María Florinda Ushco Ayala, Alisson Abigail Criollo Quiroga, Ricardo Francisco Ureña López

Neutrosophic Sets and Systems

This research explores the application of neutrosophy to understand and address the inherent complexity in the oral transmission of knowledge in family agriculture. It leverages its ability to handle contradictions and ambiguities, facilitat-ing a richer analysis of agricultural practices and social interactions. Orality, as the primary form of communication in these communities, is essential for the transmission of agricultural and cultural knowledge. This research highlights how orality acts as a vehicle for the preservation of collective identity and the transmission of ancestral knowledge. The study used Fuzzy Cognitive Maps (FCM) to describe the causal relationships between different variables of interest. …

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 …

Extended Event Calculus Using Neutrosophic Logic: Method, Implementation, Analysis, Recent Progress And Future Directions, Antonios Paraskevas

Neutrosophic Systems with Applications

Brains do not reason as digital computers do. Computers reason in clear steps with statements that are either true or false, while humans reason with vague terms of common sense. Neutrosophy is a new branch of philosophy and machine intelligence that deals with neutralities, specifically the idea of indeterminacy that is evident and experienced in our everyday lives. Indeterminacy is interpreted as everything that falls between a concept, idea, statement, declaration, etc. and its opposite. The fundamental thesis of neutrosophy is to employ neutrosophic logic, an extension of fuzzy logic, to incorporate fuzzy truth into complex schemes of formal reasoning. …

New Trends In Neutrosophic Theories And Applications, Volume Iii, Florentin Smarandache, Surapati Pramanik

Branch Mathematics and Statistics Faculty and Staff Publications

The field of neutrosophic set theory and its applications has been rapidly expanding, particularly since the introduction of the journal "Neutrosophic Sets and Systems." New theories, techniques, and algorithms are being developed at a very high rate. One of the most notable trends in neutrosophic theory is its hybridization with other set theories such as rough set theory, bipolar set theory, soft set theory, hesitant fuzzy set theory, and more. Various hybrid structures like rough neutrosophic sets, neutrosophic soft set, single valued neutrosophic hesitant fuzzy sets, among others, have been proposed in a short period. Neutrosophic sets have proven to …

Ncmpy: A Modelling Software For Neutrosophic Cognitive Maps Based On Python Package, Ilanthenral Kandasamy, Divakar Arumugam, Aryan Rathore, Ateeth Arun, Manan Jain, Vasantha Kandasamy, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

Cognitive Maps are a vital tool that can be used for knowledge representation and reasoning. Fuzzy Cognitive Maps (FCMs) are popular soft computing techniques used to model large and complex systems, and they can aid in explainable AI. FCMs, however, cannot model the indeterminacy that arises in a system due to various uncertainties. Neutrosophic Cognitive Maps (NCMs), upgraded FCMs that could model indeterminacy, was introduced to address this issue. NCMs are a generalization of FCMs, a field of cognitive science firmly based on neural networks. NCMs have been used to solve a wide range of problems. NCMs were introduced in …

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 …

A Neutrosophic Approach To Study Agnotology: A Case Study On Climate Change Beliefs, Florentin Smarandache, Maikel Leyva Vázquez

Branch Mathematics and Statistics Faculty and Staff Publications

Misinformation and biased information significantly impact public perception and political decisions, especially on critical issues such as climate change and environmental conservation. This study aims to understand how indeterminacy and contradiction influence public perception and policy formulation by applying neutrosophic theory to model the complexity and multi-dimensionality of ignorance. Using neutrosophic Likert scales, we capture a nuanced spectrum of opinions on the scientific certainty of human impact on climate change. The results are analyzed through a k-means clustering algorithm to identify patterns and segment participants into groups based on their levels of truth, indeterminacy, and falsehood. This approach reveals deeper …

Upside-Down Logics: Falsification Of The Truth And Truthification Of The False, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

This paper is about funny science, recreational mathematics, upside-down thinking, or contradictory reasoning (to think backward). Since a statement in some conditions may be true, in other conditions false, and a third type of conditions partially true and partially false. The paper presents for the first time two types of Upside-Down Logic, the first one is falsification of the Truth (when a true statement is transformed into a false one), and the second one is the opposite: Truthification of the False (when a false statement is transformed into a true one) - within the frame of Recreational Neutrosophy. All transformations …

The Dynamic Interplay Of Opposites In Zoroastrianism, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

This exploration addresses some aspects of Zoroastrianism, examining how the ancient Persian belief system aligns with the dynamic and indeterminate principles of Fuzzy, Neutrosophic, and MultiAlist systems. Zoroastrianism, rooted in the eternal struggle between good and evil, light and darkness, exhibits parallels with Neutrosophy's acknowledgment of indeterminacy, incompleteness, and the dynamic interplay of opposites. The prophet Zarathustra's vision of a neutrosophic God challenges conventional notions of divine attributes, emphasizing a dynamic and evolving universe. Before investigating these vague areas, the concept of unclear conceptual borders is explored, emphasizing the indeterminacy and imprecision inherent in defining opposites or partially opposite concepts. …

Ncmpy: A Modelling Software For Neutrosophic Cognitive Maps Based On Python Package, Ilanthenral Kandasamy, Divakar Arumugam, Aryan Rathore, Ateeth Arun, Manan Jain, Vasantha .W.B, Florentin Smarandache

Neutrosophic Systems with Applications

Cognitive maps are a vital tool that can be used for knowledge representation and reasoning. Fuzzy Cognitive Maps (FCMs) are popular soft computing techniques used to model large and complex systems, and they can aid in explainable artificial intelligence (AI). FCMs, however, cannot model the indeterminacy that arises in a system due to various uncertainties. Neutrosophic Cognitive Maps (NCMs), upgraded FCMs that could model indeterminacy, were introduced to address this issue. NCMs are a generalization of FCMs, a field of cognitive science firmly based on neural networks. NCMs have been used to solve a wide range of problems. NCMs were …

An Overview Of Plithogenic Set And Symbolic Plithogenic Algebraic Structures, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

This paper is devoted to Plithogeny, Plithogenic Set, and its extensions. These concepts are branches of uncertainty and indeterminacy instruments of practical and theoretical interest. Starting with some examples, we proceed towards general structures. Then we present definitions and applications of the principal concepts derived from plithogeny, and relate them to complex problems.

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.