Neutrosophic Twofold Superhyperalgebra And Anti Superhyperalgebra,
2025
University of New Mexico
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.
Plithogenic Duplets And Plithogenic Triplets,
2025
University of New Mexico
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.
Quantified Neutrosophic Set (Qtns)-Based Mcdm Algorithms For Sustainable Material Selection For Anti-Microbial Bio-Fabricated Textile Manufacturing,
2025
University of New Mexico
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 Types Of Hyperneutrosophic Set (2): Complex, Single-Valued Triangular, Fermatean, And Linguistic Sets,
2025
University of New Mexico
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.
Plithogenic Superhypersoft Set And Plithogenic Forest Superhypersoft Set,
2025
University of New Mexico
Plithogenic Superhypersoft Set And Plithogenic Forest Superhypersoft Set, Takaaki Fujita, Florentin Smarandache
Branch Mathematics and Statistics Faculty and Staff Publications
No abstract provided.
Reconsideration Of Neutrosophic Social Science And Neutrosophic Phenomenology With Non-Classical Logic,
2025
University of New Mexico
Reconsideration Of Neutrosophic Social Science And Neutrosophic Phenomenology With Non-Classical Logic, Takaaki Fujita, Florentin Smarandache
Branch Mathematics and Statistics Faculty and Staff Publications
Body-Mind-Soul-Spirit Fluidity is a concept rooted in psychology and phenomenology, offering significant insights into human decision-making and well-being. Similarly, in social analysis and social sciences, frameworks such as PDCA, DMAIC, SWOT, and OODA have been established to enable structured evaluation and effective p roblem-solving. Furthermore, in phenomenology and social sciences, various logical systems have been developed to address specific objectives and practical applications. This paper extends these concepts using the Neutrosophic theory, revisiting their mathematical definitions and exploring their properties. The Neutrosophic Set, an extension of the Fuzzy Set, is a highly flexible framework that has been widely studied in …
New Operation Defined Over Dual-Hesitant Fuzzy Set And Its Application In Diagnostics In Medicine,
2024
Tanta University - Faculty of Engineering
New Operation Defined Over Dual-Hesitant Fuzzy Set And Its Application In Diagnostics In Medicine, Manar Mohamed Omran, Reham Abdel-Aziz Abo-Khadra
Journal of Engineering Research
In recent decades, several types of sets, such as fuzzy sets, interval-valued fuzzy sets, intuitionistic fuzzy sets, interval-valued intuitionistic fuzzy sets, type 2 fuzzy sets, type n fuzzy sets, and hesitant fuzzy sets, have been introduced and investigated widely. In this paper, we propose dual hesitant fuzzy sets (DHFSs), which encompass fuzzy sets, intuitionistic fuzzy sets, hesitant fuzzy sets, and fuzzy multi-sets as special cases. Then we investigate the basic operations and properties of DHFSs. We also discuss the relationships among the sets mentioned above, and then propose an extension principle of DHFSs. Additionally, we give an example to illustrate …
Decision-Making In Diagnosing Heart Failure Problems Using Dual Hesitant Fuzzy Sets,
2024
Universityof Tanta, Faculty of Engineering
Decision-Making In Diagnosing Heart Failure Problems Using Dual Hesitant Fuzzy Sets, Manar Mohamed Omran, Reham Abdel-Aziz Abo-Khadra
Journal of Engineering Research
In recent decades, several types of sets, such as fuzzy sets, interval-valued fuzzy sets, intuitionistic fuzzy sets, interval-valued intuitionistic fuzzy sets, type 2 fuzzy sets, type n fuzzy sets, and hesitant fuzzy sets, have been introduced and investigated widely. In this paper, we propose dual hesitant fuzzy sets (DHFSs), which encompass fuzzy sets, intuitionistic fuzzy sets, hesitant fuzzy sets, and fuzzy multi-sets as special cases. Then we investigate the basic operations and properties of DHFSs. We also discuss the relationships among the sets mentioned above, and then propose an extension principle of DHFSs. Additionally, we give an example to illustrate …
Discordium Mathematica - A Symphony In Aleph Minor,
2024
Aravali Asset Management
Discordium Mathematica - A Symphony In Aleph Minor, Vijay Fafat
Journal of Humanistic Mathematics
