Open Access. Powered by Scholars. Published by Universities.®
- Institution
- Keyword
-
- Neutrosophic logic (67)
- Neutrosophic Set (37)
- Neutrosophic Logic (34)
- Neutrosophy (33)
- Neutrosophic set (27)
-
- Mathematics (19)
- Decision making (12)
- Set Theory (11)
- HyperNeutrosophic set. (10)
- Physics (9)
- SuperhyperNeutrosophic set (9)
- Indeterminacy (8)
- Soft Set (8)
- Uncertainty (8)
- Fuzzy set (7)
- Intuitionistic Fuzzy Set (7)
- Neutrosophic Probability (7)
- Neutrosophic statistics (7)
- Neutrosophication (7)
- Soft set (7)
- Neutrosophic (6)
- Neutrosophic soft set (6)
- Plithogenic set (6)
- SuperHyperAlgebra (6)
- Algebraic structures (5)
- Artificial intelligence (5)
- NeutroGeometry (5)
- Neutrosophic Cognitive Maps (5)
- Neutrosophic Sets (5)
- Neutrosophic algebraic structures (5)
- Publication Year
- Publication
- Publication Type
Articles 1 - 30 of 455
Full-Text Articles in Entire DC Network
(R2170) Delta-Continuous Functions In Interval-Valued Neutrosophic Soft Topological Spaces And An Application Using Distance And Similarity Measures, B. Vijayalakshmi, S. Madhunika
(R2170) Delta-Continuous Functions In Interval-Valued Neutrosophic Soft Topological Spaces And An Application Using Distance And Similarity Measures, B. Vijayalakshmi, S. Madhunika
Applications and Applied Mathematics: An International Journal (AAM)
This paper introduces delta-continuous functions in interval-valued neutrosophic soft topological spaces and investigates their fundamental properties. Additionally, delta-irresolute functions are introduced within the same framework. The relationships between these functions and existing function classes are explored. Several theorems, accompanied by illustrative examples, are provided to support the theoretical findings. The study also includes an application of the proposed concepts to distance and similarity measures.
(R2175) Application Of Similarity Measures On Bipolar Complex Neutrosophic Matrices In United Nations’ Sdg-17 Using Python, T. Muthuraji, N. Krishnapraveen
(R2175) Application Of Similarity Measures On Bipolar Complex Neutrosophic Matrices In United Nations’ Sdg-17 Using Python, T. Muthuraji, N. Krishnapraveen
Applications and Applied Mathematics: An International Journal (AAM)
The increasing complexity of decision-making environments demands mathematical frameworks capable of modeling bipolar, indeterminate, and phase-dependent uncertainty simultaneously. Bipolar Complex Neutrosophic theory provides such a structure, but the extension of similarity measures to matrix-based environments remains largely unexplored. In this study, we formally develop cosine, Dice, Jaccard, and hybrid vector similarity measures for Bipolar Complex Neutrosophic Matrices (BCNMs). Each matrix element is represented by a Bipolar Complex Neutrosophic Number (BCNN), enabling structured representation of multidimensional uncertainty within a matrix framework. We also design and implement efficient Python-based computational tools to automate similarity evaluation for BCNMs. The proposed algorithms reduce computational …
(R2185) Operations On Bipolar Complex Neutrosophic Matrices And Its Application In Un’S Sdg-14 & Sdg-3 Using Python, N. Krishnapraveen, T. Muthuraji
(R2185) Operations On Bipolar Complex Neutrosophic Matrices And Its Application In Un’S Sdg-14 & Sdg-3 Using Python, N. Krishnapraveen, T. Muthuraji
Applications and Applied Mathematics: An International Journal (AAM)
Decision-making in sustainability oriented environments frequently involves bipolar evaluations, indeterminate information and phase dependent uncertainty that cannot be adequately represented by existing neutrosophic matrix models. To address this limitation, this study introduces a Bipolar Complex Neutrosophic Matrix (BCNM) framework that integrates bipolar semantics with complex valued uncertainty in a coherent algebraic structure. Fundamental operations and structural properties are rigorously established to ensure mathematical consistency. To facilitate practical multi criteria decision analysis (MCDA), novel score, accuracy, and hybrid aggregation operators are developed. The computational feasibility of the proposed approach is analyzed, demonstrating linear complexity with respect to the number of alternatives …
(R2187) Analysis Of Neurological Impairments In Hospitalized Patients Using Cubic Neutrosophic Sets, B. Anitha, M. Lavanya
(R2187) Analysis Of Neurological Impairments In Hospitalized Patients Using Cubic Neutrosophic Sets, B. Anitha, M. Lavanya
Applications and Applied Mathematics: An International Journal (AAM)
This study introduces an MCDM-based framework for identifying neurological diseases in hospitalized patients using symptom-based evaluations. A team of interns, guided by the chief doctor, was responsible for determining each patient’s precise condition from the presented neurological symptoms. To enhance diagnostic accuracy, the interns employed the TOPSIS and WASPAS methods to assess and rank the potential disease options. The combined analysis yielded a clear identification of the highest ranked disease for every patient, highlighting the effectiveness of these MCDM techniques in supporting clinical decision making.
