Other Mathematics Commons^™

Rendering Hypercomplex Fractals, Anthony Atella

Honors Projects

Fractal mathematics and geometry are useful for applications in science, engineering, and art, but acquiring the tools to explore and graph fractals can be frustrating. Tools available online have limited fractals, rendering methods, and shaders. They often fail to abstract these concepts in a reusable way. This means that multiple programs and interfaces must be learned and used to fully explore the topic. Chaos is an abstract fractal geometry rendering program created to solve this problem. This application builds off previous work done by myself and others [1] to create an extensible, abstract solution to rendering fractals. This paper covers …

Fundamentals Of Neutrosophic Logic And Sets And Their Role In Artificial Intelligence (Fundamentos De La Lógica Y Los Conjuntos Neutrosóficos Y Su Papel En La Inteligencia Artificial ), Florentin Smarandache, Maykel Leyva-Vazquez

Branch Mathematics and Statistics Faculty and Staff Publications

Neutrosophy is a new branch of philosophy which studies the origin, nature and scope of neutralities. This has formed the basis for a series of mathematical theories that generalize the classical and fuzzy theories such as the neutrosophic sets and the neutrosophic logic. In the paper, the fundamental concepts related to neutrosophy and its antecedents are presented. Additionally, fundamental concepts of artificial intelligence will be defined and how neutrosophy has come to strengthen this discipline.

Foreword By Guest Editors Maa 2018 Volume 18 Issue 4, Frank Prendergast, A. César González-García, Gary Wells, Juan Antonio Belmonte

Conference Papers

MAA SPECIAL ISSUE VOL 18 ISSUE 4:

Sixty-three (63) Selected (peer reviewed) Papers of the INSAP X – Oxford XI – SEAC 25th Joint Conference ‘ROAD TO THE STARS’, held in Santiago de Compostela, Spain, 18th–22nd September 2017

Mediterranean Archaeology and Archaeometry (MAA) is an Open Access Journal published since 2001 by The University of the Aegean, Department of Mediterranean Studies, Rhodes, Greece.

It covers the dual nature of archaeology and cultural heritage with science which includes, amongst others, natural science applied to archaeology (physics, chemistry, biology, geology, geophysics, astronomy), archaeology, ancient history, cultural sustainability, astronomy in culture, physical anthropology, …

Subset Vertex Graphs For Social Networks, Florentin Smarandache, W.B. Vasantha Kandasamy, K. Ilanthenral

Branch Mathematics and Statistics Faculty and Staff Publications

In this book authors for the first time introduce the notion of subset vertex graph using the vertex set as the subset of the power set P(S), S is assumed in this book to be finite; however it can be finite or infinite. We have defined two types of subset vertex graphs, one is directed and the other one is not directed. The most important fact which must be kept in record is that for a given set of vertices there exists one and only one subset vertex graph be it of type I or type II. Several important and …

Conjunto Plitogénico, Una Extensión De Los Conjuntos Crisp, Difusos, Conjuntos Difusos Intuicionistas Y Neutrosóficos Revisitado, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

En el presente artículo, introducimos el conjunto plitogénico (como generalización de conjuntos nítidos, borrosos, intuicionistas, borrosos y neutrosóficos), que es un conjunto cuyos elementos se caracterizan por los valores de muchos atrib utos. Un valor de atributo v tiene un grado correspondiente (difuso, intuicionista difuso o neutrosófico) de pertenencia d (x, v) del elemento x, al conjunto P, con respecto a algunos criterios dados. Para obtener una mejor precisión para los operadores d e agregación plitogénica en el conjunto plitogénico, y para una inclusión más exacta (orden parcial), se define un grado de contradicción (disimilitud difusa, intuicionista difusa o neutrosófica) …

Special Subset Vertex Subgraphs For Social Networks, Florentin Smarandache, W. B. Vasantha Kandasamy, Ilanthenral K

Branch Mathematics and Statistics Faculty and Staff Publications

In this book authors for the first time introduce the new notion of special subset vertex subgraph of subset vertex graphs introduced recently in [46]. These subset vertex graphs takes the vertex set values from the power set P(X) of any set X. The main speciality of these subset vertex graphs is that once a set of subsets from P(X) is given, the edges of the graph are fixed in a unique way, so for a given collection of subset vertices the graph is always unique [46]. The special subset vertex subgraphs of G are the ones, which have the …

Modelo De Recomendación Basado En Conocimiento Y Números Svn, Maykel Leyva-Vazquez, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

Recommendation models are useful in the decision-making process that allow the user a set of options that are expected to meet their expectations. Recommendation models are useful in the decision-making process that offer the user a set of options that are expected to meet their SVN expectations to express linguistic terms.

International Students’ Expectations Of Information Literacy Instruction, Nicole Johnston, Meggan Houlihan, Jodi Neindorf

Research outputs 2014 to 2021

This paper presents the findings of a case study that investigated international university students’ expectations and experiences of information literacy across two countries. The results from this case study provide insights that can be utilized by librarians working with international students, to plan and develop their information literacy instruction classes and programs. Armed with an awareness of what international students’ expectations and experiences with information literacy programs are, librarians can develop more meaningful instruction that better meets the information needs of international students. Moving beyond the pilot survey, the researchers aim to improve the survey instrument and collaborate with librarians …

Neutrosophic Logic: The Revolutionary Logic In Science And Philosophy -- Proceedings Of The National Symposium, Florentin Smarandache, Huda E. Khalid, Ahmed K. Essa

