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On Heptagonal Neutrosophic Semi-Open Sets In Heptagonal Neutrosophic Topological Spaces: Testing Proofs By Examples, Subasree R, Basarikodi K May 2024

On Heptagonal Neutrosophic Semi-Open Sets In Heptagonal Neutrosophic Topological Spaces: Testing Proofs By Examples, Subasree R, Basarikodi K

Neutrosophic Systems with Applications

In terms of heptagonal neutrosophic topological spaces, the purpose of this paper is to present the idea of heptagonal neutrosophic semi-open sets. Additionally, we examine a few of its characterizations and heptagonal neutrosophic semi-interior and heptagonal neutrosophic semi-closure operators.


Magdm Model Using Single-Valued Neutrosophic Credibility Matrix Energy And Its Decision-Making Application, Jun Ye, Rui Yong, Wanlu Du May 2024

Magdm Model Using Single-Valued Neutrosophic Credibility Matrix Energy And Its Decision-Making Application, Jun Ye, Rui Yong, Wanlu Du

Neutrosophic Systems with Applications

This paper aims to develop a MAGDM model using single-valued neutrosophic credibility matrix (SVNCM) energy in a SVNCM scenario. To do it, first, SVNCM energy and its score function are presented as a conceptual extension of existing single-valued neutrosophic matrix (SVNM) energy. Then, a MAGDM model is developed in terms of SVNCM energy and its score function in a SVNCM scenario and also its decision algorithm is provided to solve MAGDM problems with SVNCMs. Finally, the developed MAGDM model is applied in the school site selection problem as an actual example, then the comparative investigation of the decision results in …


Bv2trs Appraiser Model: Enforcing Bharat Version2 In Tree Soft Modelling For Appraising E-Mobility Hurdles, Mona Mohamed, Florentin Smarandache, Michael Voskoglou Apr 2024

Bv2trs Appraiser Model: Enforcing Bharat Version2 In Tree Soft Modelling For Appraising E-Mobility Hurdles, Mona Mohamed, Florentin Smarandache, Michael Voskoglou

Neutrosophic Systems with Applications

Electric vehicles (EVs) are being introduced to lessen greenhouse gas (GHG) emissions, air pollution, and reliance on fossil fuels. As a result of the government's aggressive promotion of EVs and rising environmental consciousness, EVs are quickly rising to the top of the low-carbon transportation market. Several viewpoints suggested that shifting to electric vehicles has been seen as a potential way to achieve sustainable mobility. Nevertheless, many studies discussed the obstacles and hurdles that obstruct the embracing of various electric-mobility (E-mobility) as EVs and electric-scooters (E-scooters) as eco-friendly means. Herein, we discussed these hurdles and determined them through surveys for prior …


A Novel Approach On Energy Of Λj-Dominating Single-Valued Neutrosophic Graph Structure, S.N. Suber Bathusha, S. Angelin Kavitha Raj Apr 2024

A Novel Approach On Energy Of Λj-Dominating Single-Valued Neutrosophic Graph Structure, S.N. Suber Bathusha, S. Angelin Kavitha Raj

Neutrosophic Systems with Applications

The concept of dominance is one of the most important ideas in graph theory for handling random events, and it has drawn the interest from many scholars. Research related to graph energy has garnered a lot focus recently. The application of single-valued neutrosophic graphs (SVNGs) for energy, Laplacian energy, and dominating energy has been recommended by previous studies. In this research, we apply the concepts of single-valued neutrosophic sets (SVNS) to graph structures (GSs) and investigate some intriguing features of single-valued neutrosophic graph structures (SVNGS). Moreover, the notions of λJ-dominating energy GS in an SVNGS environment are analyzed in this …


Choosing Optimal Supply Radius Of Transformer Substations (Tss) In Iraq’S Cities Using Geometric Programming With Neutrosophic Coefficients, Ahmed K. Essa, Montifort Blessings Andrew Mitungwi, Tuweh Prince Gadama, Ahmed A. Salama Apr 2024