How did Mathematics arise? Who created it? Why is it subject to Godel’s Incompleteness Theorems? And what does all this have to do with Coleridge’s poem, “Kubla Khan”, and “The Person from Porlock”? Here is a complete mythology of Mathematics set in an epic poetry format, fusing thoughts and verses from Western religions and Eastern mysticism… Those with immense patience and careful reading shall reap the fruit… (best read on a large screen or in printed form)
Nidus Idearum. Scilogs, Xiv: Superhyperalgebra,
2024
University of New Mexico
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 …
Sigma_N-Correct Forcing Axioms,
2024
CUNY Graduate Center
Sigma_N-Correct Forcing Axioms, Benjamin P. Goodman
Dissertations, Theses, and Capstone Projects
I introduce a new family of axioms extending ZFC set theory, the Sigma_n-correct forcing axioms. These assert roughly that whenever a forcing name a' can be forced by a poset in some forcing class Gamma to have some Sigma_n property phi which is provably preserved by all further forcing in Gamma, then a' reflects to some small name such that there is already in V a filter which interprets that small name so that phi holds. Sigma_1-correct forcing axioms turn out to be equivalent to classical forcing axioms, while Sigma_2-correct forcing axioms for Sigma_2-definable forcing classes are consistent relative to …
Largeness And Accessibility Of Sparse Sets,
2024
Bridgewater State University
Largeness And Accessibility Of Sparse Sets, Oscar Quester
Honors Program Theses and Projects
One of the main goals in the study of Ramsey Theory is to find “order” in seemingly “random” structures. For example, Van der Waerden’s Theorem tells us that given any r-coloring of the positive integers, there will exist arbitrarily long monochromatic arithmetic progressions. The theorem places no requirement on the gap (common difference), d, of the arithmetic progression – it can be any natural number. With this in mind, we ask if we are still guaranteed arbitrarily long monochromatic arithmetic progressions when we restrict the possible values of d to some subset D ⊆ N. We also ask a similar …
Associated A Nexus With A Treesoft Sets And Vice Versa,
2024
University of New Mexico
Associated A Nexus With A Treesoft Sets And Vice Versa, Akbar Rezae, Karim Ghadimi, Florentin Smarandache
Branch Mathematics and Statistics Faculty and Staff Publications
We recall the definitions of a nexus and a TreeSoft Set, and investigate the relation between them. We associated a nexus with a TreeSoft Set induced by a tree graph and vice versa.
Super Hiper Funcion Y Super Hiper Estructura Y Sus Correspondientes Super Hiper Funcion Neutrosofica Y Super Hiper Estructura Neutrosofica,
2024
University of New Mexico
Super Hiper Funcion Y Super Hiper Estructura Y Sus Correspondientes Super Hiper Funcion Neutrosofica Y Super Hiper Estructura Neutrosofica, Florentin Smarandache
Branch Mathematics and Statistics Faculty and Staff Publications
El n-ésimo Conjunto Potencia de un Conjunto {o Pn(S)} describe mejor nuestro mundo real, porque un sistema S (que puede ser una empresa, institución, asociación, país, sociedad, conjunto de objetos/plantas/animales/seres, conjunto de conceptos/ideas/proposiciones, etc.) está formado por subsistemas, que a su vez están formados por sub-subsistemas, y así sucesivamente. Demostramos que la Super Hiper Función es una generalización de la Función clásica, Super Función y la Hiper Función. Y el Super Hiper Álgebra, Super Hiper Gráfico son parte de la Super Hiper Estructura. Casi todas las estructuras en nuestro mundo real son Super Hiper Estructuras Neutrosóficas ya que tienen …
Nuevos Tipos De Conjuntos Suaves: Conjunto Hiper Suave, Conjunto Suave Indeterminado, Conjunto Hiper Suave Indeterminado Y Conjunto Suave De Árbol,
2024
University of New Mexico
Nuevos Tipos De Conjuntos Suaves: Conjunto Hiper Suave, Conjunto Suave Indeterminado, Conjunto Hiper Suave Indeterminado Y Conjunto Suave De Árbol, Florentin Smarandache
Branch Mathematics and Statistics Faculty and Staff Publications
This is an updated article, where we present the definitions and practical applications of the Soft Set and its extensions to the Hyper Soft Set, Indeterminate Soft Set, Indeterminate Hyper Soft Set, and Tree Soft Set.
