Logic and Foundations Commons^™

Neutrosophic Hough Transform, Florentin Smarandache, Umit Budak, Yanhui Guo, Abdulkadir Sengur

Branch Mathematics and Statistics Faculty and Staff Publications

Hough transform (HT) is a useful tool for both pattern recognition and image processing communities. In the view of pattern recognition, it can extract unique features for description of various shapes, such as lines, circles, ellipses, and etc. In the view of image processing, a dozen of applications can be handled with HT, such as lane detection for autonomous cars, blood cell detection in microscope images, and so on. As HT is a straight forward shape detector in a given image, its shape detection ability is low in noisy images. To alleviate its weakness on noisy images and improve its …

Graph Structures In Bipolar Neutrosophic Environment, Florentin Smarandache, Muhammad Akram, Muzzamal Sitara

Branch Mathematics and Statistics Faculty and Staff Publications

A bipolar single-valued neutrosophic (BSVN) graph structure is a generalization of a bipolar fuzzy graph. In this research paper, we present certain concepts of BSVN graph structures. We describe some operations on BSVN graph structures and elaborate on these with examples. Moreover, we investigate some related properties of these operations.

Ideas And Graphs, Martin Zwick

Complex Systems Faculty Publications and Presentations

A graph can specify the skeletal structure of an idea, onto which meaning can be added by interpreting the structure.

This paper considers graphs (but not hypergraphs) consisting of four nodes, and suggests meanings that can be associated with several different directed and undirected graphs.

Drawing on Bennett's "systematics," specifically on the Tetrad that systematics offers as a model of 'activity,' the analysis here shows that the Tetrad is versatile model of problem-solving, regulation and control, and other processes.

Slides are available below.

Formalizing The Panarchy Adaptive Cycle With The Cusp Catastrophe [Presentation], Martin Zwick, Joshua Hughes

Complex Systems Faculty Publications and Presentations

The panarchy adaptive cycle, a general model for change in natural and human systems, can be formalized by the cusp catastrophe of René Thom's topological theory. Both the adaptive cycle and the cusp catastrophe have been used to model ecological, economic, and social systems in which slow and small continuous changes in two control variables produce fast and large discontinuous changes in system behavior. The panarchy adaptive cycle, the more recent of the two models, has been used so far only for qualitative descriptions of typical dynamics of such systems. The cusp catastrophe, while also often employed qualitatively, is a …

Neutrosophic N -Structures And Their Applications In Semigroups, Florentin Smarandache, Madad Khan, Saima Anis, Young Bae Jun

Branch Mathematics and Statistics Faculty and Staff Publications

The notion of neutrosophic N -structure is introduced, and applied it to semigroup. The notions of neutrosophic N -subsemigroup, neutrosophic N -product and ε-neutrosophic N -subsemigroup are introduced, and several properties are investigated. Conditions for neutrosophic N -structure to be neutrosophic N -subsemigroup are provided. Using neutrosophic N -product, characterization of neutrosophic N -subsemigroup is discussed. Relations between neutrosophic N -subsemigroup and εneutrosophic N -subsemigroup are discussed. We show that the homomorphic preimage of neutrosophic N -subsemigroup is a neutrosophic N - subsemigroup, and the onto homomorphic image of neutrosophic N - subsemigroup is a neutrosophic N -subsemigroup.

Neutrosophic N -Structures Applied To Bck/Bci-Algebras, Florentin Smarandache, Young Bae Jun, Hashem Bordbar

Branch Mathematics and Statistics Faculty and Staff Publications

Neutrosophic N -structures with applications in BCK/BC I-algebras is discussed. The notions of a neutrosophic N -subalgebra and a (closed) neutrosophic N -ideal in a BCK/BC I-algebra are introduced, and several related properties are investigated. Characterizations of a neutrosophic N -subalgebra and a neutrosophic N -ideal are considered, and relations between a neutrosophic N -subalgebra and a neutrosophic N -ideal are stated. Conditions for a neutrosophic N -ideal to be a closed neutrosophic N -ideal are provided.

Neutrosophic Commutative N-Ideals In Bck-Algebras, Florentin Smarandache, Seok-Zun Song, Young Bae Jun

Branch Mathematics and Statistics Faculty and Staff Publications

The notion of a neutrosophic commutative N -ideal in BCK-algebras is introduced, and several properties are investigated. Relations between a neutrosophic N -ideal and a neutrosophic commutative N -ideal are discussed. Characterizations of a neutrosophic commutative N -ideal are considered.