Choosing Optimal Supply Radius Of Transformer Substations (Tss) In Iraq’S Cities Using Geometric Programming With Neutrosophic Coefficients, Ahmed K. Essa, Montifort Blessings Andrew Mitungwi, Tuweh Prince Gadama, Ahmed A. Salama

Neutrosophic Systems with Applications

Numerous uncertainties exist in various electricity power system problems due to the size, complexity, geographical distribution, and influence of unforeseen events in these systems, making it difficult for traditional mathematics tools based on crisp set theory to have an impact on and solve many power system problems. As a new branch of mathematical uncertainty techniques, the neutrosophic expert systems approach has therefore emerged with the development of electric power systems and has proven successful when correctly linked. The expert typically uses ambiguous or neutrosophic language to describe their empirical knowledge, such as "very likely," "quite likely," "if x is large, …


Choosing Optimal Supply Radius Of Transformer Substations (Tss) In Iraq’S Cities Using Geometric Programming With Neutrosophic Coefficients, Ahmed K. Essa, Montifort Blessings Andrew Mitungwi, Tuweh Prince Gadama, Ahmed A. Salama Apr 2024

Choosing Optimal Supply Radius Of Transformer Substations (Tss) In Iraq’S Cities Using Geometric Programming With Neutrosophic Coefficients, Ahmed K. Essa, Montifort Blessings Andrew Mitungwi, Tuweh Prince Gadama, Ahmed A. Salama

Neutrosophic Systems with Applications

Numerous uncertainties exist in various electricity power system problems due to the size, complexity, geographical distribution, and influence of unforeseen events in these systems, making it difficult for traditional mathematics tools based on crisp set theory to have an impact on and solve many power system problems. As a new branch of mathematical uncertainty techniques, the neutrosophic expert systems approach has therefore emerged with the development of electric power systems and has proven successful when correctly linked. The expert typically uses ambiguous or neutrosophic language to describe their empirical knowledge, such as "very likely," "quite likely," "if x is large, …


Modeling Metaverse Perceptions For Bolstering Traffic Safety Using Novel Trss-Based Owcm-Ram Mcdm Techniques: Purposes And Strategies, Mona Mohamed, Asmaa Elsayed, Marwa Sharawi Apr 2024

Modeling Metaverse Perceptions For Bolstering Traffic Safety Using Novel Trss-Based Owcm-Ram Mcdm Techniques: Purposes And Strategies, Mona Mohamed, Asmaa Elsayed, Marwa Sharawi

Neutrosophic Systems with Applications

The Metaverse has the potential to revolutionize various aspects of human life, including transportation systems. The integration of the Metaverse into intelligent transportation systems has the potential to significantly improve traffic safety in smart cities. By creating a virtual replica of the physical world, the Metaverse can provide a platform for testing new traffic management systems, road designs, and vehicle technologies in a controlled and safe environment before implementing them in the real world. One way to integrate the Metaverse into intelligent transportation systems (ITS) is by enhancing traffic safety. This can be achieved by developing an evaluation model that …


Modeling Metaverse Perceptions For Bolstering Traffic Safety Using Novel Trss-Based Owcm-Ram Mcdm Techniques: Purposes And Strategies, Mona Mohamed, Asmaa Elsayed, Marwa Sharawi Apr 2024

Modeling Metaverse Perceptions For Bolstering Traffic Safety Using Novel Trss-Based Owcm-Ram Mcdm Techniques: Purposes And Strategies, Mona Mohamed, Asmaa Elsayed, Marwa Sharawi

Neutrosophic Systems with Applications

The Metaverse has the potential to revolutionize various aspects of human life, including transportation systems. The integration of the Metaverse into intelligent transportation systems has the potential to significantly improve traffic safety in smart cities. By creating a virtual replica of the physical world, the Metaverse can provide a platform for testing new traffic management systems, road designs, and vehicle technologies in a controlled and safe environment before implementing them in the real world. One way to integrate the Metaverse into intelligent transportation systems (ITS) is by enhancing traffic safety. This can be achieved by developing an evaluation model that …


