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 The Graduate Center, City University of New York

#### 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 …

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.

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.

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.

An Unsupervised Machine Learning Algorithm For Clustering Low Dimensional Data Points In Euclidean Grid Space, 2024 Bard College

#### An Unsupervised Machine Learning Algorithm For Clustering Low Dimensional Data Points In Euclidean Grid Space, Josef Lazar

*Senior Projects Spring 2024*

Clustering algorithms provide a useful method for classifying data. The majority of well known clustering algorithms are designed to find globular clusters, however this is not always desirable. In this senior project I present a new clustering algorithm, GBCN (Grid Box Clustering with Noise), which applies a box grid to points in Euclidean space to identify areas of high point density. Points within the grid space that are in adjacent boxes are classified into the same cluster. Conversely, if a path from one point to another can only be completed by traversing an empty grid box, then they are classified …

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 …

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 …

Foundations Of Memory Capacity In Models Of Neural Cognition, 2023 California Polytechnic State University, San Luis Obispo

#### Foundations Of Memory Capacity In Models Of Neural Cognition, Chandradeep Chowdhury

*Master's Theses*

A central problem in neuroscience is to understand how memories are formed as a result of the activities of neurons. Valiant’s neuroidal model attempted to address this question by modeling the brain as a random graph and memories as subgraphs within that graph. However the question of memory capacity within that model has not been explored: how many memories can the brain hold? Valiant introduced the concept of interference between memories as the defining factor for capacity; excessive interference signals the model has reached capacity. Since then, exploration of capacity has been limited, but recent investigations have delved into the …

Reverse Mathematics Of Ramsey's Theorem, 2023 California State University, San Bernardino

#### Reverse Mathematics Of Ramsey's Theorem, Nikolay Maslov

*Electronic Theses, Projects, and Dissertations*

Reverse mathematics aims to determine which set theoretic axioms are necessary to prove the theorems outside of the set theory. Since the 1970’s, there has been an interest in applying reverse mathematics to study combinatorial principles like Ramsey’s theorem to analyze its strength and relation to other theorems. Ramsey’s theorem for pairs states that for any infinite complete graph with a finite coloring on edges, there is an infinite subset of nodes all of whose edges share one color. In this thesis, we introduce the fundamental terminology and techniques for reverse mathematics, and demonstrate their use in proving Kőnig's lemma …

Minimal Sets, Union-Closed Families, And Frankl's Conjecture, 2023 Virginia Commonwealth University

#### Minimal Sets, Union-Closed Families, And Frankl's Conjecture, Christopher S. Flippen

*Theses and Dissertations*

The most common statement of Frankl's conjecture is that for every finite family of sets closed under the union operation, there is some element which belongs to at least half of the sets in the family. Despite its apparent simplicity, Frankl's conjecture has remained open and highly researched since its first mention in 1979. In this paper, we begin by examining the history and previous attempts at solving the conjecture. Using these previous ideas, we introduce the concepts of minimal sets and minimally-generated families, some ideas related to viewing union-closed families as posets, and some constructions of families involving poset-defined …

A Comparison Of Cryptographic Methods, 2022 Liberty University

#### A Comparison Of Cryptographic Methods, Christopher Gilmore

*Senior Honors Theses*

While elliptic curve cryptography and quantum cryptography are significantly different branches of cryptography, they provide a suitable reference point for comparison of the value of developing methods used in the present and investing in methods to be used in the future. Elliptic curve cryptography is quite common today, as it is generally secure and efficient. However, as the field of cryptography advances, the value of quantum cryptography’s inherent security from its basic properties should be considered, as a fully realized quantum cryptosystem has the potential to be quite powerful. Ultimately, it is of critical importance to determine the value of …

Unomaha Problem Of The Week (2021-2022 Edition), 2022 University of Nebraska at Omaha

#### Unomaha Problem Of The Week (2021-2022 Edition), Brad Horner, Jordan M. Sahs

*UNO Student Research and Creative Activity Fair*

The University of Omaha math department's Problem of the Week was taken over in Fall 2019 from faculty by the authors. The structure: each semester (Fall and Spring), three problems are given per week for twelve weeks, with each problem worth ten points - mimicking the structure of arguably the most well-regarded university math competition around, the Putnam Competition, with prizes awarded to top-scorers at semester's end. The weekly competition was halted midway through Spring 2020 due to COVID-19, but relaunched again in Fall 2021, with massive changes.

Now there are three difficulty tiers to POW problems, roughly corresponding to …

Unknowable Truths: The Incompleteness Theorems And The Rise Of Modernism, 2022 Belmont University

#### Unknowable Truths: The Incompleteness Theorems And The Rise Of Modernism, Caroline Tvardy

*Honors Scholars Collaborative Projects*

This thesis evaluates the function of the current history of mathematics methodologies and explores ways in which historiographical methodologies could be successfully implemented in the field. Traditional approaches to the history of mathematics often lack either an accurate portrayal of the social and cultural influences of the time, or they lack an effective usage of mathematics discussed. This paper applies a holistic methodology in a case study of Kurt Gödel’s influential work in logic during the Interwar period and the parallel rise of intellectual modernism. In doing so, the proofs for Gödel’s Completeness and Incompleteness theorems will be discussed as …