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Neutrosophic Sets And Systems, Vol. 98, 2026, Florentin Smarandache, Muhammad Abdel-Baset, Maikel Leyva-Vázquez

Neutrosophic Sets and Systems

This edition of “Neutrosophic Sets and Systems” presents a diverse collection of studies that contribute to the theoretical development and practical application of neutrosophic, fuzzy, hypersoft, and generalized algebraic systems in complex decision-making and information analysis environments. The published works explore innovative mathematical structures, including generalized neutrosophic topological spaces, neutrosophic algebraic systems, hypersoft and dual hesitant frameworks, multi-valued and n-fold algebraic models, and advanced decision-making methodologies designed to address indeterminacy, inconsistency, vagueness, and multidimensional uncertainty. Several contributions introduce new classes of neutrosophic closed sets, contra continuous mappings, and generalized algebraic operators, extending existing theories in topology, algebra, and set theory. …

Horizontal And Vertical Generalized N-Fold Algebra: Formal Construction And Applications In Multi-Dimensional Modeling, Florentin Smarandache

Neutrosophic Sets and Systems

This paper extends the recently developed framework of Neutrosophic Logic-based Two-Fold Algebra (TFA), which was designed to integrate classical algebraic operations with fuzzy and neutrosophic components for modeling uncertainty alongside deterministic structures. Although TFA successfully combines algebraic operations with uncertainty descriptors, its binary structure becomes restrictive in applications requiring the simultaneous integration of multiple independent qualification dimensions, such as risk, sustainability, reliability, and performance assessment. To address this limitation, the paper introduces two generalized frameworks: Horizontal n-Fold Algebra and Vertical n-Fold Algebra, together forming the generalized n-Fold Algebra (n-FA), together with the extension from two-valued to multi-valued operations where m≥2. …

Sustainable Framework For Performance-Based Learning Assessment Under Uncertainty: Computational Modeling, Mona Gharib, Muhammad Imran, Zaka Ur Rehman

Sustainable Machine Intelligence Journal

Evaluating performance-based learning, such as dance or performing arts education, poses significant computational challenges due to uncertainty, subjectivity, and heterogeneous evaluation data. Conventional scoring models fail to capture the coexistence of quantitative indicators (timing, attendance) and qualitative judgments (artistry, expressiveness).

This study introduces a computational neutrosophic functional framework that models ambiguity using set-valued, indeterminate representations within a rigorous analytic structure. We construct a neutrosophic function space CN(X) and a Hilbert C*-module HN for integrating evaluator signals through algebraic fusion. A strongly continuous neutrosophic operator semigroup (T(t)) is developed to model temporal …

A Neutrosophic Random Forest Framework For Uncertainty-Aware Classification Of Nursery School Applications, Franklin Parrales-Bravo, Roberto Tolozano-Benites, Manuel Reyes-Wagnio, Dayron Rumbaut-Rangel, Leonel Vasquez-Cevallos

Neutrosophic Sets and Systems

This paper presents a novel framework that integrates Random Forest classification with neutrosophic logic to address the challenge of uncertainty-aware decision-making in nursery school application processes. Using the publicly available Nursery dataset—which includes socio-familial attributes such as parental occupation, financial standing, and health conditions—the proposed model not only achieves high predictive accuracy (approximately 95%) but also quantifies uncertainty explicitly through neutrosophic sets defined by truth (T), indeterminacy (I), and falsity (F) membership degrees. This approach allows for a nuanced interpretation of classification confidence, distinguishing between clear-cut cases that can be automated and borderline instances requiring human expert review. By enabling …

Multineutrosophic Analysis With The Aras Method For Selecting Trading Strategies, Alberto Sánchez Pena, Yunisleydis García Ramírez, Irina Reyes Martinez, Tatiana Velázquez Ramírez, Lisbet Eunice Pérez Anzardo

Neutrosophic Sets and Systems

Deciding on optimal business solutions is a perennial problem for firms challenged by ever-changing market environments. Currently, the choice of a solution entails multidimensional requirements in addition to similar uncertainties and vagueness factoring human fallibility and ever-challenging market conditions. Even though thousands of systems for decision-making support exist, the dedicated scholarly literature does not support any advancement that would ease an all-encompassing evaluation of strategic solutions during complete uncertainty or information vagueness. Therefore, this research aims to fill this theoretical gap by creating a new approach based on practical application. This new approach is based on the employment of the …

Analysis Of The Evolution Of Expert Opinion On Sustainability Policies Through The Neutrosophic Statis Method, Purificación Vicente Galindo