Ct Image Segmentation Using Optimization Techniques Under Neutrosophic Domain, Doaa El-Shahat, Nourhan Talal, Jun Ye, Wen-Hua Cui Apr 2024

Ct Image Segmentation Using Optimization Techniques Under Neutrosophic Domain, Doaa El-Shahat, Nourhan Talal, Jun Ye, Wen-Hua Cui

Neutrosophic Systems with Applications

In this paper, we introduce a hybrid technique between optimization algorithms and neutrosophic theory. This new hybridization can deal with uncertainties in brain computed tomography (CT) images in three different memberships very effectively. To prove the real-time application of this theory, a new segmentation method for brain CT medical images is presented. The grayscale medical image suffers from uncertainties and inconsistencies in the gray levels due to their bad luminance. The proposed technique addressed this problem by performing neutrosophic operations on gray levels based on the S membership function.


Q-Rung Neutrosophic Sets And Topological Spaces, Michael Gr. Voskoglou, Florentin Smarandache, Mona Mohamed Mar 2024

Q-Rung Neutrosophic Sets And Topological Spaces, Michael Gr. Voskoglou, Florentin Smarandache, Mona Mohamed

Neutrosophic Systems with Applications

The concept of the q-rung orthopair neutrosophic set is introduced in this paper, and fundamental properties of it are studied. Also, the ordinary notion of topological space is extended to the q-rung orthopair neutrosophic environment, as well as the fundamental concepts of convergence, continuity, compactness, and Hausdorff topological space. All these generalizations are illustrated by suitable examples.


Neutrosophic Insights Into Military Interventions: Assessing Legitimacy And Consequences In International Law, Salame Ortiz Mónica Alexandra, Jiménez Martínez Roberto Carlos, Piñas Piñas Luis Fernando Feb 2024

Neutrosophic Insights Into Military Interventions: Assessing Legitimacy And Consequences In International Law, Salame Ortiz Mónica Alexandra, Jiménez Martínez Roberto Carlos, Piñas Piñas Luis Fernando

Neutrosophic Systems with Applications

This scientific paper analyzes the legitimacy of military interventions within the framework of international law and their potential consequences. It highlights the need to support these interventions with robust legal and moral reasoning due to their complexity and controversy in the international community. The interpretation of legal and ethical principles can be subjective and lead to disagreements among states and international actors. The consequences of military interventions are explored, ranging from loss of life and infrastructure destruction to population displacement, political instability, and humanitarian crises. Legality and proportionality in interventions are essential to ensuring their legitimacy, and the potential consequences …


Multi-Agent System For Portfolio Profit Optimization For Future Stock Trading, Usha Devi, Mohan R Feb 2024

Multi-Agent System For Portfolio Profit Optimization For Future Stock Trading, Usha Devi, Mohan R

Karbala International Journal of Modern Science

Stock trading highly contributes to the economic growth of the country. The stock trading objective is to earn profits with buy/sell/hold decisions on the set of stocks in the portfolio. The portfolio optimization problem is finding the decision sequence that leads to higher profit and lower risk. Portfolio optimization is challenging due to complex price history patterns and an uncertain environment. Incorrect decisions in stock trading lead to massive losses. The proposed Multi-Agent System for Portfolio Profit Optimization (MASPPO) aims to optimize trading profit and reduce risk with accurate predictions. The proposed model integrates the Fuzzy c-means with the Deep …


Blood Cell Image Segmentation And Classification: A Systematic Review, Muhammad Shahzad, Farman Ali, Syed Hamad Shirazi, Assad Rasheed, Awais Ahmad, Babar Shah, Daehan Kwak Feb 2024

Blood Cell Image Segmentation And Classification: A Systematic Review, Muhammad Shahzad, Farman Ali, Syed Hamad Shirazi, Assad Rasheed, Awais Ahmad, Babar Shah, Daehan Kwak