Classes Of Analytic Functions Defined By Salagean Derivative Operator Associated With Neutrosophic Generalized Poisson Distribution, Soliu O. Opeyemi Okunola, Olushola Adeyemo, Sayo A. Abidemi Gbangbala, Folorunso I. Isola Akinwale
Classes Of Analytic Functions Defined By Salagean Derivative Operator Associated With Neutrosophic Generalized Poisson Distribution, Soliu O. Opeyemi Okunola, Olushola Adeyemo, Sayo A. Abidemi Gbangbala, Folorunso I. Isola Akinwale
Neutrosophic Systems with Applications
This study introduces and analyses new subclasses of analytic functions by applying the Salagean derivative operator to the Neutrosophic Generalized Poisson Distribution (NGPD) series. We develop a model where the mean parameter is treated as an interval or set to account for indeterminacy in complex systems. By employing Stirling numbers of the second kind and decreasing factorials, we derive necessary and sufficient coefficient inequalities and inclusion relations for these new subclasses. Numerical results and graphical illustrations demonstrate the sensitivity of these functions to orientation and the neutrosophic parameter, providing a framework for applications in fields like medical imaging and network …
Decision Making For Large-Scale Problems Under Uncertainty And Conflict, Benjamin J. Hamlin
Decision Making For Large-Scale Problems Under Uncertainty And Conflict, Benjamin J. Hamlin
All Dissertations
Large-scale decision-making problems appear in many areas including long-range forecasting such as energy generation forecasting. Many such problems are subject to conflicting objectives and uncertain data, and can be modeled as linear optimization problems. We study novel theoretical results and algorithms for large-scale linear decision problems under conflict and uncertainty. First, we propose a parametric Benders decomposition algorithm for solving large-scale linear optimization problems with multiple objectives or deterministically uncertain objectives. Second, we extend the parametric Benders decomposition to a multi-stage setting, developing a parametric stochastic dual dynamic programming algorithm, which enables decision-making when conflicts and uncertainty have planning impacts …
A Comparative Analysis Of Data-Driven And Model-Based Neutrosophication Methods: Advancing True Neutrosophic Logic In Medical Data Transformation, Maikel Yelandi Leyva Vázquez, Lorenzo Cevallos-Torres, Omar Mar Cornelio, Florentin Smarandache
A Comparative Analysis Of Data-Driven And Model-Based Neutrosophication Methods: Advancing True Neutrosophic Logic In Medical Data Transformation, Maikel Yelandi Leyva Vázquez, Lorenzo Cevallos-Torres, Omar Mar Cornelio, Florentin Smarandache
Branch Mathematics and Statistics Faculty and Staff Publications
Neutrosophic logic extends fuzzy logic by explicitly modeling indeterminacy (I), offering a robust framework for uncertainty representation. The transformation of crisp data into neutrosophic triplets {T, I, F}—known as neutrosophication—is crucial for applying neutrosophic models in real-world analysis. However, comparative evaluations of existing neutrosophication methods remain limited. This study presents a systematic comparison of five approaches: three model-based methods (Parabolic, Threshold Distance, Fuzzy Membership), one density-based method (Kernel Density Estimation), and a proposed data-driven K-Means clustering method integrating sigmoid membership functions. Using a medical dataset of 299 patients and six continuous clinical variables, we assessed statistical behavior, consistency, and alignment …
Local-Neutrosophic Logic And Local-Neutrosophic Sets: Incorporating Locality With Applications, Florentin Smarandache, Takaaki Fujita
Local-Neutrosophic Logic And Local-Neutrosophic Sets: Incorporating Locality With Applications, Florentin Smarandache, Takaaki Fujita
Branch Mathematics and Statistics Faculty and Staff Publications
