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On The Two-Fold Fuzzy N-Refined Neutrosophic Rings For 2≤N≤3, Abdallah Shihadeh, Khaled Ahmad Mohammad Matarneh, Raed Hatamleh, Mowafaq Omar Al-Qadri, Abdallah Al-Husban

Neutrosophic Sets and Systems

The objective of this paper is to study the two-fold fuzzy algebra based on n-refined neutrosophic rings for some different special values of n, where we study some of the special elements in the case of two-fold 2-refined neutrosophic ring and 3-refined neutrosophic rings such as units, idempotents, and nilpotent elements. Also, we present the concept of two-fold ring homomorphism with its elementary properties.

Combined Topsis Technique For Magdm Based On The Distance Measures And Critic Under Single-Valued Neutrosophic Sets And Applications To Quality Evaluation Of Whole Process Engineering Consulting Service Modes, Xia Wang, Yingxia Hou, Jing Peng, Jiekun Hu, Yue Li, Qiang Cai, Guiwu Wei

Neutrosophic Sets and Systems

According to survey data released by the National Bureau of Statistics, from 2011 to 2022, the total output value of China's construction industry showed an increasing trend year by year. From 2018 to 2021, infrastructure investment has always maintained a positive growth, indicating that the current construction industry is in a rapid development stage. In order to improve the development quality of the construction industry as much as possible, it is of great significance to develop the whole Process engineering consulting service model. The quality evaluation of whole process engineering consulting service modes is MAGDM. The single-valued neutrosophic sets (SVNSs) …

Fusing Type -2 Neutrosophic In Decision-Making Methodology For Appreciation Blockchain Capabilities In Securing Environment Of Vehicles Fog: Practice Realistic Scenarios, Alaa Salem, Mona Mohamed

Neutrosophic Sets and Systems

Right now, Contemporary technologies have become imperative in many domains to achieve societal safety. As is practiced in transportation systems through merging information and communication technologies (ICTs) in transportation to be an intelligent sector. As well Internet of Vehicles (IoVs) for facilitating communication between vehicles for safe driving. Similarly, fog computing in Vehicular Ad Hoc Networking (VANET) contributes significantly to addressing timing and latency issues by enabling cloud services for nearby vehicles. Nonetheless, there are hazards of cyber-attacks on vehicles in VFN, which makes it uneasy to disclose personal information to unidentified fog devices. Consequently, an online criminal might target …

Pentapartitioned Neutrosophic Subtraction Algebra, Rakhal Das, Suman Das

Neutrosophic Sets and Systems

This paper aims to define the concepts of Semi-group and Pentapartitioned Neutrosophic Subtraction Algebra. We also examine a few of their fundamental characteristics. Additionally, we provide a few appropriate instances on Pentapartitioned Neutrosophic Subtraction Algebra.

On Nct- Set Theory, Dheargham Ali Abdulsada, L. A. A. Al-Swidi, Mustafa H. Hadi

Neutrosophic Sets and Systems

We introduce a new class of neutrosophic crisp set, and then it presented some operations via this sets like, ������ −intersection, ������ −union and algebraic ������−difference to arrive at the algebraic ring construction. Also, we introduce the ������ − points, which showed that a ������ –set is ������−union of its ������−points, and so did we introduced the concept of the function on this sets, called ������ – function and some of their important properties. Finally, we introduced the concept of the topology and some of the concepts entrusted to it, as an introduction to those spaces that can be studied …

Assessment Of Deep Learning Techniques For Bone Fracture Detection Under Neutrosophic Domain, Doaa El-Shahat, Ahmed Tolba

Neutrosophic Sets and Systems

With the increasing strain on the health system, there is a growing need for automatic medical image diagnosis. Emerging technologies for medical diagnosis can help to achieve the goals of sustainable development. However, analyzing medical images can be challenging due to uncertain data, ambiguity, and impreciseness. To address this issue, we have developed a novel BoneNet-NS technique to classify fractures in X-ray bone images. The proposed approach is based on the power of deep learning (DL) and neutrosophic set (NS) to deal with aleatoric uncertainty. Moreover, we present two frameworks for integrating NS with DL models: BoneNet-NS1 and BoneNet-NS2. We …