A Comprehensive Study On Decision-Making Algorithms In Retail And Project Management Using Double Framed Hypersoft Sets,
2024
University of New Mexico
A Comprehensive Study On Decision-Making Algorithms In Retail And Project Management Using Double Framed Hypersoft Sets, Ajoy Kanti Das, Florentin Smarandache, Rakhal Das, Suman Das
Branch Mathematics and Statistics Faculty and Staff Publications
In today's dynamic business environment, effective decision-making plays a crucial role in the success of retail businesses and project management endeavors. This paper presents a comprehensive study of decision-making algorithms, focusing on the utilization of Double Framed Hypersoft Sets (DFHS) in retail and project management contexts. The study explores the theoretical foundations of DFHS and its practical applications in customer segmentation, personalized marketing, project selection, and resource allocation. Various algorithms and methodologies incorporating DFHS are discussed and analyzed, highlighting their advantages, limitations, and real-world implications. Through a series of numerical examples, case studies, and comparative analyses, this study provides valuable …
An Entropy Measure For N-Cylindrical Fuzzy Neutrosophic Sets,
2024
University of New Mexico
An Entropy Measure For N-Cylindrical Fuzzy Neutrosophic Sets, Sarannya Kumari R., Sunny Joseph Kalayathankal, Mathews M. George, Florentin Smarandache
Branch Mathematics and Statistics Faculty and Staff Publications
n-Cylindrical fuzzy neutrosophic set (n-CyFNS) is a new variant of fuzzy neutrosophic sets. In this paper our aim is to introduce an entropy measure for n-CyFNS. Here we explained its properties along with examples. Two real life applications, one on better way of shopping and the second on teacher evaluation, based on this proposed entropy measure are also illustrated.
Q-Rung Neutrosophic Sets And Topological Spaces,
2024
University of New Mexico
Q-Rung Neutrosophic Sets And Topological Spaces, Michael Gr. Voskoglou, Florentin Smarandache, Mona Mohamed
Branch Mathematics and Statistics Faculty and Staff Publications
The concept of 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 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.
Assuming Photon As Extended Point Particle In The Hypersoft Topological Space And Other Hypotheses: Issues And Trend Analysis,
2024
University of New Mexico
Assuming Photon As Extended Point Particle In The Hypersoft Topological Space And Other Hypotheses: Issues And Trend Analysis, Victor Christianto, Florentin Smarandache
Branch Mathematics and Statistics Faculty and Staff Publications
Following our preceding article, where we discussed alternative interpretations of the advanced perihelion of Mercury, the present article revisits the 1919 solar eclipse expedition led by Arthur Eddington, which famously provided the first observational confirmation of Einstein's theory of general relativity. We focus on the deflection of starlight data obtained during the eclipse, a cornerstone of this validation. Here, we explore three alternative explanations for the observed light bending that challenge the sole attribution to general relativity. Firstly, the paper begins by arguing based on criticisms raised by Tullio Levi-Civita, a contemporary mathematician, regarding Einstein's use of pseudo-tensors in his …
New Trends In Neutrosophic Theories And Applications, Volume Iii,
2024
University of New Mexico
New Trends In Neutrosophic Theories And Applications, Volume Iii, Florentin Smarandache, Surapati Pramanik
Branch Mathematics and Statistics Faculty and Staff Publications
The field of neutrosophic set theory and its applications has been rapidly expanding, particularly since the introduction of the journal "Neutrosophic Sets and Systems." New theories, techniques, and algorithms are being developed at a very high rate. One of the most notable trends in neutrosophic theory is its hybridization with other set theories such as rough set theory, bipolar set theory, soft set theory, hesitant fuzzy set theory, and more. Various hybrid structures like rough neutrosophic sets, neutrosophic soft set, single valued neutrosophic hesitant fuzzy sets, among others, have been proposed in a short period. Neutrosophic sets have proven to …