The study of uncertainty has been a significant area of research, with concepts such as fuzzy sets [87], fuzzy graphs [51], and neutrosophic sets [58] receiving extensive attention. In Neutrosophic Logic, indeterminacy often arises from real-world complexities. This paper explores the concept of locality as a key factor in determining indeterminacy, building upon the framework introduced by F. Smarandache in [73]. Locality refers to processes constrained within a specific region, where an object or system is directly influenced by its immediate surroundings. In contrast, nonlocality involves effects that transcend spatial or temporal boundaries, where changes in one location have direct …
Neutrosophic Twofold Superhyperalgebra And Anti Superhyperalgebra, Takaaki Fujita, Florentin Smarandache
Neutrosophic Twofold Superhyperalgebra And Anti Superhyperalgebra, Takaaki Fujita, Florentin Smarandache
Branch Mathematics and Statistics Faculty and Staff Publications
Neutrosophic Sets are conceptual frameworks designed to address uncertainty. A Neutrosophic TwoFold Algebra is a hybrid algebraic structure defined over a neutrosophic set, combining classical algebraic operations with neutrosophic components. Concepts such as Hyperalgebra and Superhyperalgebra extend classical Algebra using Power Sets and 𝑛-th powersets. Additionally, structures such as NeutroAlgebra and AntiAlgebra have been defined in recent y ears. This paper explores several related concepts, including TwoFold SuperhyperAlgebra and Anti SuperhyperAlgebra.
Symbolic Hyperplithogenic Set, Takaaki Fujita, Florentin Smarandache
Symbolic Hyperplithogenic Set, Takaaki Fujita, Florentin Smarandache
Branch Mathematics and Statistics Faculty and Staff Publications
Concepts such as Fuzzy Sets, Neutrosophic Sets, and Plithogenic Sets have been widely investigated for tackling uncertainty, with numerous applications explored across various domains. As extensions of the Plithogenic Set, the HyperPlithogenic Set and the SuperHyperPlithogenic Set are also recognized. A Symbolic Plithogenic Set (SPS) is a structured set defined by symbolic components 𝑃𝑖 and coefficients 𝑎𝑖 , enabling flexible algebraic operations under a specified prevalence order. In this paper, we examine concepts including the Symbolic HyperPlithogenic Set and the Symbolic 𝑛-SuperhyperPlithogenic Set.
Some Types Of Hyperneutrosophic Set (4): Cubic, Trapozoidal, Q-Rung Orthopair, Overset, Underset, And Offset, Florentin Smarandache, Takaaki Fujita
Some Types Of Hyperneutrosophic Set (4): Cubic, Trapozoidal, Q-Rung Orthopair, Overset, Underset, And Offset, Florentin Smarandache, Takaaki Fujita
Branch Mathematics and Statistics Faculty and Staff Publications
This paper builds upon the foundational work presented in [38–40]. The Neutrosophic Set provides a comprehensive mathematical framework for managing uncertainty, defined by three membership functions: truth, indeterminacy, and falsity. Recent advancements have introduced extensions such as the Hyperneutrosophic Set and the SuperHyperneutrosophic Set, which are specifically designed to address increasingly complex and multidimensional problems. The formal definitions of these sets are available in [30]. In this paper, we extend the Neutrosophic Cubic Set, Trapezoidal Neutrosophic Set, q-Rung Orthopair Neutrosophic Set, Neutrosophic Overset, Neutrosophic Underset, and Neutrosophic Offset using the frameworks of the Hyperneutrosophic Set and the SuperHyperneutrosophic Set. Furthermore, …
Some Types Of Hyperneutrosophic Set (3): Dynamic, Quadripartitioned, Pentapartitioned, Heptapartitioned, M-Polar, Takaaki Fujita, Florentin Smarandache
Some Types Of Hyperneutrosophic Set (3): Dynamic, Quadripartitioned, Pentapartitioned, Heptapartitioned, M-Polar, Takaaki Fujita, Florentin Smarandache
Branch Mathematics and Statistics Faculty and Staff Publications
This paper builds upon the foundation established in [50, 51]. The Neutrosophic Set provides a robust mathematical framework for handling uncertainty, defined by three membership functions: truth, indeterminacy, and falsity. Recent developments have introduced extensions such as the Hyperneutrosophic Set and SuperHyperneutrosophic Set to tackle increasingly complex and multidimensional problems. In this study, we explore further extensions, including the Dynamic Neutrosophic Set, Quadripartitioned Neutrosophic Set, Pentapartitioned Neutrosophic Set, Heptapartitioned Neutrosophic Set, and m-Polar Neutrosophic Set, to address advanced challenges and applications.