Neutrosophic Spherical Sets In Mcdm, S. Bhuvaneshwari, C. Antony Crispin Sweety

Neutrosophic Sets and Systems

Decision-making plays a crucial role in achieving success across various scenarios, especially when confronted with complex issues inundated with abundant facts and information. Employing multi criteria decision-making (MCDM) methods and techniques becomes particularly indispensable in tackling such formidable challenges. This study introduces novel neutrosophic SWGM and SWAM accuracy functions, which enhance traditional aggregation operators. Furthermore, it introduces the CODAS technique tailored for addressing Multiple Attribute Group Decision Making problems utilizing the newly defined operators. To exemplify the proposed methodology, a supplier selection problem is examined.

The Indefinite Refined Neutrosophic Integrals By Parts, Yaser Ahmad Alhasan, Ahmad Abdullah Almekhlef, Mohamed Elghazali Ali Mohieldin Mohamed, Raja Abdullah Abdulfatah

Neutrosophic Sets and Systems

this article's goal is to present the indefinite refined neutrosophic integrals by parts. All situations where integration by parts can be used are covered, including the use of rotating integrals to solve recurring and non-terminating functions like the product of trigonometric and exponential functions. Furthermore, the Tabular method has been implemented in the computation of the indefinite refined neutrosophic integrals

A Robust Framework For Medical Diagnostics Based On Interval-Valued Q-Neutrosophic Soft Sets With Aggregation Operators, Enad Ghazi, Sinan O. Al-Salihi

Neutrosophic Sets and Systems

The best way to deal with complicated life scenarios that accompany the decision-making process is to update previous concepts constantly. Therefore, researchers must constantly discover powerful mathematical tools that suit the accompanying circumstances. In this regard, we combine both soft set, neutrosophic set, and interval setting under Q-two-dimensional universal information to introduce a new hybrid innovative model called interval valued-Q-neutrosophic soft sets. The core goal of this model is to keep the features of previous models like soft sets, neutrosophic sets, and Q-Fuzzy sets in dealing with the lack of uncertainty and neutrality associated with real-life issues. This new approach …

Evaluation Of The Shortest Path Based On The Traveling Salesman Problem With A Genetic Algorithm In A Neutrosophic Environment, Prasanta Kumar Raut, Siva Prasad Behera, Said Broumi, Arindam Dey, Mohamed Talea, Amarendra Baral

Neutrosophic Sets and Systems

In The traveling salesman problem (TSP) is an essential and the most popular conventional combinatorial optimization network problem in operations research, in which the TSP evaluates the shortest route or path in a network. In TSP, every node has been visited only once, excluding the starting node. In TSP, edge lengths are usually expressed to indicate journey time and expenses instead of distance from a location. The exact arc length can't be predicted because journey times and expenses vary depending on the amount of payload, climate, highway conditions, and so on. As a result, the Neutrosophic numbers introduce a new …

Treesoft Approach For Refining Air Pollution Analysis: A Case Study, M. Myvizhi, Ahmed A. Metwaly, Ahmed M. Ali

Neutrosophic Sets and Systems

The ongoing research employs both the neutrosophic set and the Decision Making and Evaluation Method (DEMATEL) to analyze and determine the factors influencing supplier selection within the realm of Supply Chain Management (SCM). Recognized as a proactive strategy for enhancing performance and securing competitive advantages, DEMATEL guides this investigation. The study utilizes neutrosophic set Theory to refine overall assessments, introducing a novel scale to distinctly represent each value. Through a practical case study focusing on selecting the optimal supplier for a distribution company, the proposed methodology's application is illustrated. The research framework integrates a neutrosophic DEMATEL approach for data collection, …

On Generalized Difference Rough Ideal Statistical Convergence In Neutrosophic Normed Spaces, Manpreet Kaur, Meenakshi Chawla

Neutrosophic Sets and Systems

This article’s main goal is to provide and investigate a novel statistical convergence generalisation for generalized difference sequences in Neutrosophic Normed Spaces (NNS) called rough ideal statistical con vergence. The collection of approximate optimal statistical limit points and cluster points is defined, and their algebraic and topological features are examined. Additionally, we included the relationship for generalized dif ference sequences in NNS between rough I-statistical cluster points and rough I-statistical limit points.