Neutrosophic Sets and Systems

Yet the problem of evaluating sustainability policies over time stems from needing to monitor the changing nature of expert agreement needed for dependency-based improvements in the environment. While this is undoubtedly helpful for relatively sustainable action, easier said than done requires methodological systems to assess how agreement grows and solidifies. Here it should be noted that the conventional STATIS approach, while successful in multivariate assessment, lacks the capacity to evaluate expert assessments factoring uncertainty, indeterminacy, and subjectivity. Therefore, this research goes on to fill this void with the neutrosophic STATIS method applied to a panel of experts assessing ten (10) …

Study Of The Transformation Of Ecuador's Productive Structure, Technology, And Gdp In Recent Years Using The Iadov Plithogenic Method, Pedro Gustavo Correa Mendoza, Albert Joao Nieto Pacheco, Shakila Devi G T, Darvin Manuel Ramírez Guerra

Neutrosophic Sets and Systems

This study investigates the transformation of Ecuador's productive structure, technological integration, and its impact on GDP over the last decade, using the novel Plithogenic IADOV method. This approach, based on neu-trosophic logic, allows for the analysis of complex economic scenarios characterized by indeterminacy and con-tradiction, aspects often overlooked by traditional methods. Through questionnaires administered to 40 experts, the research evaluates five key dimensions: economic diversification, technological integration, GDP growth, public policy formulation, and economic resilience. Findings reveal progress in diversification and technological integration, albeit limited, with a persistent strong reliance on primary sectors and technological gaps, especial-ly for SMEs. While …

Multineutrosophic Analysis Of The Impact Of The Circular Economy On The Regional Supply Chain., Ana María Correa Vaca, Fidel Márquez-Sánchez, Oscar José Alejo Machado, Cesar Pozo-Estupiñán, Orlando Arencibia-Montero

Neutrosophic Sets and Systems

This research was conducted to evaluate the influence of the circular economy on the sustainability of supply chains at the regional level through multineutrosophic theory for uncertainty in decision-making. Empirical analysis was performed through a quantitative and qualitative assessment, includ-ing a questionnaire completed by 50 regional companies, mathematical calculations based on neutro-sophic theory, and a multineutrosophic assessment of the diverse input/output resource flows for sup-ply chains associated with manufacturing and agricultural endeavors. The major results indicate that by incorporating aspects of the circular economy, recyclability/reusability of resources was 20% more ef-fective and 15% less expensive to operate, while 30% of …

Neutrosophic Assessment Of Legal Certainty In The Digital Transformation Of Logistics In Callao: A Comparative Study Based On Svnn And The Neutrosophic Analytic Hierarchy Process (Ahp)., Edwin Collazos Paucar, Jorge Luis Mera Ramírez, Rilke Chong Vela, Jorge Luis Arrué Flores, Víctor Linares Pezo, José Regulo Ramírez Águila, Víctor Raúl Reategui Paredes

Neutrosophic Sets and Systems

The digitalization of the logistics sector in Callao challenges the notion of legal certainty. The implementation of new technologies such as electronic signatures and smart contracts generates uncertainty, exposing individuals and legal entities to greater risks if adequate legal protection is not in place. Although prior research on regulatory compliance exists, little has been done to certify legality over time and in the present. To address legal ambiguity and contradictions, this study proposes a neutrosophic approach. A model is constructed by applying the logic of Single Valued Neutrosophic Numbers (SVNN) and weighting through the Neutrosophic Analytic Hierarchy Process (AHP). By …

A Neutrosophic Multi-Objective Optimization Framework For Sustainable Design Of Water Supply Systems, Jesús Rafael Hechavarría Hernández, Maikel Yelandi Leyva Vázquez

Neutrosophic Sets and Systems

The study addresses the challenge of optimizing water supply systems (WSS) under conditions of uncertainty, variability, and multiple. In a context where sustainability is a key criterion, traditional Multiobjective optimization approaches are often insufficient to handle the imprecision and indeterminacy inherent in data and models. This work proposes a Neutrosophic Multi-Objective Model (NMM) that integrates Neutrosophic Logic to capture uncertainty in decision variables, objective functions, and constraints. Unlike conventional methods, NMM allows considering degrees of truth, indeterminacy, and falsity, offering a more robust and flexible framework for decision-making in WSS. The relevance of this study lies in its ability to …

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 Comparative Analysis Of Data-Driven And Model-Based Neutrosophication Methods: Advancing True Neutrosophic Logic In Medical Data Transformation, Maikel Yelandi Leyva Vázquez, Lorenzo Cevallos-Torres, Omar Mar Cornelio, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

