Logic and Foundations Commons^™

The Positivication Of Coalgebraic Logics, Fredrik Dahlqvist, Alexander Kurz

Engineering Faculty Articles and Research

We present positive coalgebraic logic in full generality, and show how to obtain a positive coalgebraic logic from a boolean one. On the model side this involves canonically computing a endofunctor T': Pos->Pos from an endofunctor T: Set->Set, in a procedure previously defined by the second author et alii called posetification. On the syntax side, it involves canonically computing a syntax-building functor L': DL->DL from a syntax-building functor L: BA->BA, in a dual procedure which we call positivication. These operations are interesting in their own right and we explicitly compute posetifications and positivications in the case …

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 …

Neutrosophic Triplet Groups And Their Applications To Mathematical Modelling, Florentin Smarandache, W.B. Vasantha Kandasamy, Ilanthenral K.

Branch Mathematics and Statistics Faculty and Staff Publications

The innovative notion of neutrosophic triplet groups, introduced by Smarandache and Ali in 2014-2016, happens to yield the anti-element and neutral element once the element is given. It is established that the neutrosophic triplet group collection forms the classical group under product for Zn, for some specific n. However the collection is not even closed under sum. These neutrosophic triplet groups are built using only modulo integers or Cayley tables. Several interesting properties related with them are defined. It is pertinent to record that in Zn, when n is a prime number, we cannot get a neutral element which can …

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 …

Generalized Interval Valued Neutrosophic Graphs Of First Type, Florentin Smarandache, Said Broumi, Mohamed Talea, Assia Bakali, Ali Hassan

Branch Mathematics and Statistics Faculty and Staff Publications

In this paper, motivated by the notion of generalized single valued neutrosophic graphs of first type, we defined a new neutrosophic graphs named generalized interval valued neutrosophic graphs of first type (GIVNG1) and presented a matrix representation for it and studied few properties of this new concept. The concept of GIVNG1 is an extension of generalized fuzzy graphs (GFG1) and generalized single valued neutrosophic of first type (GSVNG1).

Computation Of Shortest Path Problem In A Network With Sv-Triangular Neutrosophic Numbers, Florentin Smarandache, Said Broumi, Assia Bakali, Mohamed Talea

Branch Mathematics and Statistics Faculty and Staff Publications

In this article, we present an algorithm method for finding the shortest path length between a paired nodes on a network where the edge weights are characterized by single valued triangular neutrosophic numbers. The proposed algorithm gives the shortest shortest path length from source node to destination node based on a ranking method. Finally, a numerical example is also presented to illustrate the efficiency of the proposed approach.

Neutrosophic Operational Research - Vol. 2, Florentin Smarandache, Mohamed Abdel Basset, Victor Chang

Branch Mathematics and Statistics Faculty and Staff Publications

Foreword John R. Edwards This book is an excellent exposition of the use of Data Envelopment Analysis (DEA) to generate data analytic insights to make evidence-based decisions, to improve productivity, and to manage cost-risk and benefitopportunity in public and private sectors. The design and the content of the book make it an up-to-date and timely reference for professionals, academics, students, and employees, in particular those involved in strategic and operational decisionmaking processes to evaluate and prioritize alternatives to boost productivity growth, to optimize the efficiency of resource utilization, and to maximize the effectiveness of outputs and impacts to stakeholders. It …

Complex Valued Graphs For Soft Computing, 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 in a systematic way the notion of complex valued graphs, strong complex valued graphs and complex neutrosophic valued graphs. Several interesting properties are defined, described and developed. Most of the conjectures which are open in case of usual graphs continue to be open problems in case of both complex valued graphs and strong complex valued graphs. We also give some applications of them in soft computing and social networks. At this juncture it is pertinent to keep on record that Dr. Tohru Nitta was the pioneer to use complex valued graphs …

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 …

The Use Of The Pivot Pairwise Relative Criteria Importance Assessment Method For Determining The Weights Of Criteria, Florentin Smarandache, Dragisa Stanujkic, Edmundas Kazimieras Zavadskas, Darjan Karabasevic, Zenonas Turskis

