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Neutrosophic Sets In Neural Networks: Theory, Applications, And Challenges, Vladimir Simic, Dragan Pamucar, Hafiz Muhammad Athar Farid

Neutrosophic Systems with Applications

The integration of neutrosophic sets into neural networks presents a novel approach to handling uncertainty, indeterminacy, and falsity in data. Traditional neural networks typically operate under the assumption of precise and complete data, but real-world applications often involve noisy, incomplete, or ambiguous information. Neutrosophic sets extend fuzzy logic by incorporating three components: truth, indeterminacy, and falsity, allowing for a more nuanced representation of uncertain data. This paper explores the theoretical foundations of neutrosophic sets and their integration with neural networks, highlighting the challenges in computational complexity, training, and optimization. The paper also discusses the potential applications of neutrosophic neural networks …

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 …

Triadic Dynamics Of Clinical Decisions In Apical Surgery Based On Neutrosophic N-Alectic, Emma Arroyo Lalama, Edison Haro Pujos

Neutrosophic Sets and Systems

This study explored the creation of a clinical decision-making model in apical surgery via Neutrosophic N-Alectic, blending affirmative (operate), negative (observe), and neutral (retry conventional endodontics) based on equivocal findings to offer potential solutions to the presentation of periapical lesions. The methodology consisted of dialectic considerations of previous surgeries retrospectively, meaning attributable elements such as lesion severity and response to previous treatment were assessed via a neutrosophic approach to assess the degree of truth, degree of falsity and degree of indeterminacy across all treatment options. The main findings are the neutrosophic model assists in determining the best decisions based on …

Neutrosophic Decision Making Methodology For Sustainable Diabetic Diet: Balancing Health And Environment, Rayan Hussein

Neutrosophic Systems with Applications

Sustainable diabetic diet for balancing health and environment is a decision-making problem and contain uncertainty affect negatively in different decisions. So, this paper proposes a decision-making methodology with the neutrosophic set to solve uncertainty in this decision-making problem. We use the MOOSRA method to rank the alternatives. The criteria weights are computed using the average method. Case study with nine criteria and 16 alternatives are proposed for sustainable diabetic diet. The sensitivity analysis is conducted in this case study to show the stability of the ranks. Nine cases are proposed in this study. The results show the ranks of alternatives …

Analysis Of Customer Perception Of A New Product Using The Neutrosophic Biplot Method, Purificación Galindo-Villardón

Neutrosophic Sets and Systems

This paper sought to propose and apply the Neutrosophic Biplot analysis method to understand consumer perception of a new technological product with uncertain attributes while addressing the shortcomings that a conventional approach would present. Data was collected through a survey experiment with neutrosophic rating scales where 50 subjects slid on one scale to indicate how much they agreed (A), were neutral, or indifferent (I), and disagreed (D) about each of the eight features of a new smartphone they received. A neutrosophic data matrix was formed and converted into a real-valued matrix using a scoring function, allowing for the application of …

Fundamentals Of The New Neutrosophic Matrices, Adebisi Sunday Adesina, Ogunmuyiwa Sodiq Damilola

Neutrosophic Systems with Applications

The New Neutrosophic Matrices provides a mathematical extension of classical and fuzzy matrix theory that incorporates the element of indeterminacy alongside truth and falsity. Neutrosophic logic, pioneered by FlorentinSmarandache, provides a richer framework for dealing with uncertainty and vagueness in real-world data. This study explores the definitions, classifications, and algebraic operations onneutrosophic matrices, including addition, multiplication, scalar operations, and the formation of identities.A comparative analysis is presented to highlight the distinctions between classical, fuzzy, and neutrosophic matrices. From the concepts, potential applications could be proposed most especially, for more problem solving as well as for future exploration.Findingsaffirmthat neutrosophic matrices offer …

Assessing The Sustainable Blockchain-Metaverse-Iot Platform In The Healthcare Industry: An Intelligent Decision Support Model, Ibrahim M. Hezam, Ahmed M. Ali, Ibrahim A. Hameed, Karam Sallam, Mohamed Abdel-Basset

Neutrosophic Systems with Applications

Healthcare services must fulfill patients' desires for secure data sharing and high accessibility. Blockchain technology, through blockchain platforms (BPs), can overcome healthcare challenges. This study develops a decision-making methodology for selecting the best BP, by integrating blockchain with IoT and Metaverse, the proposed approach ensures data integrity, quality, privacy and security, secure data sharing, and interoperability. The decision-making methodology uses the multi-criteria decision-making (MCDM) methodology to handle conflicting criteria. Two MCDM methods are used in this study: CRiteria Importance Through Intercriteria Correlation (CRITIC) for weight computation, and Ranking of Alternatives with Weights of Criterion (RAWEC) for alternative ranking. To deal …