Neutrosophic logic extends fuzzy logic by explicitly modeling indeterminacy (I), offering a robust framework for uncertainty representation. The transformation of crisp data into neutrosophic triplets {T, I, F}—known as neutrosophication—is crucial for applying neutrosophic models in real-world analysis. However, comparative evaluations of existing neutrosophication methods remain limited. This study presents a systematic comparison of five approaches: three model-based methods (Parabolic, Threshold Distance, Fuzzy Membership), one density-based method (Kernel Density Estimation), and a proposed data-driven K-Means clustering method integrating sigmoid membership functions. Using a medical dataset of 299 patients and six continuous clinical variables, we assessed statistical behavior, consistency, and alignment …

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 …

Artificial Intelligence, Society 5.0 And Smart City Adaptation Initiatives For Businesses: An Integrated Approach, Inês A.M. Gil, Fernando A.F. Ferreira, Neuza C.M.Q.F. Ferreira, Florentin Smarandache, Momtaj Khanam, Tugrul Daim

Branch Mathematics and Statistics Faculty and Staff Publications

The unprecedented migration of populations to urban areas has created major challenges for municipalities and service providers. To address these issues, decision-makers must embrace smart city and Society 5.0 paradigms, both of which focus on adaptability and sustainable development. Artificial intelligence (AI) plays a pivotal role by expanding service capacity, enabling automation, and processing vast data to align urban development with the UN’s Sustainable Development Goals (SDGs). This paper develops a multi-criteria analysis system designed to support decision-making in complex socio-technological contexts. Using cognitive mapping and the Decision-Making Trial and Evaluation Laboratory (DEMATEL) technique within a neutrosophic environment, the study …

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 Cox Proportional Hazards Model For Robust Variable Selection In Survival Analysis, Ibrahim Yasser, Aya A. Abd El-Khalek, A. A. Salama, Doaa A. Abdo

Neutrosophic Systems with Applications

This paper introduces a novel approach for variable selection in survival analysis by integrating neutrosophic logic into the Cox Proportional Hazards (Cox PH) model to address the limitations of recent studies related to high dimensionality. Neutrosophic logic, is a mathematical framework that allows for uncertainty, indeterminacy, and inconsistency, and particularly well suited for handling the complexity and often-ambiguous nature of biological data. By incorporating neutrosophic sets into the Cox PH model, we aim to enhance model robustness, improve variable selection, and address the curse of dimensionality. We compare the performance of the neutrosophic-enhanced Cox PH model with traditional variable selection …

Neutrosophic Logic-Based Crop Yield Prediction And Risk Assessment Using Least Squares Regression, M. Srikanth, R.N.V. Jagan Mohan, M. Chandra Naik

Neutrosophic Systems with Applications

Agriculture faces significant challenges due to climate change and unpredictable environmental factors, which impact crop yields and threaten food security. This study proposes a novel approach to crop yield prediction and risk assessment using neutrosophic logic and least squares regression. By integrating these methods, we aim to improve accuracy in predicting crop losses under uncertain conditions. The model classifies crops based on profitability and environmental risks, utilizing the independence test to evaluate the relationships between crop attributes. Our approach leverages deep learning techniques, such as restricted Boltzmann machines (RBM), to enhance the analysis of crop data and provide farmers with …

Complex Analysis Of Family And Social Problems In The Context Of Parenting Competencies: Implementation Of Neutrosophic Cognitive Maps (Ncm) For The Evaluation And Resolution Of Conflicts, Yoya B. Flores-Pérez, José M. Vázquez Antonio, Rigoberto Navarrete Flores, Luz H. Cruzado Saucedo

Neutrosophic Sets and Systems

At the intersection of family and social problems, complex challenges arise that demand an innovative and profound ap-proach - This article explores how parental competencies, essential for family dynamics, can be better understood and strengthened through the implementation of Neutrosophic Cognitive Maps (NCM) ̣Using a multidimensional approach, real cases are analyzed where family conflicts and tensions are intertwined with broader social problems, revealing the need for advanced analytical tools that allow a detailed and accurate evaluation ̣NCM emerges as a robust methodology, capable of capturing the ambiguity and uncertainty inherent in human interactions, offering a new perspective for intervention and …

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 …

Software Reliability Model Estimation For An Indeterministic Crime Cluster Through Reinforcement Learning, Dileep Kumar Kadali, R.N.V. Jagan Mohan, M. Chandra Naik