Plithogenic Duplets And Plithogenic Triplets, Takaaki Fujita, Florentin Smarandache
Plithogenic Duplets And Plithogenic Triplets, Takaaki Fujita, Florentin Smarandache
Branch Mathematics and Statistics Faculty and Staff Publications
A Neutrosophic Set is a mathematical framework that represents degrees of truth, indeterminacy, and falsehood to address uncertainty in membership values [41, 42]. In contrast, a Plithogenic Set extends this concept by incorporating attributes, their possible values, and the corresponding degrees of appurtenance and contradiction [50]. Among the related concepts of Neutrosophic Sets, Neutrosophic Duplets and Neutrosophic Triplets are well-known. This paper defines Plithogenic Duplets and Plithogenic Triplets as extensions of these concepts using the Plithogenic Set framework and briefly examines their relationship with existing concepts.
Some Types Of Hyperneutrosophic Set (2): Complex, Single-Valued Triangular, Fermatean, And Linguistic Sets, Takaaki Fujita, Florentin Smarandache
Some Types Of Hyperneutrosophic Set (2): Complex, Single-Valued Triangular, Fermatean, And Linguistic Sets, Takaaki Fujita, Florentin Smarandache
Branch Mathematics and Statistics Faculty and Staff Publications
This paper is a continuation of the work presented in [35]. The Neutrosophic Set provides a mathematical framework for managing uncertainty, characterized by three membership functions: truth, indeterminacy, and falsity. Recent advancements have introduced extensions such as the Hyperneutrosophic Set and SuperHyperneutrosophic Set to address more complex and multidimensional challenges. In this study, we extend the Complex Neutrosophic Set, Single-Valued Triangular Neutrosophic Set, Fermatean Neutrosophic Set, and Linguistic Neutrosophic Set within the frameworks of Hyperneutrosophic Sets and SuperHyperneutrosophic Sets. Furthermore, we investigate their mathematical structures and analyze their connections with other set-theoretic concepts.
Soft Directed N-Superhypergraphs With Some Real-World Applications, Takaaki Fujita, Florentin Smarandache
Soft Directed N-Superhypergraphs With Some Real-World Applications, Takaaki Fujita, Florentin Smarandache
Branch Mathematics and Statistics Faculty and Staff Publications
This paper introduces the Directed Soft Super Hyper Graph, a unified framework for modeling complex, multi-layered directed networks. It combines directionality, recursive hyperstructure, and soft-set parameterization to address the integration of Soft Super HyperGraphs and Directed SuperHyperGraphs, which remains largely unexplored. The paper provides formal definitions, core operations, and real-world examples, such as urban infrastructure and transportation networks, to demonstrate the framework's effectiveness in managing deep hierarchies and uncertain relationships simultaneously.
Beyond Dialectics, Paradoxes, And Binary Logic, Florentin Smarandache
Beyond Dialectics, Paradoxes, And Binary Logic, Florentin Smarandache
Branch Mathematics and Statistics Faculty and Staff Publications
Philosophy, long defined by its pursuit of truth, has historically been a battleground for dichotomies: truth vs. falsehood, materialism vs. idealism, reason vs. emotion. These oppositions often provide a framework for understanding philosophical discourse, but they fail to capture the full nuances of reality. To challenge these binary oppositions, I introduced the neutrosophic perspective in philosophy, rooted in Mathematics, and Many-Valued Logics.1 By emphasizing the interrelation of affirmation, negation, and neutrality, neutrosophy allows for the reconciliation of seemingly irreconcilable viewpoints, providing a new lens through which to reinterpret age-old philosophical questions.
