Interval-Valued Neutrosophic Oversets, Neutrosophic Undersets, And Neutrosophic Offsets, 2016 University of New Mexico
Interval-Valued Neutrosophic Oversets, Neutrosophic Undersets, And Neutrosophic Offsets, Florentin Smarandache
Branch Mathematics and Statistics Faculty and Staff Publications
We have proposed since 1995 the existence of degrees of membership of an element with respect to a neutrosophic set to also be partially or totally above 1 (over-membership), and partially or totally below 0 (under-membership) in order to better describe our world problems [published in 2007].
Neutrosophic Overset, Neutrosophic Underset, And Neutrosophic Offset. Similarly For Neutrosophic Over-/Under-/Off- Logic, Probability, And Statistics, 2016 University of New Mexico
Neutrosophic Overset, Neutrosophic Underset, And Neutrosophic Offset. Similarly For Neutrosophic Over-/Under-/Off- Logic, Probability, And Statistics, Florentin Smarandache
Branch Mathematics and Statistics Faculty and Staff Publications
Neutrosophic Over-/Under-/Off-Set and -Logic were defined for the first time by Smarandache in 1995 and published in 2007. They are totally different from other sets/logics/probabilities.
He extended the neutrosophic set respectively to Neutrosophic Overset {when some neutrosophic component is > 1}, 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 with respect to the classical fuzzy set/logic, intuitionistic fuzzy set/logic, or classical/imprecise probability, where the values are not allowed outside the interval [0, 1], since our real-world has …
Strong Neutrosophic Graphs And Subgraph Topological Subspaces, 2016 University of New Mexico
Strong Neutrosophic Graphs And Subgraph Topological Subspaces, Florentin Smarandache, W.B. Vasantha Kandasamy, Ilantheral K
Branch Mathematics and Statistics Faculty and Staff Publications
In this book authors for the first time introduce the notion of strong neutrosophic graphs. They are very different from the usual graphs and neutrosophic graphs. Using these new structures special subgraph topological spaces are defined. Further special lattice graph of subgraphs of these graphs are defined and described. Several interesting properties using subgraphs of a strong neutrosophic graph are obtained. Several open conjectures are proposed. These new class of strong neutrosophic graphs will certainly find applications in NCMs, NRMs and NREs with appropriate modifications.
Neutrosophic Set Approach To Algebraic Structures, 2016 University of New Mexico
Neutrosophic Set Approach To Algebraic Structures, Florentin Smarandache, Madad Khan, Fazal Tahir
Branch Mathematics and Statistics Faculty and Staff Publications
Real world is featured with complex phenomenons. As uncertainty is inevitably involved in problems arise in various elds of life and classical methods failed to handle these type of problems. Dealing with imprecise, uncertain or imperfect information was a big task for many years. Many modelswerepresentedinordertoproperlyincorporateuncertaintyintosystem description, LotA.Zadeh in 1965 introduced the idea of a fuzzy set. Zadeh replaced conventional characteristic function of classical crisp sets which takes on its values in f0;1g by membership function which takes on its values in closed interval [0;1]. Fuzzy set theory is conceptually a very powerful technique to deal with another aspect or …
Applying Dijkstra Algorithm For Solving Neutrosophic Shortest Path Problem, 2016 University of New Mexico
Applying Dijkstra Algorithm For Solving Neutrosophic Shortest Path Problem, Florentin Smarandache, Luige Vladareanu, Said Broumi, Assia Bakali, Muhammad Akram
Branch Mathematics and Statistics Faculty and Staff Publications
The selection of shortest path problem is one the classic problems in graph theory. In literature, many algorithms have been developed to provide a solution for shortest path problem in a network. One of common algorithms in solving shortest path problem is Dijkstra’s algorithm. In this paper, Dijkstra’s algorithm has been redesigned to handle the case in which most of parameters of a network are uncertain and given in terms of neutrosophic numbers. Finally, a numerical example is given to explain the proposed algorithm.