Branch Mathematics and Statistics Faculty and Staff Publications

The first part of this book is an introduction to the activities of the National Symposium, as well as a presentation of Neutrosophic Scientific International Association (NSIA), based in New Mexico, USA, also explaining the role and scope of NSIA - Iraqi branch. The NSIA Iraqi branch presents a suggestion for the international instructions in attempting to organize NSIA's work. In the second chapter, the pivots of the Symposium are presented, including a history of neutrosophic theory and its applications, the most important books and papers in the advancement of neutrosophics, a biographical note of Prof. Florentin Smarandache in Arabic …

Special Issue: Algebraic Structures Of Neutrosophic Triplets, Neutrosophic Duplets, Or Neutrosophic Multisets, Vol. I, Florentin Smarandache, Xiaohong Zhang, Mumtaz Ali

Branch Mathematics and Statistics Faculty and Staff Publications

Neutrosophy (1995) is a new branch of philosophy that studies triads of the form (, , ), where is an entity (i.e., element, concept, idea, theory, logical proposition, etc.), is the opposite of , while is the neutral (or indeterminate) between them, i.e., neither nor [1]. Based on neutrosophy, the neutrosophic triplets were founded; they have a similar form: (x, neut(x), anti(x), that satisfy some axioms, for each element x in a given set [2–4]. This book contains the successful invited submissions [5–56] to a special issue of Symmetry, reporting on state-of-the-art and recent advancements of neutrosophic triplets, neutrosophic …

Neutrosophic Linear Programming Problems, Florentin Smarandache, Abdel-Nasser Hussian, Mai Mohamed, Mohamed Abdel-Baset

Branch Mathematics and Statistics Faculty and Staff Publications

Smarandache presented neutrosophic theory as a tool for handling undetermined information. Wang et al. introduced a single valued neutrosophic set that is a special neutrosophic sets and can be used expediently to deal with real-world problems, especially in decision support. In this paper, we propose linear programming problems based on neutrosophic environment. Neutrosophic sets are characterized by three independent parameters, namely truth-membership degree (T), indeterminacy-membership degree (I) and falsity-membership degree (F), which are more capable to handle imprecise parameters. We also transform the neutrosophic linear programming problem into a crisp programming model by using neutrosophic set parameters. To measure the …

Operadores Con Conjunto Neutrosóficos De Valor Único Oversets, Undersets Y Offset, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

Neutrosophic Over-/Under-/Off-Set and Logic were defined for the first time in 1995 and published in 2007. During 1995-2016 was presented them to various national and international conferences and seminars. These new notions are totally different from other sets/logics/probabilities. We extended the neutrosophic set respectively to Neutrosophic Overset {when some neutrosophic component is > 1}, to Neutrosophic Underset {when some neutrosophic component is < 0}, and to Neutrosophic Offset {when some neutrosophic components are off the interval [0, 1], i.e. some neutrosophic component > 1 and other neutrosophic component < 0}. This is no surprise since our realworld has numerous examples and applications of over-/under-/off-neutrosophic components. Palabras clave. desbordado neutrosophic, underset neutrosophic, neutrosophic offset, neutrosophic sobre la lógica, neutrosophic bajo la lógica, neutrosophic off lógica, neutrosophic sobre la probabilidad, neutrosophic bajo probabilidad, neutrosophic de probabilidad, más de miembros (grado de pertenencia> 1), bajo de miembros (grado de pertenencia <0) , (grado de pertenencia fuera del intervalo [0, 1]) offmembership.

Neutrosophic Computing With Sympy (Computación Neutrosófica Mediante Sympy ), Maykel Leyva-Vazquez, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

In this article the concept of neutrosophic number is presented. Jupyter through Google Colaboratory is introduced for calculations. The Sympy library is used to perform the process of neutrosophic computation. Systems of linear neutrosóficas equations are solved by means of the symbolic computation in python. A case study was developed for the determination of vehicular traffic with indeterminacy. As future works are the development of new applications in different areas of engineering and science.

N-Valued Refined Neutrosophic Logic And Its Applications To Physics (Lógica Neutrosófica Refinada N-Valuada Y Sus Aplicaciones A La Física), Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

In this paper we present a short history of logics: from particular cases of 2-symbol or numerical valued logic to the general case of n-symbol or numerical valued logic. We show generalizations of 2-valued Boolean logic to fuzzy logic, also from the Kleene’s and Lukasiewicz’ 3-symbol valued logics or Belnap’s 4-symbol valued logic to the most general nsymbol or numerical valued refined neutrosophic logic. Examples of applications of neutrosophic logic to physics are listed in the last section. Similar generalizations can be done for n-Valued Refined Neutrosophic Set, and respectively.

Mental Models And Neutrosophic Cognitive Maps (Modelos Mentales Y Mapas Cognitivos Neutrosóficos), Maykel Leyva-Vazquez, Rebeca Escobar-Jara, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

In this work, elements related to mental models elicitation and analysis are addressed through causal models. Issues related to the need to include indeterminacy in causal relationships through neutrophic cognitive maps are discussed. A proposal for static analysis in neutrosophic cognitive maps is presented. The following activities are included in the proposal: Calculate, measures of centrality, Classify nodes, De-neutrosification, and Ranking nodes. As future works, the incorporation of new metrics of centrality in neutrosophic cognitive maps is proposed. The inclusion of scenario analysis to the proposal is another area of future work.

Multipliers Between Model Spaces, Emmanuel Fricain, Andreas Hartmann, William T. Ross

Department of Math & Statistics Faculty Publications

In this paper we examine the multipliers from one model space to another.