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Double-Valued Complex Neutrosophic Graphs, Suriyakumar G, V. J. Sudhakar, Takaaki Fujita

Neutrosophic Systems with Applications

This paper introduces a novel graph-theoretic framework, called the double-valued complex neutrosophic graph, as an extension of double-valued neutrosophic set theory. Within this framework, we investigate several important classes of such graphs, including self-complementary, strong, and full double-valued complex neutrosophic graphs, and establish a number of their fundamental properties. To clarify the proposed concepts and demonstrate their structural behavior, several relevant illustrative examples are also provided.

A Hybrid Multi-Criteria Decision-Making Approach For Sustainable Forest Fire Monitoring Using Unmanned Aerial Vehicles, Mohamed Eassa, Ahmed Abdelhafeez, Ahmad M. Nagm

Neutrosophic Systems with Applications

Unmanned aerial vehicles (UAVs) have become an effective tool for forest fire monitoring. This study evaluates UAVs for forest fire management, addressing the challenges posed by ambiguous and uncertain factors. Single-valued neutrosophic sets (SVNSs) are employed to model complex uncertainties, as they incorporate three distinct membership values: false, true, and indeterminate. The evaluation of UAVs is a multifaceted task due to the variety of factors involved. To address this complexity, multi-criteria decision-making (MCDM) methods are used. Specifically, the Analytic Hierarchy Process (AHP) and the Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS) are integrated with SVNS to …

N-Dqn: Neutrosophic Deep Q-Network For Uncertainty-Aware Forecasting And Decision Optimization, Rania Lutfi

Neutrosophic Systems with Applications

Uncertainty remains a critical challenge in dynamic spatiotemporal forecasting. This study proposes the Neutrosophic Deep Q-Network (N-DQN), a framework that integrates neutrosophic logic with deep reinforcement learning to enhance decision optimization under uncertainty. Features are modeled through truth, indeterminacy, and falsity membership functions, enabling robust handling of ambiguous data. The framework incorporates attention-guided preprocessing and horizon-aware optimization to adapt predictions across short- and long-term intervals. Experiments on benchmark traffic datasets (METR-LA and PEMS-BAY) demonstrate improved forecasting accuracy and reduced error rates compared with established baselines. The results highlight the scalability and resilience of N-DQN, positioning it as a promising approach …

Single-Valued, Double-Valued, Triple-Valued, Quadruple-Valued, And Quintuple-Valued Neutrosophic Graph, Takaaki Fujita, Arif Mehmood, Arkan A. Ghaib

Neutrosophic Systems with Applications

Concepts such as fuzzy sets, neutrosophic sets, rough sets, and plithogenic sets have been extensively studied as formal tools for modeling uncertainty, and they have found broad applications across many disciplines. A Double-Valued Neutrosophic Set (DVNS) extends the classical neutrosophic framework by splitting indeterminacy into two distinct components: one leaning toward truth and the other leaning toward falsity. In recent years, further refinements—namely Triple-Valued, Quadruple-Valued, and Quintuple-Valued Neutrosophic Sets—have also been introduced and investigated. These uncertainty models have naturally been lifted to graph-theoretic settings, where vertices and edges represent entities and relationships under ambiguity. Although fuzzy graphs and neutrosophic graphs …

Evaluating Domains' Trustworthiness Based On Uncertainty-Driven Methodologies In The Era Of Sixth Generation, Zekra Sakr, Mona Mohamed

Neutrosophic Systems with Applications

The onset of today's innovations pledges to have a beneficial influence on contemporary civilization in an era of intelligent revolutions, setting a precedent for unrivaled efficiency, creativity, and connectedness. The integration between these technologies contributes to the mutual benefit of each one, wherein this relation is a so-called ``reciprocal partnership''. For instance, the sixth generation (6G) wireless networks permit blockchain nodes to coordinate huge volumes of transaction data in real-time. On the other hand, blockchain is considered a secure valve because spectrum sharing can be automated with blockchain and smart contracts. Accordingly, analyzing and evaluating the contribution of these technologies …

Neutrosophic Finsler–Cohomological Framework For Engineering Systems Under Uncertainty, Mona Gharib, Ghulam Muhammad, Muhammad Idrees, Zeeshan Gul