All Works

Background Blood diseases such as leukemia, anemia, lymphoma, and thalassemia are hematological disorders that relate to abnormalities in the morphology and concentration of blood elements, specifically white blood cells (WBC) and red blood cells (RBC). Accurate and efficient diagnosis of these conditions significantly depends on the expertise of hematologists and pathologists. To assist the pathologist in the diagnostic process, there has been growing interest in utilizing computer-aided diagnostic (CAD) techniques, particularly those using medical image processing and machine learning algorithms. Previous surveys in this domain have been narrowly focused, often only addressing specific areas like segmentation or classification but lacking …


A Multi-Criteria Decision Making Model For Sustainable And Resilient Supplier Selection And Management, Samah Ibrahim Abdel Aal Jan 2024

A Multi-Criteria Decision Making Model For Sustainable And Resilient Supplier Selection And Management, Samah Ibrahim Abdel Aal

Neutrosophic Systems with Applications

Sustainable and resilient supplier selection and management are essential to building environmentally responsible and resilient supply chains. Selecting sustainable and resilient suppliers enables organizations to ensure the long-term viability of the supply chain. To do that, there is a need to identify suitable suppliers that align with sustainability and resilience goals. This study aims to provide an overview of the requirements and criteria for selecting and managing sustainable and resilient suppliers and emphasizes the significance of integrating sustainability and resilience principles throughout the supply chain. Multi-criteria decision-making (MCDM) is used to deal with various criteria. The double normalization-based multi-aggregation (DNMA) …


Foundation Of Appurtenance And Inclusion Equations For Constructing The Operations Of Neutrosophic Numbers Needed In Neutrosophic Statistics, Florentin Smarandache Jan 2024

Foundation Of Appurtenance And Inclusion Equations For Constructing The Operations Of Neutrosophic Numbers Needed In Neutrosophic Statistics, Florentin Smarandache

Neutrosophic Systems with Applications

We introduce for the first time the appurtenance equation and inclusion equation, which help in understanding the operations with neutrosophic numbers within the frame of neutrosophic statistics. The way of solving them resembles the equations whose coefficients are sets (not single numbers).


Unveiling Efficiency: Investigating Distance Measures In Wastewater Treatment Using Interval-Valued Neutrosophic Fuzzy Soft Set, Muhammad Saeed, Kinza Kareem, Fatima Razzaq, Muhammad Saqlain Jan 2024

Unveiling Efficiency: Investigating Distance Measures In Wastewater Treatment Using Interval-Valued Neutrosophic Fuzzy Soft Set, Muhammad Saeed, Kinza Kareem, Fatima Razzaq, Muhammad Saqlain

Neutrosophic Systems with Applications

To reduce the threats that wastewater poses to human health and the environment, water treatment techniques must be improved. The use of a procedure that includes preparation, testing, primary and secondary treatments, filtration, disinfection, and continuous monitoring is therefore required. The objective of this research is to create a hybrid notion that extends the idea of an interval-valued neutrosophic fuzzy soft set (IVNFSS) to an interval-valued neutrosophic fuzzy set. Operations like complement, union, and integration are included in the idea. To improve decision-making accuracy, a quality-assessment distance measure is incorporated, offering a numerical representation of the disparity between various factors. …


Neutrosophic Statistical Analysis Of Temperatures Of Cities In The Southeastern Anatolia Region Of Turkey, Hacer Şengül Kandemir, Nazlım Deniz Aral, Murat Karakaş, Mikail Et Jan 2024

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.


