Logic and Foundations Commons^™

The Rubbish Researchers Puzzle, Michael W. Lucht

Journal of Humanistic Mathematics

The Rubbish Researchers Puzzle is a humorous short story about the Blue-Eyed Islanders Puzzle, cultural insensitivity in logic problems, and the quality of research.

Reconstructability And Dynamics Of Elementary Cellular Automata, Martin Zwick

Complex Systems Faculty Publications and Presentations

Reconstructability analysis (RA) is a method to determine whether a multivariate relation, defined set- or information-theoretically, is decomposable with or without loss into lower ordinality relations. Set-theoretic RA (SRA) is used to characterize the mappings of elementary cellular automata. The decomposition possible for each mapping w/o loss is a better predictor than the λ parameter (Walker & Ashby, Langton) of chaos, & non-decomposable mappings tend to produce chaos. SRA yields not only the simplest lossless structure but also a vector of losses for all structures, indexed by parameter τ. These losses are analogous to transmissions in information-theoretic RA (IRA). IRA …

Introduction To Reconstructability Analysis, Martin Zwick

Complex Systems Faculty Publications and Presentations

This talk will introduce Reconstructability Analysis (RA), a data modeling methodology deriving from the 1960s work of Ross Ashby and developed in the systems community in the 1980s and afterwards. RA, based on information theory and graph theory, is a member of the family of methods known as ‘graphical models,’ which also include Bayesian networks and log-linear techniques. It is designed for exploratory modeling, although it can also be used for confirmatory hypothesis testing. RA can discover high ordinality and nonlinear interactions that are not hypothesized in advance. Its conceptual framework illuminates the relationships between wholes and parts, a subject …

Preliminary Results Of Bayesian Networks And Reconstructability Analysis Applied To The Electric Grid, Marcus Harris, Martin Zwick

Complex Systems Faculty Publications and Presentations

Reconstructability Analysis (RA) is an analytical approach developed in the systems community that combines graph theory and information theory. Graph theory provides the structure of relations (model of the data) between variables and information theory characterizes the strength and the nature of the relations. RA has three primary approaches to model data: variable based (VB) models without loops (acyclic graphs), VB models with loops (cyclic graphs) and state-based models (nearly always cyclic, individual states specifying model constraints). These models can either be directed or neutral. Directed models focus on a single response variable whereas neutral models focus on all relations …

Beyond Spatial Autocorrelation: A Novel Approach Using Reconstructability Analysis, David Percy, Martin Zwick

Complex Systems Faculty Publications and Presentations

Raster data are digital representations of spatial phenomena that are organized into rows and columns that typically have the same dimensions in each direction. They are used to represent image data at any scale. Common raster data are medical images, satellite data, and photos generated by modern smartphones.
Satellites capture reflectance data in specific bands of wavelength that correspond to red, green, blue, and often some infrared and thermal bands. These composite vectors can then be classified into actual land use categories such as forest or water using automated techniques. These classifications are verified on the ground using hand-held sensors. …

Homomorphism Of Fuzzy Multigroups And Some Of Its Properties, P. A. Ejegwa

Applications and Applied Mathematics: An International Journal (AAM)

In a way, the notion of fuzzy multigroups is an application of fuzzy multisets to the theory of group. The concept of fuzzy multigroups is a new algebraic structure of uncertainty which generalizes fuzzy groups. Fuzzy multigroup is a multiset of X x [0; 1] satisfying some set of axioms, where X is a classical group. In this paper, we propose the concept of homomorphism in fuzzy multigroups context. Some homomorphic properties of fuzzy multigroups are explicated. Again, we show that the homomorphic image and homomorphic preimage of fuzzy multigroups are also fuzzy multigroups. Finally, we present some homomorphic properties …

System Reliability Using Generalized Intuitionistic Fuzzy Rayleigh Lifetime Distribution, Ali Ebrahimnejad, Ezzatallah B. Jamkhaneh

Applications and Applied Mathematics: An International Journal (AAM)