Branch Mathematics and Statistics Faculty and Staff Publications

The weights of evaluation criteria could have a significant impact on the results obtained by applying multiple criteria decision-making methods. Therefore, the two extensions of the SWARA method that can be used in cases when it is not easy, or even is impossible to reach a consensus on the expected importance of the evaluation criteria are proposed in this paper. The primary objective of the proposed extensions is to provide an understandable and easy-to-use approach to the collecting of respondents’ real attitudes towards the significance of evaluation criteria and to also provide an approach to the checking of the reliability …

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.

Foreword: Special Issue On Coalgebraic Logic, Alexander Kurz

Engineering Faculty Articles and Research

The second Dagstuhl seminar on coalgebraic logics took place from October 7-12, 2012, in the Leibniz Forschungszentrum Schloss Dagstuhl, following a successful earlier one in December 2009. From the 44 researchers who attended and the 30 talks presented, this collection highlights some of the progress that has been made in the field. We are grateful to Giuseppe Longo and his interest in a special issue in Mathematical Structures in Computer Science.

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 …

Reduction Of A Nilpotent Intuitionistic Fuzzy Matrix Using Implication Operator, Riyaz A. Padder, P. Murugadas

Applications and Applied Mathematics: An International Journal (AAM)

A problem of reducing intuitionistic fuzzy matrices is examined and some useful properties are obtained with respect to nilpotent intutionistic fuzzy matrices. First, reduction of irreflexive and transitive intuitionistic fuzzy matrices are considered, and then the properties are applied to nilpotent intutionistic fuzzy matrices. Nilpotent intuitionistic fuzzy matrices are intuitionistic fuzzy matrices which signify acyclic graphs, and the graphs are used to characterize consistent systems. The properties are handy for generalization of various systems with intuitionistic fuzzy transitivity.

Secondary Analysis Of Concussion Data, Martin Zwick, Stephanie Kolakowsky-Hayner, Nancy Carney, Maya Balamane, Tracie Nettleton, D. Wright

Complex Systems Faculty Publications and Presentations

Clinical studies are expensive & time-consuming. Typically in these studies specific hypotheses are subjected to confirmatory test. Yet the data may harbor evidence of unanticipated relations between variables. It is thus desirable to subject the data to secondary analyses in the hope of discovering novel & valuable associations. Exploratory analysis, however, is tentative: findings should be replicated in new data. This presentation reports some secondary analyses on concussion data. Data mining on 2 datasets will be discussed, & some unexpected findings reported. The analyses use reconstructability analysis (RA), a probabilistic graphical modeling method implemented in the Occam software package developed …

Computation Of Shortest Path Problem In A Network With Sv-Trapezoidal Neutrosophic Numbers, Florentin Smarandache, Said Broumi, Assia Bakali, Mohamed Talea, Luige Vladareanu

Branch Mathematics and Statistics Faculty and Staff Publications

In this work, a neutrosophic network method is proposed for finding the shortest path length with single valued trapezoidal neutrosophic number. The proposed algorithm gives the shortest path length using score function from source node to destination node. Here the weights of the edges are considered to be single valued trapezoidal neutrosophic number. Finally, a numerical example is used to illustrate the efficiency of the proposed approach

Exploring Mathematical Strategies For Finding Hidden Features In Multi-Dimensional Big Datasets, Tri Duong, Fang Ren, Apurva Mehta

STAR Program Research Presentations

With advances in technology in brighter sources and larger and faster detectors, the amount of data generated at national user facilities such as SLAC is increasing exponentially. Humans have a superb ability to recognize patterns in complex and noisy data and therefore, data is still curated and analyzed by humans. However, a human brain is unable to keep up with the accelerated pace of data generation, and as a consequence, the rate of new discoveries hasn't kept pace with the rate of data creation. Therefore, new procedures to quickly assess and analyze the data are needed. Machine learning approaches are …