A New Simulation Framework For Analyzing Neutrosophic Data In Experimental Design, Muhammad Aslam, Nasrullah Khan, Florentin Smarandache
A New Simulation Framework For Analyzing Neutrosophic Data In Experimental Design, Muhammad Aslam, Nasrullah Khan, Florentin Smarandache
Branch Mathematics and Statistics Faculty and Staff Publications
A recent simulation-based classical analysis has been developed for interval data. However, a review of the literature indicates that these existing simulations have notable limitations and fail to conform to the neutrosophic statistical framework. In this paper, we propose a novel simulation process designed to analyze neutrosophic data within an appropriate and rigorous neutrosophic framework. We demonstrate that the proposed simulation is more comprehensive and aligns closely with the principles of neutrosophic theory. The results will be obtained through simulation and compared with those of existing methods, with the expectation that the proposed approach provides substantial improvements and is better …
Some Types Of Hyperneutrosophic Set (1): Bipolar, Pythagorean, Double-Valued, Interval-Valued Set, Takaaki Fujita, Florentin Smarandache
Some Types Of Hyperneutrosophic Set (1): Bipolar, Pythagorean, Double-Valued, Interval-Valued Set, Takaaki Fujita, Florentin Smarandache
Branch Mathematics and Statistics Faculty and Staff Publications
The Neutrosophic Set is a mathematical framework designed to manage uncertainty, characterized by three membership functions: truth (T), indeterminacy (I), and falsity (F). In recent years, extensions such as the Hyperneutrosophic Set and SuperHyperneutrosophic Set have been introduced to address more complex scenarios. This paper proposes new concepts by extending Bipolar Neutrosophic Sets, Interval-Valued Neutrosophic Sets, Pythagorean Neutrosophic Sets, and Double-Valued Neutrosophic Sets using the frameworks of Hyperneutrosophic and SuperHyperneutrosophic Sets. Additionally, a brief analysis of these extended concepts is presented.
Exploring Concepts Of Hyperfuzzy, Hyperneutrosophic, And Hyperplithogenic Sets (I), Florentin Smarandache, Takaaki Fujita
Exploring Concepts Of Hyperfuzzy, Hyperneutrosophic, And Hyperplithogenic Sets (I), Florentin Smarandache, Takaaki Fujita
Branch Mathematics and Statistics Faculty and Staff Publications
This work investigates the evolution of traditional set theory to address complex and ambiguous real-world phenomena. It introduces hierarchical hyperstructures and superhyperstructures, where superhyperstructures are formed by iteratively applying power sets to create nested abstractions. The focus is placed on three foundational set-based frameworks—Fuzzy Sets, Neutrosophic Sets, and Plithogenic Sets and their extensions into Hyperfuzzy Sets, HyperNeutrosophic Sets, and Hyperplithogenic Sets. These extensions are applied to various domains, including Statistics, TOPSIS, K-means Clustering, Evolutionary Theory, Topological Spaces, Decision Making, Probability, and Language Theory. By exploring these generalized forms, this paper seeks to guide and inspire further research and development in …
Some Types Of Hyperneutrosophic Set (7): Type-M, Nonstationary, Subset-Valued, And Complex Refined, Takaaki Fujita, Florentin Smarandache
Some Types Of Hyperneutrosophic Set (7): Type-M, Nonstationary, Subset-Valued, And Complex Refined, Takaaki Fujita, Florentin Smarandache
Branch Mathematics and Statistics Faculty and Staff Publications
This paper builds upon the foundational advancements introduced in [26,39–43]. TheNeutrosophic Set provides a versatile mathematical framework for addressing uncertainty through its three membership functions: truth, indeterminacy, and falsity [84]. Extensions such as the Hyperneutrosophic Set and the SuperHyperneutrosophic Set have been recently proposed to address increasingly complex and multidimensional problems. Detailed formal definitions of these concepts can be found in [33]. In this paper, we extend the Type-𝑚, Nonstationary, Subset-Valued, and Complex Refined Neutrosophic Sets using the Hyperneutrosophic Set and the SuperHyperneutrosophic Set frameworks.