Interstructure Lattices And Types Of Peano Arithmetic, Athar Abdul-Quader

Dissertations, Theses, and Capstone Projects

The collection of elementary substructures of a model of PA forms a lattice, and is referred to as the substructure lattice of the model. In this thesis, we study substructure and interstructure lattices of models of PA. We apply techniques used in studying these lattices to other problems in the model theory of PA.

In Chapter 2, we study a problem that had its origin in Simpson, who used arithmetic forcing to show that every countable model of PA has an expansion to PA^∗ that is pointwise definable. Enayat later showed that there are 2^ℵ₀ models with …

Ns-K-Nn: Neutrosophic Set-Based K-Nearest Neighbors Classifier, Florentin Smarandache, Yaman Akbulut, Abdulkadir Sengur, Yanhui Guo

Branch Mathematics and Statistics Faculty and Staff Publications

k-nearest neighbors (k-NN), which is known to be a simple and efficient approach, is a non-parametric supervised classifier. It aims to determine the class label of an unknown sample by its k-nearest neighbors that are stored in a training set. The k-nearest neighbors are determined based on some distance functions. Although k-NN produces successful results, there have been some extensions for improving its precision. The neutrosophic set (NS) defines three memberships namely T, I and F. T, I, and F shows the truth membership degree, the false membership degree, and the indeterminacy membership degree, respectively. In this paper, the NS …

Complex Neutrosophic Soft Set, Florentin Smarandache, Said Broumi, Assia Bakali, Mohamed Talea, Mumtaz Ali, Ganeshsree Selvachandran

Branch Mathematics and Statistics Faculty and Staff Publications

In this paper, we propose the complex neutrosophic soft set model, which is a hybrid of complex fuzzy sets, neutrosophic sets and soft sets. The basic set theoretic operations and some concepts related to the structure of this model are introduced, and illustrated. An example related to a decision making problem involving uncertain and subjective information is presented, to demonstrate the utility of this model.

Shortest Path Problem Under Triangular Fuzzy Neutrosophic Information, Florentin Smarandache, Said Broumi, Assia Bakali, Mohamed Talea, Luige Vladareanu

Branch Mathematics and Statistics Faculty and Staff Publications

In this paper, we develop a new approach to deal with neutrosphic shortest path problem in a network in which each edge weight (or length) is represented as triangular fuzzy neutrosophic number. The proposed algorithm also gives the shortest path length from source node to destination node using ranking function. Finally, an illustrative example is also included to demonstrate our proposed approach.

Complex Neutrosophic Graphs Of Type 1, Florentin Smarandache, Said Broumi, Assia Bakali, Mohamed Talea

Branch Mathematics and Statistics Faculty and Staff Publications

In this paper, we introduced a new neutrosophic graphs called complex neutrosophic graphs of type1 (CNG1) and presented a matrix representation for it and studied some properties of this new concept. The concept of CNG1 is an extension of generalized fuzzy graphs of type 1 (GFG1) and generalized single valued neutrosophic graphs of type 1 (GSVNG1).

Joint Laver Diamonds And Grounded Forcing Axioms, Miha Habič

Dissertations, Theses, and Capstone Projects

In chapter 1 a notion of independence for diamonds and Laver diamonds is investigated. A sequence of Laver diamonds for κ is joint if for any sequence of targets there is a single elementary embedding j with critical point κ such that each Laver diamond guesses its respective target via j. In the case of measurable cardinals (with similar results holding for (partially) supercompact cardinals) I show that a single Laver diamond for κ yields a joint sequence of length κ, and I give strict separation results for all larger lengths of joint sequences. Even though the principles get …

Representation And Decomposition Of An Intuitionistic Fuzzy Matrix Using Some (Α, Α') Cuts, T. Muthuraji, S. Sriram

Applications and Applied Mathematics: An International Journal (AAM)

The aim of this paper is to study the properties of various (α, α') cuts on Intuitionistic Fuzzy Matrices. Here we introduce different kinds of cuts on Intuitionistic Fuzzy Sets. We discuss some properties of the cuts with some other existing operators on Intuitionistic Fuzzy Matrix. Finally some representation and decomposition of an Intuitionistic Fuzzy Matrix using (α, α') cuts are given.

Neutrosophy, A Sentiment Analysis Model, Florentin Smarandache, Mirela Teodorescu, Daniela Gifu

Branch Mathematics and Statistics Faculty and Staff Publications

This paper describes the importance of Neutrosophy Theory in order to find a method that could solve the uncertainties arising on discursive analysis. The aim of this pilot study is to find a procedure to diminish the uncertainties from public discourse induced, especially, by humans (politicians, journalists, etc.). We consider that Neutrosophy Theory is a sentiment analysis specific case regarding processing of the three states: positive, negative, and neutral. The study is intended to identify a method to answer to uncertainties solving in order to support politician's staff, NLP specialists, artificial intelligence researchers and generally the electors.