The Impact Of Individual Techno-Characteristics On Information Privacy Concerns In The Diffusion Of Mobile Contact Tracing, Jiesen Lin, Dapeng Liu, Lemuria Carter Jan 2024

The Impact Of Individual Techno-Characteristics On Information Privacy Concerns In The Diffusion Of Mobile Contact Tracing, Jiesen Lin, Dapeng Liu, Lemuria Carter

KSU Proceedings on Cybersecurity Education, Research and Practice

In the wake of the global health crisis, mobile contact tracing applications have emerged as important tools in managing disease spread. However, their effectiveness heavily relies on mass adoption, significantly influenced by the public's information privacy concerns. To date, systematic examination of how these privacy concerns relate to the innovation adopter categories in mobile contact tracing remains sparse. Furthermore, the influence of individual techno-characteristics on these concerns is to be explored. This research seeks to fill these gaps. Drawing on the diffusion of innovation theory, we examine the impact of the key techno-characteristics—adopter category, propensity for identification misrepresentation, and exposure …


Extended Event Calculus Using Neutrosophic Logic: Method, Implementation, Analysis, Recent Progress And Future Directions, Antonios Paraskevas Jan 2024

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. …


Finding A Basic Feasible Solution For Neutrosophic Linear Programming Models: Case Studies, Analysis, And Improvements, Maissam Jdid, Florentin Smarandache Jan 2024

Finding A Basic Feasible Solution For Neutrosophic Linear Programming Models: Case Studies, Analysis, And Improvements, Maissam Jdid, Florentin Smarandache

Neutrosophic Systems with Applications

Since the inception of operations research, linear programming has received the attention of researchers in this field due to the many areas of its use. The focus was on the methods used to find the optimal solution for linear models. The direct simplex method, with its three basic stages, begins by writing the linear model in standard form and then finding a basic solution that is improved according to the simplex steps until We get the optimal solution, but we encounter many linear models that do not give us a basic solution after we put it in a standard form, …


Fuzzy Inference Full Implication Method Based On Single Valued Neutrosophic T-Representable T-Norm: Purposes, Strategies, And A Proof-Of-Principle Study, Minxia Luo, Ziyang Sun, Donghui Xu, Lixian Wu Jan 2024

Fuzzy Inference Full Implication Method Based On Single Valued Neutrosophic T-Representable T-Norm: Purposes, Strategies, And A Proof-Of-Principle Study, Minxia Luo, Ziyang Sun, Donghui Xu, Lixian Wu

Neutrosophic Systems with Applications

As a generalization of intuitionistic fuzzy sets, single-valued neutrosophic sets have certain advantages in solving indeterminate and inconsistent information. In this paper, we study the fuzzy inference full implication method based on single-valued neutrosophic t-representable t-norm. Firstly, single-valued neutrosophic fuzzy inference triple I principles for fuzzy modus ponens and fuzzy modus tollens are given. Then, single-valued neutrosophic R-type triple I solutions for FMP and FMT are given. Finally, the robustness of the full implication triple I method based on the left-continuous single-valued neutrosophic t-representable t-norm is investigated. As a special case of the main results, the sensitivity of full implication …


Pairing New Approach Of Tree Soft With Mcdm Techniques: Toward Advisory An Outstanding Web Service Provider Based On Qos Levels, Sara Fawaz Al-Baker, Ibrahim El-Henawy, Mona Mohamed Jan 2024

Pairing New Approach Of Tree Soft With Mcdm Techniques: Toward Advisory An Outstanding Web Service Provider Based On Qos Levels, Sara Fawaz Al-Baker, Ibrahim El-Henawy, Mona Mohamed

Neutrosophic Systems with Applications

Web services (WSs) have become dynamic because of technological advancements and internet usage. Hence, selecting a WS provider among a variety of WS providers that perform the same function is a critical process. However, the crucial point is that various consumers may have varied needs when it comes to the quality attributes of services, such as cost, response time, throughput, security, availability, etc. These aspects of Web services are known as quality of service (QoS), or non-functional characteristics. Hence, this issue is the robust motivator for conducting this study. The objective of this study is to evaluate a set of …


The Energy Of Interval-Valued Complex Neutrosophic Graph Structures: Framework, Application And Future Research Directions, S.N. Suber Bathusha, Sowndharya Jayakumar, S. Angelin Kavitha Raj Jan 2024

The Energy Of Interval-Valued Complex Neutrosophic Graph Structures: Framework, Application And Future Research Directions, S.N. Suber Bathusha, Sowndharya Jayakumar, S. Angelin Kavitha Raj