Quantified Neutrosophic Set (Qtns)-Based Mcdm Algorithms For Sustainable Material Selection For Anti-Microbial Bio-Fabricated Textile Manufacturing, Muhammad Saeed, Neha Andaleeb Khalid, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

This paper proposes a modified structure for the neutrosophic set called the Quantified Neutrosophic Set (QtNS) with a parameterized setting. Unlike conventional approaches, the QtNS provides a quantified environment for the indeterminacy by its dependence on truthness and falsity components. This innovative approach quantifies the uncertainty and improves the assessment process via expert-guided opinions, customising it according to the specific situations in real-world decision-making scenarios. Some QtNS operations along with useful characteristics are addressed. Furthermore, two algorithms, QtNSUI and QtNSAO, are developed for the proposed operations of union, intersection, AND, and OR based on QtNS. In the world of sustainable …

Using The Neutrosophic N-Ahp Method To Prioritize Variables And Expert Analysis, Oswaldo Lıber Andrade Salazar, Lenı Cecılıa Campaña Muñoz, Second Huacón Farm, Angel Braulio Martinez Vasquez

Neutrosophic Sets and Systems

The study focuses on addressing a growing challenge in complex decision-making: how to prioritize key variables in an environment of inherent uncertainty and contradiction. In this context, the research explores the implementation of the neutrosophic N-AHP method, a variant of Hierarchical Process Analysis (HPA) that incorporates neutrosophic logic to handle ambiguity and indeterminacy in the evaluation of critical variables. Although traditional HPA has been widely used to prioritize options, it has been limited in contexts where expert perceptions are not clear-cut or are marked by high levels of uncertainty. This work seeks to overcome those limitations, proposing a more flexible …

Use Of Delphi-Ahp Neutrosophic Methods For The Analysis Of School Indicators, Alex Fabian Solano Moreno, Carlos Javier Lizcano Charpeta, Beatrice Del Carmen Viteri Naranjo, Jean Pierre Ramos-Carpio

Neutrosophic Sets and Systems

The study addresses the complex task of analyzing school indicators through the combined application of the Delphi-AHP neutrosophic methods, seeking to overcome the limitations of traditional approaches in educational assessment. The research focuses on the urgent need to develop more robust models that can handle the uncertainty, imprecision, and ambiguity inherent in educational data. Although previous research has been conducted on the analysis of school indicators, conventional approaches fail to effectively integrate the multiple dimensions and degree of uncertainty of the data. This study proposes an innovative solution by integrating neutrosophic tools, which allow for a more flexible and detailed …

Nidus Idearum. Scilogs, Xiv: Superhyperalgebra, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

In this fourteenth book of scilogs – one may find topics on examples where neutrosophics works and others don’t, law of included infinitely-many-middles, decision making in games and real life through neutrosophic lens, sociology by neutrosophic methods, Smarandache multispace, algebraic structures using natural class of intervals, continuous linguistic set, cyclic neutrosophic graph, graph of neutrosophic triplet group , how to convert the crisp data to neutrosophic data, n-refined neutrosophic set ranking, adjoint of a square neutrosophic matrix, neutrosophic optimization, de-neutrosophication, the n-ary soft set relationship, hypersoft set, extending the hypergroupoid to the superhypergroupoid, alternative ranking, Dezert-Smarandache Theory (DSmT), reconciliation between …

Neutrosophic Decision Making Model For Investment Portfolios Selection And Optimizing Based On Wide Variety Of Investment Opportunities And Many Criteria In Market, Ayman H. Abdel-Aziem, Hoda K. Mohamed, Ahmed Abdelhafeez

Neutrosophic Systems with Applications

Investment portfolio selection is a difficult subject due to the presence of competing factors. Choosing a portfolio for one's investments is a major choice that may have far-reaching effects on one's financial well-being. Risk tolerance, time horizon, investing objectives, asset allocation, and investment selection are only a few of the factors that will be studied in this article. The Stable Preference Ordering Towards Ideal Solution (SPOTIS) technique is the basis for our proposed integrated multi-criteria decision-making (MCDM) model. This paper used the single-valued neutrosophic set as a framework to deal with uncertain data. The purpose of the suggested SPOTIS–Neutrosophic model …

Neutrosophic Decision Making Model For Investment Portfolios Selection And Optimizing Based On Wide Variety Of Investment Opportunities And Many Criteria In Market, Ayman H. Abdel-Aziem, Hoda K. Mohamed, Ahmed Abdelhafeez

Neutrosophic Systems with Applications

Investment portfolio selection is a difficult subject due to the presence of competing factors. Choosing a portfolio for one's investments is a major choice that may have far-reaching effects on one's financial well-being. Risk tolerance, time horizon, investing objectives, asset allocation, and investment selection are only a few of the factors that will be studied in this article. The Stable Preference Ordering Towards Ideal Solution (SPOTIS) technique is the basis for our proposed integrated multi-criteria decision-making (MCDM) model. This paper used the single-valued neutrosophic set as a framework to deal with uncertain data. The purpose of the suggested SPOTIS–Neutrosophic model …