Neutrosophic Systems with Applications

This paper introduces a novel mathematical framework that combines Neutrosophic Finsler Geometry with Neutrosophic Cohomology for evaluating the performance of Brushless Direct Current (BLDC) motors under uncertain and indeterminate operating conditions. Classical motor performance models typically assume precise measurements of torque, current, and efficiency; however, in real-world settings, these parameters are often affected by noise, incomplete information, and conflicting observations. By embedding motor operating states into a neutrosophic Finsler space, the proposed approach captures variations not only in magnitude but also in direction, uncertainty, and conflict of performance metrics. In addition, neutrosophic Cohomology is employed to characterize global invariants of …

An Uncertainty-Aware Entropy-Oreste Framework For Big Data Platform Selection In Complex Multi-Sector Environments, Ahmed M. Ali, Ibrahim Alrashdi, Karam M. Sallam

Neutrosophic Systems with Applications

The increasing reliance on Big Data platforms across various industries has necessitated the development of systematic decision-support frameworks to guide their evaluation and selection. Given the diversity of available platforms, each offering different capabilities, scalability, and computational efficiency, choosing the optimal solution remains a complex challenge. This research proposes a novel analytical framework that integrates Spherical Fuzzy Sets (SFS) with the Entropy and ORESTE methods to address uncertainty and enhance the accuracy and robustness of Big Data platform evaluation. This hybrid integration, not previously applied to Big Data platform selection, enables objective criteria weighting through the Entropy method and comprehensive …

Single-Valued Neutrosophic Pessimistic Multi-Granulation Rough Set Model Based On (A,B,C)-Cut Relations And Its Applications, Xu-Xi Wu, Hu Zhao, Qiao-Ling Song, Xiong-Wei Zhang

Neutrosophic Systems with Applications

To address uncertainty in multi-source data, this paper proposes a single-valued neutrosophic pessimistic multi-granulation rough set (P-SVN-MGRS) model based on (a,b,c)-cut relations. In this framework, each neutrosophic relation is characterized by three membership-degree functions: T(x,y), I(x,y), and F(x,y). These functions correspond to truth-membership, indeterminacy, and falsity, respectively. The (α,β,γ)-cut relation employs parameters α,β,γ∈(0,1] as thresholds for the three functions. A pair (x,y) belongs to …

Pythagorean Neutrosophic Mathematical Modelling, M. Kavitha, R. Irene Hepzibah

Neutrosophic Systems with Applications

Survey-based assessments often suffer from ambiguity, inconsistency, and uncertainty, which weaken the reliability of decision-making outcomes. To address these challenges, this study proposes a novel decision-support framework for data fuzzification, ranking, and agility measurement using Pythagorean Neutrosophic Fuzzy Sets (PNFS). The proposed method offers three major advantages: (i) enhanced ability to capture high levels of indeterminacy compared with classical fuzzy and intuitionistic models, (ii) improved ranking accuracy through a newly developed score function and ranking algorithm, and (iii) greater robustness in scenarios involving conflicting, incomplete, or imprecise expert judgments. The framework includes a refined Pythagorean Neutrosophic fuzzification technique, mathematically supported …

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 Study Of Regular And Irregular Complex Neutrosophic Vague Graphs, Suriyakumar G, V. J. Sudhakar

Neutrosophic Systems with Applications

In this paper, We define the regular complex neutrosophic vague graph and the irregular complex neutrosophic vague graph for this purpose. We specify a node’s degree and total degree in a normal complex neutrosophic vague graph. A few features and theorems of those regular and irregular complex neutrosophic vague graphs are presented. This article defines busy and free nodes in a normal complex neutrosophic vague graph. Also, we describe a regular and irregular complex neutrosophic vague graph with a cycle as the underlying crisp graph.

From Uncertainty To Lucidity: Awareness Neutrosophic Kähler-Einstein Innovative Evaluator Methodological In Era Of Green Artificial Intelligence, Mona Mohamed, Ahmed M. Ali

Neutrosophic Systems with Applications

The rapid development of generative artificial intelligence (Gen AI) is a double-edged sword. On the positive side, Large Language Models (LLMs) of Gen AI as chatbot considered intelligent friend. Due to its potential to stimulate the maturation of ideas and cultivate fundamental general abilities like problem-solving and critical thinking. The advancement of Gen AI continued after that, moving from “chatbots” to “AI agents” that carry out multi-step activities in addition to responding to queries.