A Survey On Neutrosophic Principles For Inventory Management Problem, Ankit Dubey, Arindam Dey, Said Broumi, Ranjan Kumar

Neutrosophic Sets and Systems

This paper presents a thorough assessment and classi cation of di erent uncertain environments used by researchers to analyze inventory management(IM) systems across various sectors, such as ABC anal ysis, Last In, First Out (LIFO), and batch tracking. Moreover, it introduces the concepts of the neutrosophic principle and fuzzy principle in inventory management. it also investigates the di culties associated with the traditional inventory model. The primary focus of the study lies in inventory management under the Neu trosophic principle, speci cally addressing uncertain demand and imprecise data. By shedding light on the potential of neutrosophic principle, this manuscript contributes …

On Rough Statistical Convergence In Neutrosophic Normed Spaces, Reena Antal, Meenakshi Chawla, Vijay Kumar

Neutrosophic Sets and Systems

In this paper, we have presented rough statistical convergence of sequence on neutrosophic normed spaces as an important convergence criterion. As neutrosophication can handle partially dependent compo nents, partially independent components and even independent components involved in real-world problems. By examining some properties related to rough convergence in these spaces we provide some useful functional tools in the situations of inconsistency and indeterminacy in the real world. Further, we have established some equivalent conditions on the set of statistical limit points as well as on the set of cluster points in these spaces for rough statistically convergent sequences.

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 …

Triplemask Spatial Linear Filter And Neutrosophic Entropy For Video Denoising, Face Detection And Recognition In Forensic Crime Analysis Using Deep Learning, Anita Sigamani, Prema Selvaraj

Neutrosophic Sets and Systems

Forensic Science is the application of Scientific methods to resolve crime and legal issues. It involves various disciplines, such as Computer Science, Biology, Chemistry and Anthropology. Forensic scientists examine and analyze evidence from crime scenes, such as fingerprints, DNA, blood, or weapons. Digital proof is one of the forms of forensic evidence. It provide real time eye witness of the incident. Video recordings enable investigators to find out what exactly has transpired. Investigators use video evidence as a source for witness statements, and it aids in the search for the missing person or suspect. Video evidence is also used to …

Single-Valued Pentapartitioned Neutrosophic Soft Set, Bimal Shil, Suman Das, Rakhal Das, Surapati Pramanik

Neutrosophic Sets and Systems

Soft set (SS) and neutrosophic set (NS) are important mathematical concepts to deal with uncertainty. NS was further extended to pentapartitioned neutrosophic set (PNS) to deal with uncertainty comprehensively. In order to expand the concept of single-valued pentapartitioned neutrosophic set (SVPNS) and SS, the paper aims to introduce the concept of single-valued pentapartitioned neutrosophic soft set (SVPNS-Set) by adding the ideas of SS and SVPNS together. Furthermore, based on SVPNS-Set, several definitions, examples, properties, propositions and theorems have been established.

Approach To Multi-Criteria Decision-Making In A Neutrosophic Picture Hyper-Soft Set Environment Using Generalized Neutrosophic Topsis, Manpreet Kaur, Akanksha Singh

Neutrosophic Sets and Systems

Given the complexity of today’s world, we might need to work with numbers requiring multi-attribute functions, such as those having positive, neutral, and negative membership and those having truth, indeterminacy, and falsity membership. Adding these numbers together to get a single real number is the most important factor. In situations like this, decision-makers have more difficult choices and are unable to apply the single attribute function of the soft set theory. To address this constraint, the hyper-soft set theory with multi-attribute functions is introduced. We combine the notion of neutrosophic hypersoft set with picture fuzzy hypersoft set to form a …

