Logic and Foundations Commons^™

Some Operations Over Pythagorean Fuzzy Matrices Based On Hamacher Operations, I. Silambarasan, S. Sriram

Applications and Applied Mathematics: An International Journal (AAM)

Pythagorean fuzzy matrix is a powerful tool for describing the vague concepts more precisely. The Pythagorean fuzzy matrix based models provide more flexibility in handling the human judgment information as compared to other fuzzy models. The objective of this paper is to apply the concept of intuitionistic fuzzy matrices to Pythagorean fuzzy matrices. In this paper, we briefly introduce the Pythagorean fuzzy matrices and some theorems and examples are applied to illustrate the performance of the proposed methods. Then we define the Hamacher scalar multiplication (n._hA) and Hamacher exponentiation (A^^hn) operations on Pythagorean fuzzy matrices and …

Derivable Single Valued Neutrosophic Graphs Based On Km-Fuzzy Metric, Florentin Smarandache, Mohammad Hamidi

Branch Mathematics and Statistics Faculty and Staff Publications

In this paper we consider the concept of KM-fuzzy metric spaces and we introduce a novel concept of KM-single valued neutrosophic metric graphs based on KM-fuzzy metric spaces. Then we investigate the finite KM-fuzzy metric spaces with respect to KM-fuzzy metrics and we construct the KMfuzzy metric spaces on any given non-empty sets. We try to extend the concept of KM-fuzzy metric spaces to a larger class of KM-fuzzy metric spaces such as union and product of KM-fuzzy metric spaces and in this regard we investigate the class of products of KM-single valued neutrosophic metric graphs. In the final, we …

A Paradox Solved (Or 3), Lee Grisham

Scholars Day Conference

I gained an interest in paradoxes when I was introduced to the Grandfather paradox as a child, and began studying time travel, along with all the effects and thought experiments it could lead to. This, in turn, led to my researching many more paradoxes and having something to do in my free time that didn’t require anything outside my own thoughts. Several paradoxes I found stumped me then, and still do to this day. However, there are some that I have recently begun to feel like I am understanding much more clearly. One day this past semester, I was thinking …

Inductive Constructions In Logic And Graph Theory, Davis Deaton

Honors Scholars Collaborative Projects

Just as much as mathematics is about results, mathematics is about methods. This thesis focuses on one method: induction. Induction, in short, allows building complex mathemati- cal objects from simple ones. These mathematical objects include the foundational, like logical statements, and the abstract, like cell complexes. Non-mathematicians struggle to find a common thread throughout all of mathematics, but I present induction as such a common thread here. In particular, this thesis discusses everything from the very foundations of mathematics all the way to combina- torial manifolds. I intend to be casual and opinionated while still providing all necessary formal rigor. …

Collaboration (Reacting To The Past/Math/History/Writing), James Hayashi

Q2S Enhancing Pedagogy

This is an assignment for a Freshman level course in the College of Natural Science. By the end students will have an understanding of valid research, collaboration and communication skills. Faculty that chooses to use this assignment will be preparing students for an active learning environment, and understanding a “Big Idea”, valid research, technology and communication skills.

Faculty should give an example of what is valid research. As students are completing this assignment mini deadlines (check-ins) shall be set. With the check-ins for this assignment focus on how the group will communicate the check point and the collaboration.

The focus …

Semi De Morgan Logic Properly Displayed, Giuseppe Greco, Fei Qin, M. Andrew Moshier, Alessandra Palmigiano

Mathematics, Physics, and Computer Science Faculty Articles and Research

In the present paper, we endow semi De Morgan logic and a family of its axiomatic extensions with proper multi-type display calculi which are sound, complete, conservative, and enjoy cut elimination and subformula property. Our proposal builds on an algebraic analysis of the variety of semi De Morgan algebras, and applies the guidelines of the multi-type methodology in the design of display calculi.

Math 220p Foundations Of Mathematics, Nicholas Vlamis

Open Educational Resources

No abstract provided.

Introduction To Game Theory: A Discovery Approach, Jennifer Firkins Nordstrom

Linfield Authors Book Gallery

Game theory is an excellent topic for a non-majors quantitative course as it develops mathematical models to understand human behavior in social, political, and economic settings. The variety of applications can appeal to a broad range of students. Additionally, students can learn mathematics through playing games, something many choose to do in their spare time! This text also includes an exploration of the ideas of game theory through the rich context of popular culture. It contains sections on applications of the concepts to popular culture. It suggests films, television shows, and novels with themes from game theory. The questions in …

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 …

Fifteenth International Photovideoanthology On Paradoxism, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

Paradoxism is an international movement in science and culture, founded by Florentin Smarandache in 1980s, based on excessive use of antitheses, oxymoron, contradictions, and paradoxes. During three decades (1980-2020) hundreds of authors from tenth of countries around the globe contributed papers to 15 international paradoxist anthologies.

In 1995, the author extended the paradoxism to a new branch of philosophy called neutrosophy, that gave birth to many scientific branches, such as: neutrosophic logic, neutrosophic set, neutrosophic probability and statistics, neutrosophic algebraic structures and so on with multiple applications in engineering, computer science, administrative work, medical research etc.

“May your imagination blossom …

N-Refined Neutrosophic Rings, Florentin Smarandache, Mohammad Abobala

Branch Mathematics and Statistics Faculty and Staff Publications

The aim of this paper is to introduce the concept of n-refined neutrosophic ring as a generalization of refined neutrosophic ring. Also, we present concept of n-refined polynomial ring. We study some basic concepts related to these rings such as AH-subrings, AH-ideals, AH-factors, and AH-homomorphisms.