Neutrosophic Systems with Applications

Graph structure is a developing field with many real-world applications and advancements, particularly effective frameworks for integrative problem-solving in computer networks and artificial intelligence systems. To define the idea of an Interval-Valued Complex Neutrosophic Graph Structure (IVCNGS), the concept of an Interval-Valued Complex Neutrosophic Set (IVCNS) is applied to the graph structure. Using the adjacency matrix to calculate the degree of vertex, we have defined some findings about the IVCNGS. Further, we compute the energy and Laplacian energy of IVCNGS. Moreover, we derive the lower and upper bounds for the energy and Laplacian energy of IVCNGS, and we have discussed …


The Energy Of Interval-Valued Complex Neutrosophic Graph Structures: Framework, Application And Future Research Directions, S.N. Suber Bathusha, Sowndharya Jayakumar, S. Angelin Kavitha Raj Jan 2024

The Energy Of Interval-Valued Complex Neutrosophic Graph Structures: Framework, Application And Future Research Directions, S.N. Suber Bathusha, Sowndharya Jayakumar, S. Angelin Kavitha Raj

Neutrosophic Systems with Applications

Graph structure is a developing field with many real-world applications and advancements, particularly effective frameworks for integrative problem-solving in computer networks and artificial intelligence systems. To define the idea of an Interval-Valued Complex Neutrosophic Graph Structure (IVCNGS), the concept of an Interval-Valued Complex Neutrosophic Set (IVCNS) is applied to the graph structure. Using the adjacency matrix to calculate the degree of vertex, we have defined some findings about the IVCNGS. Further, we compute the energy and Laplacian energy of IVCNGS. Moreover, we derive the lower and upper bounds for the energy and Laplacian energy of IVCNGS, and we have discussed …


Evaluating Blockchain Cybersecurity Based On Tree Soft And Opinion Weight Criteria Method Under Uncertainty Climate, Florentin Smarandache, Mona Mohamed, Michael Gr. Voskoglou Jan 2024

Evaluating Blockchain Cybersecurity Based On Tree Soft And Opinion Weight Criteria Method Under Uncertainty Climate, Florentin Smarandache, Mona Mohamed, Michael Gr. Voskoglou

Branch Mathematics and Statistics Faculty and Staff Publications

In the era of digital transformation (DT), many digital technologies have emerged and have had a positive impact on society. Nevertheless, because of certain issues with existing technologies, innovative technology has developed to eradicate them. Fog computing (FC) plays a vital role as an intermediate between edge layer and cloud computing (CC) to resolve limited resources and capabilities. In the same vein, blockchain technology (BCT) is responsible for resolving privacy and security issues that IoT suffers from. Due to using cryptography rules and hashing which is utilized in BCT to prevent any trickery. Hence, BC shows promise as a possible …


Enhancing Security And Performance In Vehicular Adhoc Networks: A Machine Learning Approach To Combat Adversarial Attacks, Mustafa Abdulfattah Habeeb, Yahya Layth Khaleel, Ahmed Raheem Abdulnabi Jan 2024

Enhancing Security And Performance In Vehicular Adhoc Networks: A Machine Learning Approach To Combat Adversarial Attacks, Mustafa Abdulfattah Habeeb, Yahya Layth Khaleel, Ahmed Raheem Abdulnabi

Mesopotamian Journal of Computer Science

Integrating Machine Learning (ML) techniques into Vehicular Adhoc Networks (VANETs) provides promising features in autonomous driving and ITS applications. In this paper, DSRC data is used to evaluate the effectiveness of different ML models, including Naive Bayes, Random Forest, KNN, and Gradient Boosting, in normal and adversarial scenarios. Since the dataset is relatively imbalanced, the Synthetic Minority Over-sampling Technique (SMOTE) is employed for sampling, and defensive distillation for improving model resilience to adversarial perturbations. From the results, it is clear that models such as Gradient Boosting and Random Forest show high accuracy in both cases, thus showing the potential of …