Regarding the downside, the terminology of “Red AI” era brought about by generative AI is marked by a performance at any expense that puts pressure on …

An Intuitionistic Fuzzy Hypergraph Model Enhanced ‎By Forest-Of-Walks Dynamics For Medical Image ‎Segmentation, Brinthaguru Thangaraj, Karthick Palanisamy

Mansoura Engineering Journal

The process of accurately segmenting Urolithiasis and pulmonary nodules from medical images presents significant difficulties because of three main factors which include nonuniform intensity distribution and the presence of weak object borders and the uncertainty caused by anatomical structure overlaps. The study introduces F-Zinhger as a solution to these problems through its application of the Forest of Walks technology. The method uses superpixels as fundamental elements which form a multi-scale hypergraph that establishes hyperedges through three criteria: intensity similarity, spatial proximity, and Z-intuitionistic fuzzy hesitation to capture complex contextual connections. The system incorporates a random walk-based label propagation system. The …

Underwater Image Identification Using Fuzzy Soft Planar Graph, Bhuvaneswari Natarajan Jayakar, Karthick Palanisamy

Mansoura Engineering Journal

High-attribute underwater image segmentation is fundamental to autonomous marine exploration, biodiversity monitoring, and subsea infrastructure inspection. However, underwater environments are inherently stochastic, exhibiting severe light attenuation, chromatic distortion, scattering effects, and noise, all of which significantly degrade image quality and challenge conventional computer vision techniques. Hence, Fuzzy logic which handles uncertainty and imprecision in data and Soft sets which manage parameterized information, are widely applied to underwater image analysis. Fuzzy Soft Planar Graphs (FSPGs) constitute a mathematical framework that integrates fuzzy set theory, soft set theory and planar graph structures for preserving spatial topology. The proposed methodology adopts a hybrid …

Green Ai-Enhanced Deep Learning Model For Breast Cancer Detection And Classification In Mammography Images: Bc-Net-512, Nesma Abd El-Mawla, Mohamed A. Berbar, Nawal A. El-Fishawy, Mohamed A. El-Rashidy

Mansoura Engineering Journal

This study champions a sustainable approach for developing a Deep Learning (DL) model for medical image analysis, specifically focusing on breast cancer (BC) detection in mammograms. By prioritizing low-computing algorithms to achieve high diagnostic accuracy while minimizing the model's environmental footprint, that aligns with the principles of Green AI. In this paper, an innovative architecture called BC-Net-512 was constructed for the classification of BC mammography. It is composed of lightweight Convolutional Neural Network (CNN) blocks for texture, density, and structure feature extraction and detection, a thin, fully connected layer for learning complex patterns and correlations in the extracted features, and …

Advancements In Perfect Matchings Within Neutrosophic Fuzzy Graphs: Theory And Applications, Muhammad Saeed, Fatima Razaq

Neutrosophic Systems with Applications

Graph theory has been widely used in exemplifying relational structure, and a greater generalization to fuzzy and neutrosophic space enables the exemplification of uncertainty, indeterminacy, and inconsistency in complex systems. Some of these extensions include the neutrosophic fuzzy graphs that provide a more detailed description of the loose relations between the vertices and the edges. However, unlike in classical graph theory, where the concepts of matching and perfect matching are well developed, very little has been studied on how the two concepts can be extended to neutrosophic fuzzy graphs. To seal this gap, the current paper develops and defines the …

Integrating Mcdm Techniques For Optimized Task Offloading In Multi-Uav- Enaled Mobile Edge Computing System, Amira Salam

Neutrosophic Systems with Applications

Carefully choosing a task offloading strategy is crucial for optimizing task scheduling and offloading strategies in a multi-UAV system. Regarding cost, responsiveness, scalability, and data security, each strategy has pros and cons. As a result, selecting the best offloading technique is essential to multi-UAV mobile edge computing task scheduling optimization. A methodical and well-informed decision-making process accomplishes this.

The current study introduces a new hybrid methodology for the multi-criteria decision-making (MCDM) model, known as IVNs-DEMATEL-ANP-VIKOR. The purpose of this model is to find and choose an efficient task offloading strategy. With this method, we use IVNs-DEMATEL to show how different …

Mixed Linear Equation–Inequality Systems Over The Pura Vida Neutrosophic Algebra, Muhammad Rayyanu Abdullahi, Abdulhadi Aminu

Neutrosophic Systems with Applications

This paper proposes a neutrosophic extension of max-plus algebra for solving mixed systems of linear equations and inequalities.Classical max-plus algebra is a powerful tool for modeling synchronization in discrete-event systems LastNatpreClose LastNatClose, but it assumes fully deterministic data.To incorporate uncertainty and indeterminacy, we reformulate the framework so that coefficients and variables are expressed as neutrosophic numbers

γ+λI,γ,λ∈ℝ,I∈[0,1],

where I quantifies the degree of indeterminacy.