Neutrosophic In Latin America, Advances And Perspectives (Neutrosofía En Latinoamérica, Avances Y Perspectivas), Maykel Leyva-Vazquez, Jesus Estupinan, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

Neutrosophy has given way to its own research method by constituting a unified field of logic for a transdisciplinary study that crosses the borders between the sciences. This paper analyzes the impact of neutrosophic theory in Latin America, its main drivers and the state of the research. The increase in publications since the creation of the Latin American Association of Neutrosophic Sciences is noteworthy. The most approached areas are found in the interrelation of the social sciences and neutrosophy, presenting outstanding results in these areas of research. The most outstanding university and institutions are the Autonomous Regional University of the …

A Coherent Proof Of Mac Lane's Coherence Theorem, Luke Trujillo

HMC Senior Theses

Mac Lane’s Coherence Theorem is a subtle, foundational characterization of monoidal categories, a categorical concept which is now an important and popular tool in areas of pure mathematics and theoretical physics. Mac Lane’s original proof, while extremely clever, is written somewhat confusingly. Many years later, there still does not exist a fully complete and clearly written version of Mac Lane’s proof anywhere, which is unfortunate as Mac Lane’s proof provides very deep insight into the nature of monoidal categories. In this thesis, we provide brief introductions to category theory and monoidal categories, and we offer a precise, clear development of …

Introduction To Neutroalgebraic Structures And Antialgebraic Structures (Revisited), Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

In all classical algebraic structures, the Laws of Compositions on a given set are well-defined. But this is a restrictive case, because there are many more situations in science and in any domain of knowledge when a law of composition defined on a set may be only partially-defined (or partially true) and partially-undefined (or partially false), that we call NeutroDefined, or totally undefined (totally false) that we call AntiDefined. Again, in all classical algebraic structures, the Axioms (Associativity, Commutativity, etc.) defined on a set are totally true, but it is again a restrictive case, because similarly there are numerous situations …

Neutroalgebra Is A Generalization Of Partial Algebra, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

In this paper we recall, improve, and extend several definitions, properties and applications of our previous 2019 research referred to NeutroAlgebras and AntiAlgebras (also called NeutroAlgebraic Structures and respectively AntiAlgebraic Structures). Let be an item (concept, attribute, idea, proposition, theory, etc.). Through the process of neutrosphication, we split the nonempty space we work on into three regions {two opposite ones corresponding to and , and one corresponding to neutral (indeterminate) (also denoted ) between the opposites}, which may or may not be disjoint – depending on the application, but they are exhaustive (their union equals the whole space). A NeutroAlgebra …

Quadruple Neutrosophic Theory And Applications Volume I, Florentin Smarandache, Memet Şahin, Vakkas Uluçay, Abdullah Kargin

Branch Mathematics and Statistics Faculty and Staff Publications

Neutrosophic set has been derived from a new branch of philosophy, namely Neutrosophy. Neutrosophic set is capable of dealing with uncertainty, indeterminacy and inconsistent information. Neutrosophic set approaches are suitable to modeling problems with uncertainty, indeterminacy and inconsistent information in which human knowledge is necessary, and human evaluation is needed. Neutrosophic set theory firstly proposed in 1998 by Florentin Smarandache, who also developed the concept of single valued neutrosophic set, oriented towards real world scientific and engineering applications. Since then, the single valued neutrosophic set theory has been extensively studied in books and monographs introducing neutrosophic sets and its applications, …

Neutro-Bck-Algebra, Florentin Smarandache, Mohammad Hamidi

Branch Mathematics and Statistics Faculty and Staff Publications

This paper introduces the novel concept of Neutro-BCK-algebra. In Neutro-BCK-algebra, the outcome of any given two elements under an underlying operation (neutro-sophication procedure) has three cases, such as: appurtenance, non-appurtenance, or indeterminate. While for an axiom: equal, non-equal, or indeterminate. This study investigates the Neutro-BCK-algebra and shows that Neutro-BCK-algebra are different from BCK-algebra. The notation of Neutro-BCK-algebra generates a new concept of NeutroPoset and Neutro-Hass-diagram for NeutroPosets. Finally, we consider an instance of applications of the Neutro-BCK-algebra.

On Neutro-Be-Algebras And Anti-Be-Algebras, Florentin Smarandache, Akbar Rezaei

Branch Mathematics and Statistics Faculty and Staff Publications

In this paper, the concepts of Neutro-BE-algebra and Anti-BE-algebra are introduced, and some related properties and four theorems are investigated. We show that the classes of Neutro-BE-algebra and Anti-BE-algebras are alternatives of the class of BE-algebras.

Generalizations And Alternatives Of Classical Algebraic Structures To Neutroalgebraic Structures And Antialgebraic Structures, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

In this paper we present the development from paradoxism to neutrosophy, which gave birth to neutrosophic set and logic and especially to NeutroAlgebraic Structures (or NeutroAlgebras) and AntiAlgebraic Structures (or AntiAlgebras) that are generalizations and alternatives of the classical algebraic structures.

Interval Valued Neutrosophic Shortest Path Problem By A* Algorithm, Florentin Smarandache, S. Khrisna Prabha, Said Broumi

Branch Mathematics and Statistics Faculty and Staff Publications

Many researchers have been proposing various algorithms to unravel different types of fuzzy shortest path problems. There are many algorithms like Dijkstra’s, Bellman-Ford,Floyd-Warshall and kruskal’s etc are existing for solving the shortest path problems. In this work a shortest path problem with interval valued neutrosophic numbers is investigated using the proposed algorithm. A* algorithm is extensively applied in pathfinding and graph traversal.Unlike the other algorithms mentioned above, A* algorithm entails heuristic function to uncover the cost of path that traverses through the particular state. In the structured work A* algorithm is applied to unravel the length of the shortest path …