New Similarity Measures For Neutrosophic Binary Topology Using Euclidean Distance, J. Elekiah, G. Sindhu

Neutrosophic Sets and Systems

This paper focuses on introducing a new similarity measure for the neutrosophic binary set.Similarity measure are used in multi attribute desicion making problems to find the difference be tween the alternatives.In this paper a new measure based on Euclidean distance is introduced to find the measure between two binary single valued neutrosophic set.Further its is applied in a multi attribute desicion problem to see the attainability of the proposed measure

Evaluation Strategies Of Leadership Management In Healthcare Systems: An Integrated Type-Ii Neutrosophic Optimization Approach, Areej Hamoud Alharbi, Hayam M. Jabali, Preethi Rajan

Neutrosophic Sets and Systems

This study presented a decision-making methodology to evaluate leadership management strategies in healthcare systems. This study used the multi-criteria decision-making (MCDM) methodology to deal with conflicting criteria in the decision-making process. The MCDM methodology is integrated with neutrosophic sets to deal with uncertainty and vague information in decision-making. The neutrosophic set has three memberships: truth, indeterminacy, and falsity. The type-2 neutrosophic set is a subset of the neutrosophic set with nine membership degrees. The neutrosophic set integrated with the COPRAS method to rank the alternatives. fourteen criteria and eleven alternatives are used to evaluate leadership management in healthcare systems. The …

The Indefinite Symbolic Plithogenic Trigonometric Integrals, Yaser Ahmad Alhasan, Suliman Sheen, Raja Abdullah Abdulfatah, Mohammed Mustafa Ahmed

Neutrosophic Sets and Systems

This paper discussed the indefinite plithogenic trigonometric integrals, where we presented the integrating products of plithogenic trigonometric function, also studying the plithogenic trigonometric identities, which facilitated finding the integral of the associated formulas. In addition to a set of exercises that clarify each idea.

Solving The Minimum Spanning Tree Problem Under Interval-Valued Fermatean Neutrosophic Domain, Souhail Dhouib, Vidhya K, Said Broumi, Mohamed Talea

Neutrosophic Sets and Systems

In classical graph theory, the minimal spanning tree (MST) is a subgraph that lacks cycles and efficiently connects every vertex by utilizing edges with the minimum weights. The computation of a minimum spanning tree for a graph has been a pervasive problem over time. However, in practical scenarios, uncertainty often arises in the form of fuzzy edge weights, leading to the emergence of the Fuzzy Minimum Spanning Tree (FMST). This specialized approach is adept at managing the inherent uncertainty present in edge weights within a fuzzy graph, a situation commonly encountered in real-world applications. This study introduces the initial optimization …

Single-Valued Quadripartitioned Neutrosophic D-Ideal Of D-Algebra, Bimal Shil, Rakhal Das, Carlos Granados, Suman Das, Binod Chandra Tripathy

Neutrosophic Sets and Systems

The conception of single-valued quadripartitioned neutrosophic d-ideal (SVQN-d-I) of single-valued quadripartitioned neutrosophic d-algebra (SVQN-d-A) as an expansion of neutrosophic d-Ideal and neutrosophic d-Algebra has been attempted to be introduced in this article. Additionally, we identify various characteristics of them. Additionally, SVQN-d-I and SVQN-d-A examples have been provided.

Fuzzy Metric Spaces Of The Two-Fold Fuzzy Algebra, Hazim M. Wali Al-Tameemi

Neutrosophic Sets and Systems

This paper is dedicated to defining and studying for the first time the concept of fuzzy metric spaces based on two-fold fuzzy algebras, where the elementary properties of this new concept will be studied and presented by many theorems and related examples that explain the validity of our work. Also, many different types of open and closed balls will be discussed, as well as the relationships between these metric substructures.