Significado Neutrosófico: Partes Comunes De Cosas Poco Comunes Y Partes Poco Comunes De Cosas Comunes, Florentin Smarandache
Significado Neutrosófico: Partes Comunes De Cosas Poco Comunes Y Partes Poco Comunes De Cosas Comunes, Florentin Smarandache
Branch Mathematics and Statistics Faculty and Staff Publications
Esta investigación explora la Neutrosofía, un enfoque filosófico que se centra en la identificación de elementos comunes entre conceptos opuestos y en el análisis de las diferencias entre conceptos semejantes. En este contexto, se estudian las Partes Comunes a Cosas No Comunes, que se manifiestan cuando elementos como y < antiA > comparten aspectos en su intersección, y las Partes No Comunes a Cosas Comunes, donde conceptos iguales como y difieren al exhibir elementos únicos. Este análisis permite comprender mejor la neutralidad e indeterminación representada por < neutA > y < neutB >, situados entre sus respectivos opuestos. La investigación abarca diversas áreas como la Dialéctica, el Yin …
Superhypergraph Neural Networks And Plithogenic Graph Neural Networks: Theoretical Foundations, Takaaki Fujita, Florentin Smarandache
Superhypergraph Neural Networks And Plithogenic Graph Neural Networks: Theoretical Foundations, Takaaki Fujita, Florentin Smarandache
Branch Mathematics and Statistics Faculty and Staff Publications
Hypergraphs extend traditional graphs by allowing edges to connect multiple nodes, while superhypergraphs further generalize this concept to represent even more complex relationships. Neural networks, inspired by biological systems, are widely used for tasks such as pattern recognition, data classification, and prediction. Graph Neural Networks (GNNs), a well-established framework, have recently been extended to Hypergraph Neural Networks (HGNNs), with their properties and applications being actively studied. The Plithogenic Graph framework enhances graph representations by integrating multi-valued attributes, as well as membership and contradiction functions, enabling the detailed modeling of complex relationships. In the context of handling uncertainty, concepts such as …
Some Types Of Hyperneutrosophic Set (6): Multineutrosophic Set And Refined Neutrosophic Set, Takaaki Fujita, Florentin Smarandache
Some Types Of Hyperneutrosophic Set (6): Multineutrosophic Set And Refined Neutrosophic Set, Takaaki Fujita, Florentin Smarandache
Branch Mathematics and Statistics Faculty and Staff Publications
This paper builds on the foundational advancements introduced in [22, 29–32]. The Neutrosophic Set pro-vides a flexible mathematical framework for managing uncertainty by utilizing three membership functions: truth, indeterminacy, and falsity. Recent extensions, such as the HyperNeutrosophic Set and the SuperHy-perNeutrosophic Set, have been developed to address increasingly complex and multidimensional challenges. Comprehensive formal definitions of these concepts are provided in [26]. In this paper, we further extend various specialized classes of Neutrosophic Sets. Specifically, we explore extensions of the MultiNeutrosophic Set and the Refined Neutrosophic Set using HyperNeutrosophic Sets and 𝑛-SuperHyperNeutrosophic Sets, providing detailed analysis and examples.
Some Types Of Hyperneutrosophic Set (5): Support, Paraconsistent, Faillibilist, And Others, Takaaki Fujita, Florentin Smarandache
Some Types Of Hyperneutrosophic Set (5): Support, Paraconsistent, Faillibilist, And Others, Takaaki Fujita, Florentin Smarandache
Branch Mathematics and Statistics Faculty and Staff Publications
This paper builds upon the foundational advancements introduced in [14, 25–27]. The Neutrosophic Set offers a versatile mathematical framework for addressing uncertainty through its three membership functions: truth, indeterminacy, and falsity. Extensions such as the Hyperneutrosophic Set and the SuperHyperneutrosophic Set have been recently proposed to tackle increasingly sophisticated and multidimensional problems. Detailed formal definitions of these concepts can be found in [20]. In this paper, we extend various specialized classes of Neutrosophic Sets—namely, the Support Neutrosophic Set, Neutrosophic Intuitionistic Set (distinct from the Intuitionistic Fuzzy Set), Neutrosophic Paraconsistent Set, Neutrosophic Faillibilist Set, Neutrosophic Paradoxist Set, Neutrosophic Pseudo-Paradoxist Set, Neutrosophic …
Exploring Concepts Of Hyperfuzzy, Hyperneutrosophic, And Hyperplithogenic Sets (Ii), Takaaki Fujita, Florentin Smarandache
Exploring Concepts Of Hyperfuzzy, Hyperneutrosophic, And Hyperplithogenic Sets (Ii), Takaaki Fujita, Florentin Smarandache