We redefine the max-plus semiring in this neutrosophic setting, extend solvability and uniqueness results, and adapt the ONEMLP-EI algorithm LastNatpreClose LastNatClose to handle neutrosophic …

Mapping Sustainability To Cybernetic-Generative Artificial Intelligence-Based Education: An Innovative Neutrosophic Orbifold-Lattice Methodology, Mona Mohamed, Ahmed A. Metwaly

Neutrosophic Systems with Applications

The lightning-fast development of artificial intelligence (AI), notably generative artificial intelligence (Gen AI) technologies, has intrigued multiple disciplines, particularly education. In this context, Large Language Models (LLMs) serve as beneficial cognitive resources that address knowledge deficits and provide tailored educational support for learners and staff. For learners, LLMs are regarded as knowledgeable educators who offer prompt, focused responses and rationales to tricky queries. Whereby LLMs for staff, Strength enhancer, automating tedious tasks, and creating intelligent resources.Gen AI’s rapid growth offers enormous obstacles for educational systems, compelling them to discover solutions for these obstacles.

Conceptually, cybernetics is leveraged for bridging the …

Neutrosophic Σ - Baire Spaces, R. Vijayalakshmi, F. Josephine Daisy, M. Simaringa

Neutrosophic Systems with Applications

A Neutrosophic Baire Space extends the concept of Baire Space from classical topology to the realm of neutrosophic topology which deals with sets and spaces where truth, falsehood and indeterminancy are explicitly considered. In this paper the concept of neutrosophic σ - baire spaces are introduced in Neutrosophic topological spaces. Also Neutrosophic σ - dense, Neutrosophic σ - nowhere dense, Neutrosophic σ -first category and Neutrosophic σ - second category sets are defined. Several characterizations of neutrosophic σ - baire spaces are investigated and explained using examples and the conditions under which a neutrosophic topological space becomes a neutrosophic σ …

A Comprehensive Review Of Dental Diseases Detection And Classification Based On Artificial Intelligence Techniques, Nermeen N. Noaman, Yasmin M. Alsakar, Naira E. Elazab, Waleed M. Mohamed, Mohamed E. Ezzat, Mohammed M. Elmogy

Mansoura Engineering Journal

In dentistry, many diseases, such as gum, cavities, and oral cancer, affect people of all ages. Early treatment and diagnosis are crucial for minimizing dental diseases' effect on overall health and saving money in the long run. Traditional dental diagnosis methods, such as manual probing and visual inspection, are time-consuming and can be subject to human errors. Hence, a computer-aided diagnosis system based on computer vision and artificial intelligence (AI) techniques is needed. The considerable progress in computer vision and AI techniques offers many possibilities in dental diagnosis based on dental X-ray imaging modalities. Dental X-rays are used to diagnose …

Optimizing Military Fighter Jet Selection: A Decision Analysis Approach For Nuclear-Capable Aircraft, Eni Kelechi Ofong

Theses and Dissertations

This research investigates the strategic decision-making process involved in selecting a nuclear-capable fighter aircraft for NATO (North Atlantic Treaty Organization) nations in Europe. In adaptation to the continuously changing technology landscape and the necessity for enhanced deterrence capabilities, this study evaluates three potential aircraft: the legacy Panavia Tornado (PA-200), the widely deployed F-16 Fighting Falcon (F-16), and the advanced F-35 Lightning II (F-35). Each platform presents distinct advantages and limitations regarding operational performance, mission adaptability, cost-effectiveness, and long-term sustainability. To systematically assess these alternatives, the study employs various decision analysis frameworks, including Multi-Criteria Decision Analysis (MCDA), single dimensional value function …

Neutrosophic Graded Jordan–Bialgebra Framework For Ai-Driven Analysis, Mona Gharib, Rana Muhammad Zulqarnain, Xiao Long Xin, Muhammad Gulistan, Muhammad Abid

Neutrosophic Systems with Applications

Modern Artificial Intelligence (AI) systems face significant challenges in processing and analyzing datasets characterized by high degrees of uncertainty, ambiguity, and indeterminacy, which are prevalent features in complex real-world scenarios. To address this limitation, this study introduces a novel neutrosophic graded Jordan–bialgebra framework. This framework strategically integrates the inherent structural properties of Jordan–Bialgebras with the advanced capability of Neutrosophic Graded Structures to simultaneously model degrees of truth, indeterminacy, and falsehood. The primary objective of this study is to establish a rigorous algebraic foundation that enables AI models to perform a more robust and comprehensive analysis of data containing incomplete or …