Reliability analysis as one of the important research topics in engineering has been researched by a number of authors. Reliability in classical distributions is based on precise parameters. It is usually assumed that parameters of distributions are precise real numbers. However, in the real world, the data sometimes cannot be measured and recorded precisely. In this paper, the concept of fuzzy reliability is extended by the idea of generalized intuitionistic fuzzy reliability. We investigate the reliability characteristics of systems using Rayleigh lifetime distribution, in which the lifetime parameter is assumed to be generalized intuitionistic fuzzy number. Generalized intuitionistic fuzzy reliability, …

Study Of Pseudo Bl–Algebras In View Of Left Boolean Lifting Property, B. Barani Nia, A. B. Saeid

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, we define left Boolean lifting property (right Boolean lifting property) LBLP (RBLP) for pseudo BL–algebra which is the property that all Boolean elements can be lifted modulo every left filter (right filter) and next, we study pseudo BL-algebra with LBLP (RBLP). We show that Quasi local, local and hyper Archimedean pseudo BL–algebra that have LBLP (RBLP) has an interesting behavior in direct products. LBLP (RBLP) provides an important representation theorem for semi local and maximal pseudo BL–algebra.

The Structure Of Models Of Second-Order Set Theories, Kameryn J. Williams

Dissertations, Theses, and Capstone Projects

This dissertation is a contribution to the project of second-order set theory, which has seen a revival in recent years. The approach is to understand second-order set theory by studying the structure of models of second-order set theories. The main results are the following, organized by chapter. First, I investigate the poset of T-realizations of a fixed countable model of ZFC, where T is a reasonable second-order set theory such as GBC or KM, showing that it has a rich structure. In particular, every countable partial order embeds into this structure. Moreover, we can arrange so that these embedding preserve …

Coincidence Of Bargaining Solutions And Rationalizability In Epistemic Games, Todd Stambaugh

Dissertations, Theses, and Capstone Projects

Chapter 1: In 1950, John Nash proposed the Bargaining Problem, for which a solution is a function that assigns to each space of possible utility assignments a single point in the space, in some sense representing the ’fair’ deal for the agents involved. Nash provided a solution of his own, and several others have been presented since then, including a notable solution by Ehud Kalai and Meir Smorodinsky. In chapter 1, a complete account is given for the conditions under which the two solutions will coincide for two player bargaining scenarios.

Chapter 2: In the same year, Nash …

On Rugina’S System Of Thought, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

This article investigates Rugina's orientation table and gives particular examples for several of its seven models. Leon Walras's Economics of Stable Equilibrium and Keynes's Economics of Disequilibrium are combined in Rugina's orientation table in systems which are s percent stable and 100 ÿ s percent unstable, where s may be 100, 95, 65, 50, 35, 5, and 0. Classical logic and modern logic are united in Rugina's integrated logic, and then generalized in neutrosophic logic.

Some Studies On Algebraic Integers In Q(I,√3) By Using Coset Diagram, Florentin Smarandache, Saima Anis, Seok-Zun Song, Young Bae Jun

Branch Mathematics and Statistics Faculty and Staff Publications

In this paper, we studied the action of Picard modular group PSL(2,Z[i])

Strong Degrees In Single Valued Neutrosophic Graphs, Florentin Smarandache, Said Broumi, Assia Bakali, Seema Mehra, Mohamed Talea, Manjeet Singh

Branch Mathematics and Statistics Faculty and Staff Publications

The concept of single valued neutrosophic graphs (SVNGs) generalizes the concept of fuzzy graphs and intuitionistic fuzzy graphs. The purpose of this research paper is to define different types of strong degrees in SVNGs and introduce novel concepts, such as the vertex truth-membership, vertex indeterminacy-membership and falsity-membership sequence in SVNG with proof and numerical illustrations.