Branch Mathematics and Statistics Faculty and Staff Publications
This paper delves into the advancements of classical set theory to address the complexities and uncertainties inherent in real-world phenomena. It highlights three major extensions of traditional set theory - Fuzzy Sets [288], Neutrosophic Sets [237], and Plithogenic Sets [243] - and examines their further generalizations into Hyperfuzzy [106], HyperNeutrosophic [90], and Hyperplithogenic Sets [90]. Building on previous research [83], this study explores the potential applications of HyperNeutrosophic Sets and SuperHyperNeutrosophic Sets across various domains. Specifically, it extends f undamental c oncepts such as Neutrosophic Logic, Cognitive Maps, Graph Neural Networks, Classifiers, and Triplet Groups through these advanced set structures …
Forestfuzzy, Forestneutrosophic, Forestplithogenic, And Forestrough Set, Takaaki Fujita, Florentin Smarandache
Forestfuzzy, Forestneutrosophic, Forestplithogenic, And Forestrough Set, Takaaki Fujita, Florentin Smarandache
Branch Mathematics and Statistics Faculty and Staff Publications
Concepts such as Fuzzy Sets [30, 72], Neutrosophic Sets [53, 55], Rough Sets [37], and Plithogenic Sets [59] have been extensively studied to address uncertainty, with diverse applications across various fields. Recently, TreeFuzzy, TreeNeutrosophic, TreePlithogenic, and TreeRough Sets have been defined [15]. This work examines their extensions: ForestFuzzy, ForestNeutrosophic, ForestPlithogenic, and ForestRough Sets.
Hyperplithogenic Cubic Set And Superhyperplithogenic Cubic Set, Florentin Smarandache
Hyperplithogenic Cubic Set And Superhyperplithogenic Cubic Set, Florentin Smarandache
Branch Mathematics and Statistics Faculty and Staff Publications
Concepts such as Fuzzy Sets [23, 47], Neutrosophic Sets [32, 33], and Plithogenic Sets [35] have been extensively studied for addressing uncertainty, with diverse applications across numerous fields. Building on the Plithogenic Set, the HyperPlithogenic Set and SuperHyperPlithogenic Set have also gained recognition [15]. A Plithogenic Cubic Set integrates interval-valued and single-valued fuzzy memberships, augmented by multiattribute aggregation using plithogenic structures. This paper defines the HyperPlithogenic Cubic Set and SuperHyperPlithogenic Cubic Set and explores related concepts such as the HyperPlithogenic Fuzzy Cubic Set, HyperPlithogenic Intuitionistic Fuzzy Cubic Set, and HyperPlithogenic Neutrosophic Cubic Set.
Neutrosophic Treesoft Expert Set And Forestsoft Set, Takaaki Fujita, Florentin Smarandache
Neutrosophic Treesoft Expert Set And Forestsoft Set, Takaaki Fujita, Florentin Smarandache
Branch Mathematics and Statistics Faculty and Staff Publications
Concepts such as Fuzzy Sets [28,57],Neutrosophic Sets [42,44], and Plithogenic Sets [48] have been extensively studied to address uncertainty, finding diverse applications across various fields. The Soft Set provides a framework that associates each parameter with subsets of a universal set, enabling flexible approximations [31]. The TreeSoft Set extends the Soft Set by introducing hierarchical, tree-structured parameters, allowing for multi-level data representation [53]. In this paper, we revisit the concept of the Neutrosophic TreeSoft Set, which has been discussed in other studies [8, 34]. Additionally, we propose and examine the Neutrosophic TreeSoft Expert Set by incorporating the framework of the …
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
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 …
Some Graph Parameters For Superhypertree-Width And Neutrosophictree-Width, Takaaki Fujita, Florentin Smarandache
Some Graph Parameters For Superhypertree-Width And Neutrosophictree-Width, Takaaki Fujita, Florentin Smarandache
Branch Mathematics and Statistics Faculty and Staff Publications
Graph characteristics are often studied through various parameters, with ongoing research dedicated to exploring these aspects. Among these, graph width parameters—such as treewidth—are particularly important due to their practical applications in algorithms and real-world problems. A hypergraph generalizes traditional graph theory by abstracting and extending its concepts [77]. More recently, the concept of a SuperHyperGraph has been introduced as a further generalization of the hypergraph. Neutrosophic logic [133], a mathematical framework, extends classical and fuzzy logic by allowing the simultaneous consideration of truth, indeterminacy, and falsity within an interval. In this paper, we explore Superhypertree-width, Neutrosophic treewidth, and t-Neutrosophic tree-width.