The Refined Indefinite Neutrosophic Integral, Yaser Ahmad Alhasan, Mohammed Mustafa Ahmed, Raja Abdullah Abdulfatah, Suliman Sheen

Neutrosophic Sets and Systems

This work presented the refined neutrosophic indefinite integral, where the substitution method for calculating integrals in the refined neutrosophic field that contain two part of indeterminacy (��1,��2) was presented. We also proved a theorem through which we were able to find most of the integrals for the refined neutrosophic functions.

Critical Path Method & Project Evaluation And Review Technique: A Neutrosophic Review, Navya Pratyusha M, Arindam Dey, Said Broumi, Ranjan Kumar

Neutrosophic Sets and Systems

Fuzzy, intuitionistic, and neutrosophic sets are the primary focus of the review investigation under the extension concepts. The significance and use of triangular shape for data representation are investigated. For modelling and expressing ambiguous or complex data, the triangle shape is a useful tool due to its simplicity and computational efficiency. Further study involves the tool of the operations research technique i.e., Network Analysis that helps in implementing and developing using the fuzzy extension principle. Critical Path Method (CPM) & Project Evaluation and Review Technique (PERT) plays a major part in the field of network in various decision-making scenarios using …

Harnessing Pliancy Tree Soft Sets In Heart Diseases For Extracting Beneficial Rules Of Association Rules, Gawaher S. Hussein, Khalid A. Eldrandaly, Abdelnasser H. Zaied, Samar L. Elhawy, Mona Mohamed

Neutrosophic Sets and Systems

Cardiovascular diseases (CVDs)continue to be the primary cause of mortality, accounting for approximately one-third of all fatalities globally. This spawned the proposal of models in several studies. Accordingly, this study contributed to diagnosing heart disease through suggesting soft diagnosis paradigm. Various techniques have been volunteered for serving the suggested paradigm toward achieving its objective. Additionally, this study provided set of contributions. For instance, Tree Soft Technique (TrST) is applied for the first time for forming attributes and sub attributes of patients into nodes and sub-nodes of Tree to obtain relations between it. Even, the study support stakeholders to making accurate …

N Example Of Two-Fold Fuzzy Algebras Based On Neutrosophic Real Numbers, Abdallah Shihadeh, Khaled Ahmad Matarneh, Raed Hatamleh, Randa Bashir Hijazeen, Abdallah Al-Husban, Mowafaq Omar Al-Qadri

Neutrosophic Sets and Systems

This paper is dedicated to defining and studying for the first time a two-fold algebra over the neutrosophic real number ring by merging the fuzzy set mapping with the algebraic operations of the neutrosophic real number ring. Also, we study the elementary algebraic properties of the defined two-fold algebra through its algebraic operations and substructures such as homomorphisms and ideals.

Theory Of Distances In Neutrogeometry, Erick González Caballero, Florentin Smarandache

Neutrosophic Sets and Systems

NeutroGeometry is one of the most recent approaches to geometry. In NeutroGeometry mod els, the main condition is to satisfy an axiom, definition, property, operator and so on, that is neither entirely true nor entirely false. When one of these concepts is not satisfied at all it is called AntiGeometry. One of the problems that this new theory has had is the scarcity of models. Another open problem is the definition of angle and distance measurements within the framework of NeutroGeometry. This paper aims to introduce a general theory of distance measures in any NeutroGeometry. We also present an algorithm …

A Comprehensive Decision Algorithm For The Analysis Of Renewable Energy Source Selection Problem Using Pythagorean Neutrosophic Fuzzy Sets, D. Sasirekha, P. Senthilkumar

Neutrosophic Sets and Systems

Nowadays, to achieve sustainable development and avoid devastating impacts on the environment, India is making rapid and broad changes to green energy technology. In order to provide long-term energy security with lower emissions, renewable energy sources are essential. It is well known that renewable energy technologies, or RETs, have the capacity to significantly meet the demand for electricity while lowering pollution levels. The nation has set up an ecologically friendly energy route in recent years. In this paper, we apply multi-criteria decision making (MCDM) models to determine the best renewable energy technology for India. We use the MULTIMOORA model to …