On Tarski's Axiomatic Foundations Of The Calculus Of Relations, Hajnal Andréka, Steven Givant, Peter Jipsen, István Németi

Mathematics, Physics, and Computer Science Faculty Articles and Research

It is shown that Tarski’s set of ten axioms for the calculus of relations is independent in the sense that no axiom can be derived from the remaining axioms. It is also shown that by modifying one of Tarski’s axioms slightly, and in fact by replacing the right-hand distributive law for relative multiplication with its left-hand version, we arrive at an equivalent set of axioms which is redundant in the sense that one of the axioms, namely the second involution law, is derivable from the other axioms. The set of remaining axioms is independent. Finally, it is shown that if …

Mcdm Method For N-Wise Criteria Comparisons And Inconsistent Problems, Florentin Smarandache, Azeddine Elhassouny

Branch Mathematics and Statistics Faculty and Staff Publications

The purpose of this paper is to present an e[xtension and alternative of the hybrid method based on Saaty’s Analytical Hierarchy Process and Technique for Order Preference by Similarity to Ideal Solution method (AHP-TOPSIS), that based on the AHP and its use of pairwise comparisons, to a new method called α -D MCDM-TOPSIS( α -Discounting Method for multicriteria decision making-TOPSIS). The new method overcomes limits of AHP which work only for pairwise comparisons of criteria to any-wise (n-wise) comparisons, with crisp coefficients or with interval-valued coefficients. α-D MCDM-TOPSIS is verified by some examples to demonstrate how it allows for consistency, …

Relation Algebras, Idempotent Semirings And Generalized Bunched Implication Algebras, Peter Jipsen

Mathematics, Physics, and Computer Science Faculty Articles and Research

This paper investigates connections between algebraic structures that are common in theoretical computer science and algebraic logic. Idempotent semirings are the basis of Kleene algebras, relation algebras, residuated lattices and bunched implication algebras. Extending a result of Chajda and Länger, we show that involutive residuated lattices are determined by a pair of dually isomorphic idempotent semirings on the same set, and this result also applies to relation algebras. Generalized bunched implication algebras (GBI-algebras for short) are residuated lattices expanded with a Heyting implication. We construct bounded cyclic involutive GBI-algebras from so-called weakening relations, and prove that the class of weakening …

On Benacerraf’S Dilemma, Again, Marco Panza

MPP Published Research

In spite of its enormous influence, Benacerraf’s dilemma admits no standard unanimously accepted formulation. This mainly depends on Benacerraf’s having originally presented it in a quite colloquial way, by avoiding any compact, somehow codified, but purportedly comprehensive formulation (Benacerraf 1973 cf. p. 29).

From Pythagoreans And Weierstrassians To True Infinitesimal Calculus, Mikhail Katz, Luie Polev

Journal of Humanistic Mathematics

In teaching infinitesimal calculus we sought to present basic concepts like continuity and convergence by comparing and contrasting various definitions, rather than presenting “the definition” to the students as a monolithic absolute. We hope that our experiences could be useful to other instructors wishing to follow this method of instruction. A poll run at the conclusion of the course indicates that students tend to favor infinitesimal definitions over epsilon-delta ones.

The Proscriptive Principle And Logics Of Analytic Implication, Thomas M. Ferguson

Dissertations, Theses, and Capstone Projects

The analogy between inference and mereological containment goes at least back to Aristotle, whose discussion in the Prior Analytics motivates the validity of the syllogism by way of talk of parts and wholes. On this picture, the application of syllogistic is merely the analysis of concepts, a term that presupposes—through the root ἀνά + λύω —a mereological background.

In the 1930s, such considerations led William T. Parry to attempt to codify this notion of logical containment in his system of analytic implication AI. Parry’s original system AI was later expanded to the system PAI. The hallmark of Parry’s systems—and of …

Sudoku Variants On The Torus, Kira A. Wyld

HMC Senior Theses

This paper examines the mathematical properties of Sudoku puzzles defined on a Torus. We seek to answer the questions for these variants that have been explored for the traditional Sudoku. We do this process with two such embeddings. The end result of this paper is a deeper mathematical understanding of logic puzzles of this type, as well as a fun new puzzle which could be played.