Comprehensive Risk Evaluation Framework For Reducing Errors In Critical Airport Systems, Arshad Hameed, Muhammad Umer Farooq

Neutrosophic Systems with Applications

Airports are intricate systems that are subject to a number of operational hazards that might impair safety and cause service interruptions. There is a dearth of thorough approaches designed specifically for airport operations, despite a wealth of research on risk management in several industries. In order to anticipate and prevent breakdowns in vital airport systems, we offer a thorough risk assessment approach that combines quantitative evaluation and human factor analysis. This study uses the decision-making methodology such as MARCOS method to rank the alternatives. The criteria weights are computed in this study. This study uses six criteria and 14 alternatives.

Evaluating Solar Energy Challenges And Strategies To Overcome Challenges Under Neutrosophic Decision Making Methodology, Ahmed A El-Douh, Mina Samir Shenouda

Neutrosophic Systems with Applications

Because of its reliance on fossil fuels and fast population expansion, the nation confronts severe socioeconomic problems that can result in political instability, environmental damage, health issues, and economic instability. A switch to clean energy is now necessary as a result of these problems widening the gap between supply and demand for energy. To close this gap, photovoltaic (PV) technology holds great potential. In order to reduce bias and handle ambiguity while assessing solar energy (SE) issues and regulations, this study offers a decision-making process in a single valued neutrosophic set (SVNS) environment. The neutrosophic set is used to overcome …

Integrated Neutrosophic Set For Assessing The Route Options In Overweight Complex Transportation Planning Scenarios, Muhammad Abid, Tayyaba Akhtar, Harshit Bhatt

Neutrosophic Systems with Applications

Due to improvements in lifting and transportation technology that enable the long-distance movement of heavy loads, overweight and oversized transport (O&OT) has emerged as one of the most important aspects of project logistics. This kind of transportation operation, also known as abnormal transportation, is heavily influenced by external variables like weather, traffic density, and legal regulations, as well as technical factors like the load’s weight and geometry, road surface, axle load limitations, slope, and ground strength. Decision-Makers (DMs) and practitioners who plan and carry out operations without giving these variables and factors enough thought may cause operational delays, significant hazards, …

Evaluation Of Integrating Smart Technologies Into Business Ecosystems Using Neutrosophic Uncertainty Model, Kainat Muniba, Muhammad Naveed Jafar, Adil Ahmad, Aruna Pavate

Neutrosophic Systems with Applications

This study proposes a methodological framework for Evaluation of Integrating Smart Technologies into Business Ecosystems. We use the decision-making process to deal with different criteria and alternatives. The decision-making process is used under the neutrosophic set to overcome uncertainty information. Neutrosophic set has three membership functions such as truth, indeterminacy, and falsity. These functions are used to overcome vague information. The average method is used to compute the criteria weights. The COBRA method is used to rank the alternatives based on different alternatives. This study uses 8 criteria and 15 alternatives to be evaluated to show the best option.

Neutrosophic Set Model For Effective Earthquake Disaster Risk Management: Results And Discussion, Emadaldeen Hassan Alomar, Abdullah Ali Salamai

Neutrosophic Systems with Applications

Secondary effects including landslides, tsunamis, and fires can cause significant damage and fatalities following an earthquake. Effective disaster risk management has been predicted to be built on regional fire-following earthquake (FFE) risk. Specifically, a target region’s building and geographical factors might impact the fire danger and spread. The percentage of fire-resistant building types as building characteristics and the distribution of building densities as regional characteristics were the primary factors used in this study to determine FFE risk. This study develops a decision-making methodology for risk management in the FFE. We use the single valued neutrosophic set (SVNS) to overcome uncertainty. …

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 …

Sustainable Assessing Cross-Border Renewable Energy Alliances Using Neutrosophic Numbers With Long-Term Energy Transition Planning, Kamal Alieyan, Amr A. Abd El-Mageed

Neutrosophic Systems with Applications

This paper proposes a decision-making methodology for Sustainable assessing cross-border renewable energy alliances. We used two decision-making methods such as Entropy and MABAC methods. Entropy method is used to compute the criteria weights. The MABAC method is used to rank the alternatives. Two methods are used under the neutrosophic number to solve uncertainty in the decision making. Three stages of the proposed approach are conducted. In the first stage, we compute the criteria weights. In the second stage, we rank the alternatives. In the third stage, we conducted the sensitivity analysis to show the stability of the ranks. The results …