Neutrosophic Systems with Applications

The software reliability model estimates the probability of data failure in a specific environment, significantly impacting reliability and trustworthiness. The paper study focuses on cluster crime data, i.e., indeterministic in Neutrosophic Logic, using a software reliability model. The study utilizes reinforcement learning, Neutrosophic logic, and non-homogeneous Poisson process crime data to estimate indeterministic cluster data in crime. The "Non-homogeneous Poisson Process with Neutrosophic Logic" technique performs well in evaluating and deterring crime based on crime data analysis. The crime cluster involving offenders correctly classified as failure to accomplish does better than uncertain cluster reliability estimation with least squares and logistic …

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. …

Generating Neutrosophic Random Variables Based Gamma Distribution, Maissam Ahmad Jdid, Florentin Smarandache, Khalifa Al Shaqsi

Branch Mathematics and Statistics Faculty and Staff Publications

In practical life, we encounter many systems that cannot be studied directly, either due to their high cost or because some of these systems cannot be studied directly. Therefore, we resort to the simulation method, which depends on applying the study to systems similar to real ones and then projecting these results if they are suitable for the real system. The simulation process requires a good understanding of probability distributions and the methods used to transform random numbers that follow a regular distribution in the field [0,1] into random variables that follow them, so that we can achieve the greatest …

Introduction To Upside-Down Logic: Its Deep Relation To Neutrosophic Logic And Applications, Takaaki Fujita, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

In the study of uncertainty, concepts such as fuzzy sets [113], fuzzy graphs [79], and neutrosophic sets [88] have been extensively investigated. This paper focuses on a novel logical framework known as Upside-Down Logic, which systematically transforms truths into falsehoods and vice versa by altering contexts, meanings, or perspectives. The concept was first introduced by F. Smarandache in [99]. To contribute to the growing interest in this area, this paper presents a mathematical definition of Upside-Down Logic, supported by illustrative examples, including applications related to the Japanese language. Additionally, it introduces and explores Contextual Upside-Down Logic, an advanced extension that …

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 …

A Refined Neutrosophic Components Into Subcomponents With Plausible Applications To Long Term Energy Planning Predominated By Renewable Energy, Victor Christianto, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

It is known that in the long-term planning of future energy supplies, in most countries, it is most likely that the energy mix will be predominated by renewable energy generation. While this feature of a predominating renewable energy mix appears too far fetched, such long term planning has been suggested, for instance, by Mark Jacobson from Stanford and also by John Blackburn. Here we consider two things, the first would be how to consider the long-term energy planning based on neutrosophic logic split into subcomponents.

An Exhaustive Review Of Neutrosophic Logic In Addressing Image Processing Issues, Samia Mandour

Neutrosophic Systems with Applications

Since the importance of images in our lives and the advancements in computer data gathering methods, anyone can collect a large number of images, but most of them cannot be processed manually. Image processing therefore becomes appealing since various types of data may be represented and processed digitally. Image processing has become the most popular processing method, employed in security camera films, healthcare images, images from remote sensors, and naturalistic image/videos because of fast computers and processors. In order to raise cognitive function and speed up decision-making, image processing is crucial to many information access systems. Since ambiguity now permeates …

Graphical Method For Solving Neutrosophical Nonlinear Programming Models, Maissam Jdid, Florentin Smarandache

Neutrosophic Systems with Applications

An important method for finding the optimal solution for linear and nonlinear models is the graphical method, which is used if the linear or nonlinear mathematical model contains one, two, or three variables. The models that contain only two variables are among the most models for which the optimal solution has been obtained graphically, whether these models are linear or non-linear in references and research that are concerned with the science of operations research, when the data of the issue under study is classical data. In this research, we will present a study through, which we present the graphical method …

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.

Nidus Idearum. Scilogs, Xi: In-Turns And Out-Turns, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

In this eleventh book of scilogs – called in-turns and out-turns –, one may find new and old questions and solutions, referring mostly to topics on Neutrosophy, but also Multispace, with miscellaneous addition of topics on Physics, Mathematics, or Sociology – email messages to research colleagues, or replies, notes about authors, articles, or books, spontaneous ideas, and so on.

Graphical Method For Solving Neutrosophical Nonlinear Programming Models, Florentin Smarandache, Maissam Ahmad Jdid

Branch Mathematics and Statistics Faculty and Staff Publications

An important method for finding the optimal solution for linear and nonlinear models is the graphical method, which is used if the linear or nonlinear mathematical model contains one, two, or three variables. The models that contain only two variables are among the most models for which the optimal solution has been obtained graphically, whether these models are linear or non-linear in references and research that are concerned with the science of operations research, when the data of the issue under study is classical data. In this research, we will present a study through, which we present the graphical method …