Features Of Agent-Based Models, Reiko Heckel, Alexander Kurz, Edmund Chattoe-Brown

Engineering Faculty Articles and Research

The design of agent-based models (ABMs) is often ad-hoc when it comes to defining their scope. In order for the inclusion of features such as network structure, location, or dynamic change to be justified, their role in a model should be systematically analysed. We propose a mechanism to compare and assess the impact of such features. In particular we are using techniques from software engineering and semantics to support the development and assessment of ABMs, such as graph transformations as semantic representations for agent-based models, feature diagrams to identify ingredients under consideration, and extension relations between graph transformation systems to …

A Bipolar Single Valued Neutrosophic Isolated Graphs: Revisited, Florentin Smarandache, Said Broumi, Assia Bakali, Mohamed Talea, Mohsin Khan

Branch Mathematics and Statistics Faculty and Staff Publications

In this research paper, the graph of the bipolar single-valued neutrosophic set model (BSVNS) is proposed. The graphs of single valued neutrosophic set models is generalized by this graph. For the BSVNS model, several results have been proved on complete and isolated graphs. Adding, an important and suitable condition for the graphs of the BSVNS model to become an isolated graph of the BSVNS model has been demonstrated.

Curiozităţi Ale Funcţiilor Supermatematice, Florentin Smarandache, Mircea Eugen Selariu

Branch Mathematics and Statistics Faculty and Staff Publications

No abstract provided.

Platonismes, Marco Panza

MPP Published Research

Selon la vulgata philosophique, le platonisme concernant un certain domaine de recherche est la thèse affirmant que ce domaine concerne des objets qui lui sont propres, dont l’existence est indépendante de l’activité cognitive humaine. Souvent, dans la même vulgata on parle aussi de platonisme pour se référer à une thèse un peu différente, d’après laquelle ce qu’on dit concernant ce domaine est vrai ou faux indépendamment de toute justification ou réfutation que l’on puisse apporter. Naturellement, si parmi les énoncées ayant trait à ce demain, il y en a qu’on peut prendre comme particulièrement surs du fait d’en avoir une …

Predicting Risk Of Adverse Outcomes In Knee Replacement Surgery With Reconstructability Analysis, Cecily Corrine Froemke, Martin Zwick

Complex Systems Faculty Publications and Presentations

Reconstructability Analysis (RA) is a data mining method that searches for relations in data, especially non-linear and higher order relations. This study shows that RA can provide useful predictions of complications in knee replacement surgery.

Four Years With Russell, Gödel, And Erdős: An Undergraduate's Reflection On His Mathematical Education, Michael H. Boggess

CMC Senior Theses

Senior Thesis at CMC is often described institutionally as the capstone of one’s undergraduate education. As such, I wanted my own to accurately capture and reflect how I’ve grown as a student and mathematician these past four years. What follows is my attempt to distill lessons I learned in mathematics outside the curriculum, written for incoming undergraduates and anyone with just a little bit of mathematical curiosity. In it, I attempt to dispel some common preconceptions about mathematics, namely that it’s uninteresting, formulaic, acultural, or completely objective, in favor of a dynamic historical and cultural perspective, with particular attention paid …

Introducing A Theory Of Neutrosophic Evolution: Degrees Of Evolution, Indeterminacy, And Involution, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

During the process of adaptation of a being (plant, animal, or human), to a new environment or conditions, the being partially evolves, partially devolves (degenerates), and partially is indeterminate i.e. neither evolving nor devolving, therefore unchanged (neutral), or the change is unclear, ambiguous, vague, as in neutrosophic logic. Thank to adaptation, one therefore has: evolution, involution, and indeterminacy (or neutrality), each one of these three neutrosophic components in some degree. The degrees of evolution/indeterminacy/involution are referred to both: the structure of the being (its body parts), and functionality of the being (functionality of each part, or inter-functionality of the parts …

Neutrosophic Perspectives: Triplets, Duplets, Multisets, Hybrid Operators, Modal Logic, Hedge Algebras. And Applications (Second Extended And Improved), Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

This book is part of the book-series dedicated to the advances of neutrosophic theories and their applications, started by the author in 1998. Its aim is to present the last developments in the field. For the first time, we now introduce:

— Neutrosophic Duplets and the Neutrosophic Duplet Structures;

— Neutrosophic Multisets (as an extension of the classical multisets);

— Neutrosophic Spherical Numbers;

— Neutrosophic Overnumbers / Undernumbers / Offnumbers;

— Neutrosophic Indeterminacy of Second Type;

— Neutrosophic Hybrid Operators (where the heterogeneous t-norms and t-conorms may be used in designing neutrosophic aggregations);

— Neutrosophic Triplet Loop;

— Neutrosophic Triplet …