On Characterizing Efficient And Properly Efficient Solutions For Multi- Objective Programming Problems In A Complex Space, Alhanouf Alburaikan, Hamiden Abd El-Wahed Khalifa, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

In this paper, a complex non- linear programming problem with the two parts (real and imaginary) is considered. The efficient and proper efficient solutions in terms of optimal solutions of related appropriate scalar optimization problems are characterized. Also, the Kuhn-Tuckers' conditions for efficiency and proper efficiency are derived. This paper is divided into two independently parts: The first provides the relationships between the optimal solutions of a complex single-objective optimization problem and solutions of two related real programming problems. The second part is concerned with the theory of a multi-objective optimization in complex space.

Selection Of Investment Projects In A Plithogenic Environment, Ariel Romero Fernández, Gustavo Álvarez Gómez, Sary Del Rosio Álvarez Hernández, William Roberto Álvarez Arboleda, Adonis Ricardo Rosales García

Neutrosophic Sets and Systems

Nowadays, the economic crisis affecting the countries makes more important the selection process of investment projects. Such is the case of Ecuador where the Multi-annual Public Investment Plan 2017-2021 establishes indicative amounts of public investment that are projected to be executed annually to achieve each of the nine strategic objectives of the National Development Plan that pay tribute to the Sustainable Development Goals of the UN. This plan has certain weaknesses that may not allow an effective and efficient choice at the same time. Which entails a scenario of uncertainty for the Ecuadorian investment process. So we dare to say …

Legal Causal Reasoning. Cause-Effect Analysis Using A Neutrosophic Environment, José Rodolfo Calle Santander, Rously Atencio González, Alipio Cadena Posso, Wilson René Paredes Navarrete

Neutrosophic Sets and Systems

Causal reasoning is implicit in all areas of human life, which is why it is strongly applied within the legal framework. This is valid in both criminal and civil proceedings. For the construction of legal causal models, moral reasoning and understanding of the subject are required. It is a process that implies subjectivity and neutrality. Therefore, it is intended to illustrate the usefulness of causal analysis techniques for decision-making in the dynamics of legal reasoning in a neutrosophic environment given the subjectivity of the process. For that purpose, the methods applicable to this research will be enunciated and will be …

On Solutions Of Fully Fuzzy Linear Fractional Programming Problems Using Close Interval Approximation For Normalized Heptagonal Fuzzy Numbers, Majed G. Alharbi, Hamiden Abd El- Wahed Khalifa

Applied Mathematics & Information Sciences

This paper attempts to solve the linear fractional programming problem with fully fuzzy normalized heptagonal fuzzy numbers using the close interval approximation of normalized heptagonal fuzzy number, which is one of the best interval approximations. The maximization (minimization) problem with interval objective function is converted into multi- objective based on order relations introduced by the decision makers’ preference between interval profits (costs). Finally, an example is presented to illustrate the proposed method.

Simplified Intuitionistic Neutrosophic Soft Set And Its Application On Diagnosing Psychological Disorder By Using Similarity Measure, Veerappan Chinnadurai, Albert Bobin

Applications and Applied Mathematics: An International Journal (AAM)

The primary focus of this manuscript comprises three sections. Initially, we introduce the concept of a simplified intuitionistic neutrosophic soft set. We impose an intuitionistic condition between the membership values of truth and falsity such that their sum does not exceed unity. Similarly, for indeterminacy, the membership value is a real number from the closed interval [0, 1]. Hence, the sum of membership values of truth, indeterminacy, and falsity does not exceed two. We present the notion of necessity, possibility, concentration, and dilation operators and establish some of its properties. Second, we define the similarity measure between two simplified intuitionistic …

Application Of Linguistic/Non-Numeric Fuzzy Aggregation To The Ranking Of Processed Crops, David Koloseni

Tanzania Journal of Science

A non-numeric fuzzy aggregation approach is applied for the fusion of information obtained from farmers and experts for evaluation and selection of alternatives under multiple criteria. The technique has the ability to assign linguistic variable to fused information and find consensus of gathered opinions from a number of experts on crop processing for each processed crop. The technique is illustrated with a crop processing problem by adding value to the crop and increase income to entrepreneurs. The proposed technique has been successfully applied to the ranking of the processed crops based on the expert’s opinions, thus obtaining best preferences based …

A Novel Approach For Assessing The Reliability Of Data Contained In A Single Valued Neutrosophic Number And Its Application In Multiple Criteria Decision Making, Florentin Smarandache, Dragisa Stanujkic, Darjan Karabasevic, Gabrijela Popovic

Branch Mathematics and Statistics Faculty and Staff Publications

Multiple criteria decision making is one of the many areas where neutrosophic sets have been applied to solve various problems so far.