Review Of G. Israel, Meccanicismo. Trionfi E Miserie Della Visione Meccanica Del Mondo, Marco Panza

MPP Published Research

"This is Giorgio's Israel last book, which appeared only a few weeks after his untimely death, in September 2015. For many reasons, it can be considered as his intellectual legacy, since it comes back, in a new and organic way, to many of the research topics to which he devoted his life and his many publications, which include several papers in Historia Mathematica. One of these papers, co-authored with M. Menghini, appeared in vol. 25/4, 1998 and was devoted to Poincaré's and Enriques's opposite views on qualitative analysis, which is a theme also dealt with in this book (pp. 117–122)."

Nn-Harmonic Mean Aggregation Operators-Based Mcgdm Strategy In A Neutrosophic Number Environment, Florentin Smarandache, Kalyan Mondal, Surapati Pramanik, Bibhas C. Giri

Branch Mathematics and Statistics Faculty and Staff Publications

A neutrosophic number (a + bI) is a significant mathematical tool to deal with indeterminate and incomplete information which exists generally in real-world problems, where a and bI denote the determinate component and indeterminate component, respectively. We define score functions and accuracy functions for ranking neutrosophic numbers. We then define a cosine function to determine the unknown weight of the criteria. We define the neutrosophic number harmonic mean operators and prove their basic properties. Then, we develop two novel multi-criteria group decision-making (MCGDM) strategies using the proposed aggregation operators. We solve a numerical example to demonstrate the feasibility, applicability, and …

Neutrosophic Soft Rough Graphs With Application, Florentin Smarandache, Muhammad Akram, Hafsa M. Malik, Sundas Shahzadi

Branch Mathematics and Statistics Faculty and Staff Publications

Neutrosophic sets (NSs) handle uncertain information while fuzzy sets (FSs) and intuitionistic fuzzy sets (IFs) fail to handle indeterminate information. Soft set theory, neutrosophic set theory, and rough set theory are different mathematical models for handling uncertainties and they are mutually related. The neutrosophic soft rough set (NSRS) model is a hybrid model by combining neutrosophic soft sets with rough sets. We apply neutrosophic soft rough sets to graphs. In this research paper, we introduce the idea of neutrosophic soft rough graphs (NSRGs) and describe different methods of their construction. We consider the application of NSRG in decision-making problems. In …

Statistical Analysis Of Network Change, Teresa D. Schmidt, Martin Zwick

Complex Systems Faculty Publications and Presentations

Networks are rarely subjected to hypothesis tests for difference, but when they are inferred from datasets of independent observations statistical testing is feasible. To demonstrate, a healthcare provider network is tested for significant change after an intervention using Medicaid claims data. First, the network is inferred for each time period with (1) partial least squares (PLS) regression and (2) reconstructability analysis (RA). Second, network distance (i.e., change between time periods) is measured as the mean absolute difference in (1) coefficient matrices for PLS and (2) calculated probability distributions for RA. Third, the network distance is compared against a reference distribution …

What Makes A Theory Of Infinitesimals Useful? A View By Klein And Fraenkel, Vladimir Kanovei, Karin Katz, Mikhail Katz, Thomas Mormann

Journal of Humanistic Mathematics

Felix Klein and Abraham Fraenkel each formulated a criterion for a theory of infinitesimals to be successful, in terms of the feasibility of implementation of the Mean Value Theorem. We explore the evolution of the idea over the past century, and the role of Abraham Robinson's framework therein.

Categories Of Residuated Lattices, Daniel Wesley Fussner

Electronic Theses and Dissertations

We present dual variants of two algebraic constructions of certain classes of residuated lattices: The Galatos-Raftery construction of Sugihara monoids and their bounded expansions, and the Aguzzoli-Flaminio-Ugolini quadruples construction of srDL-algebras. Our dual presentation of these constructions is facilitated by both new algebraic results, and new duality-theoretic tools. On the algebraic front, we provide a complete description of implications among nontrivial distribution properties in the context of lattice-ordered structures equipped with a residuated binary operation. We also offer some new results about forbidden configurations in lattices endowed with an order-reversing involution. On the duality-theoretic front, we present new results on …

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) …