Foundation Of Revolutionary Topologies: An Overview, Examples, Trend Analysis, Research Issues, Challenges, And Future Directions, Florentin Smarandache Dec 2023

Foundation Of Revolutionary Topologies: An Overview, Examples, Trend Analysis, Research Issues, Challenges, And Future Directions, Florentin Smarandache

Neutrosophic Systems with Applications

We now found nine new topologies, such as: NonStandard Topology, Largest Extended NonStandard Real Topology, Neutrosophic Triplet Weak/Strong Topologies, Neutrosophic Extended Triplet Weak/Strong Topologies, Neutrosophic Duplet Topology, Neutrosophic Extended Duplet Topology, Neutrosophic MultiSet Topology, and recall and improve the seven previously founded topologies in the years (2019-2023), namely: NonStandard Neutrosophic Topology, NeutroTopology, AntiTopology, Refined Neutrosophic Topology, Refined Neutrosophic Crisp Topology, SuperHyperTopology, and Neutrosophic SuperHyperTopology. They are called avantgarde topologies because of their innovative forms.


Superhyperfunction, Superhyperstructure, Neutrosophic Superhyperfunction And Neutrosophic Superhyperstructure: Current Understanding And Future Directions, Florentin Smarandache Dec 2023

Superhyperfunction, Superhyperstructure, Neutrosophic Superhyperfunction And Neutrosophic Superhyperstructure: Current Understanding And Future Directions, Florentin Smarandache

Neutrosophic Systems with Applications

The n-th PowerSet of a Set {or Pn(S)} better describes our real world, because a system S (which may be a company, institution, association, country, society, set of objects/plants/animals/beings, set of concepts/ideas/propositions, etc.) is formed by sub-systems, which in their turn by sub-sub-systems, and so on. We prove that the SuperHyperFunction is a generalization of classical Function, SuperFunction, and HyperFunction. And the SuperHyperAlgebra, SuperHyperGraph are part of the SuperHyperStructure. Almost all structures in our real world are Neutrosophic SuperHyperStructures since they have indeterminate/incomplete/uncertain/conflicting data.


Superhyperfunction, Superhyperstructure, Neutrosophic Superhyperfunction And Neutrosophic Superhyperstructure: Current Understanding And Future Directions, Florentin Smarandache Dec 2023

Superhyperfunction, Superhyperstructure, Neutrosophic Superhyperfunction And Neutrosophic Superhyperstructure: Current Understanding And Future Directions, Florentin Smarandache

Neutrosophic Systems with Applications

The n-th PowerSet of a Set {or Pn(S)} better describes our real world, because a system S (which may be a company, institution, association, country, society, set of objects/plants/animals/beings, set of concepts/ideas/propositions, etc.) is formed by sub-systems, which in their turn by sub-sub-systems, and so on. We prove that the SuperHyperFunction is a generalization of classical Function, SuperFunction, and HyperFunction. And the SuperHyperAlgebra, SuperHyperGraph are part of the SuperHyperStructure. Almost all structures in our real world are Neutrosophic SuperHyperStructures since they have indeterminate/incomplete/uncertain/conflicting data.


Some Special Refined Neutrosophic Ideals In Refined Neutrosophic Rings: A Proof-Of-Concept Study, Murhaf Riad Alabdullah Dec 2023

Some Special Refined Neutrosophic Ideals In Refined Neutrosophic Rings: A Proof-Of-Concept Study, Murhaf Riad Alabdullah

Neutrosophic Systems with Applications

In this research, we created notions of a refined neutrosophic prime (completely prime, semiprime, and completely semiprime) ideal in a refined neutrosophic ring. If R(I1, I2) is a refined neutrosophic ring, then each ideal of R(I1, I2) has the form J+KI1+LI2 are ideals of the classical ring R. The objective of this work is to find the necessary and sufficient condition on classical ideals J, L and K that makes J+KI1+LI2 a prime (completely prime, semiprime, and completely semiprime) ideal in R(I1, I2). We studied some of the elementary properties of these concepts and the most important properties that link …