A Neutrosophic Clinical Decision-Making System For Cardiovascular Diseases Risk Analysis, Florentin Smarandache, Shaista Habib, Wardat-Us- Salam, M. Arif Butt, Muhammad Akram

Branch Mathematics and Statistics Faculty and Staff Publications

Cardiovascular diseases are the leading cause of death worldwide. Early diagnosis of heart disease can reduce this large number of deaths so that treatment can be carried out. Many decision-making systems have been developed, but they are too complex for medical professionals. To target these objectives, we develop an explainable neutrosophic clinical decision-making system for the timely diagnose of cardiovascular disease risk. We make our system transparent and easy to understand with the help of explainable artificial intelligence techniques so that medical professionals can easily adopt this system. Our system is taking thirtyfive symptoms as input parameters, which are, gender, …

The Picture Fuzzy Distance Measure In Controlling Network Power Consumption, Florentin Smarandache, Ngan Thi Roan, Salvador Coll Arnau, Marina Alonso Diaz, Juan Miguel Martinez Rubio, Pedro Lopez, Fran Andujar, Son Hoang Lee, Manh Van Vu

Branch Mathematics and Statistics Faculty and Staff Publications

In order to solve the complex decision making problems, there are many approaches and systems based on fuzzy theory were proposed.

Plithogenic N- Super Hypergraph In Novel Multi -Attribute Decision Making, Florentin Smarandache, Nivetha Martin

Branch Mathematics and Statistics Faculty and Staff Publications

An optimal decision-making environment demands feasible Multi-Attribute Decision-Making methods. Plithogenic n – Super Hypergraph introduced by Smarandache is a novel concept and it involves many attributes. This article aims to bridge the concept of Plithogenic n-Super Hypergraph in the vicinity of optimal decision making. This research work introduces the novel concepts of enveloping vertex, super enveloping vertex, dominant enveloping vertex, classification of the dominant enveloping vertex (input, intervene, output dominant enveloping vertices), plithogenic connectors. An application of Plithogenic n-super hypergraph in making optimum decisions is discussed under various decision-making scenarios. Several insights are drawn from this research work and will …

Multicriteria Decision Making Using Double Refined Indeterminacy Neutrosophic Cross Entropy And Indeterminacy Based Cross Entropy, Ilanthenral Kandasamy, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

Double Refined Indeterminacy Neutrosophic Set (DRINS) is an inclusive case of the refined neutrosophic set, defined by Smarandache [1], which provides the additional possibility to represent with sensitivity and accuracy the uncertain, imprecise, incomplete, and inconsistent information which are available in real world.

More precision is provided in handling indeterminacy; by classifying indeterminacy (I) into two, based on membership; as indeterminacy leaning towards truth membership (IT ) and indeterminacy leaning towards false membership (IF ). This kind of classification of indeterminacy is not feasible with the existing Single Valued Neutrosophic Set (SVNS), but it is a particular case of the …

Α-Discounting Method For Multi-Criteria Decision Making (Α-D Mcdm), Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

In this book we introduce a new procedure called αDiscounting Method for Multi-Criteria Decision Making (α-D MCDM), which is as an alternative and extension of Saaty’s Analytical Hierarchy Process (AHP). It works for any number of preferences that can be transformed into a system of homogeneous linear equations. A degree of consistency (and implicitly a degree of inconsistency) of a decision-making problem are defined. α-D MCDM is afterwards generalized to a set of preferences that can be transformed into a system of linear and/or non-linear homogeneous and/or nonhomogeneous equations and/or inequalities. Many consistent, weak inconsistent, and strong inconsistent examples are …

New Operations Over Interval Valued Intuitionistic Hesitant Fuzzy Set, Florentin Smarandache, Said Broumi

Branch Mathematics and Statistics Faculty and Staff Publications

Hesitancy is the most common problem in decision making, for which hesitant fuzzy set can be considered as a useful tool allowing several possible degrees of membership of an element to a set. Recently, another suitable means were defined by Zhiming Zhang [1], called interval valued intuitionistic hesitant fuzzy sets, dealing with uncertainty and vagueness, and which is more powerful than the hesitant fuzzy sets. In this paper, four new operations are introduced on interval-valued intuitionistic hesitant fuzzy sets and several important properties are also studied.

Generalized Interval Neutrosophic Soft Set And Its Decision Making Problem, Said Broumi

Branch Mathematics and Statistics Faculty and Staff Publications

In this work, we introduce the concept of generalized interval neutrosophic soft set and study their operations. Finally, we present an application of generalized interval neutrosophic soft set in decision making problem.