The Varieties Of Indispensability Arguments, 2015 Chapman University
The Varieties Of Indispensability Arguments, Marco Panza, Andrea Sereni
MPP Published Research
The indispensability argument (IA) comes in many different versions that all reduce to a general valid schema. Providing a sound IA amounts to providing a full interpretation of the schema according to which all its premises are true. Hence, arguing whether IA is sound results in wondering whether the schema admits such an interpretation. We discuss in full details all the parameters on which the specification of the general schema may depend. In doing this, we consider how different versions of IA can be obtained, also through different specifications of the notion of indispensability. We then distinguish between schematic and …
Comparing The Strength Of Diagonally Non-Recursive Functions In The Absence Of Σ02 Induction, 2015 Dartmouth College
Comparing The Strength Of Diagonally Non-Recursive Functions In The Absence Of Σ02 Induction, Francois G. Dorais, Jeffry L. Hirst, Paul Shafer
Dartmouth Scholarship
We prove that the statement "there is a k such that for every f there is a k-bounded diagonally non-recursive function relative to f" does not imply weak K\"onig's lemma over RCA0+BΣ02. This answers a question posed by Simpson. A recursion-theoretic consequence is that the classic fact that every k-bounded diagonally non-recursive function computes a 2-bounded diagonally non-recursive function may fail in the absence of IΣ02.
On The Stability Of A Pexiderized Functional Equation In Intuitionistic Fuzzy Banach Spaces, 2015 Moula Netaji Vidyalaya
On The Stability Of A Pexiderized Functional Equation In Intuitionistic Fuzzy Banach Spaces, Nabin C. Kayal, Pratap Mondal, T. K. Samanta
Applications and Applied Mathematics: An International Journal (AAM)
During the last few decades several researchers have been devoted to establishing stability of different kinds of functional equations, differential equations, functional differential equations, fractional differential equations, etc. under different sufficient conditions in different spaces like Banach spaces, Banach modules, fuzzy Banach spaces etc. In this paper, we remain confined in the discussion of stability of functional equations in intuitionistic fuzzy Banach spaces. Ulam was the first person who introduced an open question concerning the stability of a group homomorphism in an international conference. Thereafter several researchers have replied and are still replying to this open question in different contexts. …
Group Decision Making Using Comparative Linguistic Expression Based On Hesitant Intuitionistic Fuzzy Sets, 2015 Lahore School of Economics
Group Decision Making Using Comparative Linguistic Expression Based On Hesitant Intuitionistic Fuzzy Sets, Ismat Beg, Tabasam Rashid
Applications and Applied Mathematics: An International Journal (AAM)
We introduce a method for aggregation of experts’ opinions given in the form of comparative linguistic expression. An algorithmic form of technique for order preference is proposed for group decision making. A simple example is given by using this method for the selection of the best alternative as well as ranking the alternatives from the best to the worst.
The Strict Higher Grothendieck Integral, 2015 University of Nebraska-Lincoln
The Strict Higher Grothendieck Integral, Scott W. Dyer
Department of Mathematics: Dissertations, Theses, and Student Research
This thesis generalizes A. Grothendieck’s construction, denoted by an integral, of a fibered category from a contravariant pseudofunctor, to a construction for n- and even ∞-categories. Only strict higher categories are considered, the more difficult theory of weak higher categories being neglected. Using his axioms for a fibered category, Grothendieck produces a contravariant pseudofunctor from which the original fibered category can be reconstituted by integration. In applications, the integral is often most efficient, constructing the fibered category with its structure laid bare. The situation generalizes the external and internal definitions of the semidirect product in group theory: fibration is …
How Does “Collaboration” Occur At All? Remarks On Epistemological Issues Related To Understanding / Working With ‘The Other’, 2015 Northern Michigan University
How Does “Collaboration” Occur At All? Remarks On Epistemological Issues Related To Understanding / Working With ‘The Other’, Don Faust, Judith Puncochar
Conference Presentations
Collaboration, if to occur successfully at all, needs to be based on careful representation and communication of each stakeholder’s knowledge. In this paper, we investigate, from a foundational logical and epistemological point of view, how such representation and communication can be accomplished. What we tentatively conclude, based on a careful delineation of the logical technicalities necessarily involved in such representation and communication, is that a complete representation is not possible. This inference, if correct, is of course rather discouraging with regard to what we can hope to achieve in the knowledge representations that we bring to our collaborations. We suggest …
Introduction To Functions And Generality Of Logic. Reflections On Frege's And Dedekind's Logicisms, 2015 University of Paris
Introduction To Functions And Generality Of Logic. Reflections On Frege's And Dedekind's Logicisms, Hourya Benis Sinaceur, Marco Panza, Gabriel Sandu
MPP Published Research
This book examines three connected aspects of Frege’s logicism: the differences between Dedekind’s and Frege’s interpretation of the term ‘logic’ and related terms and reflects on Frege’s notion of function, comparing its understanding and the role it played in Frege’s and Lagrange’s foundational programs. It concludes with an examination of the notion of arbitrary function, taking into account Frege’s, Ramsey’s and Russell’s view on the subject. Composed of three chapters, this book sheds light on important aspects of Dedekind’s and Frege’s logicisms. The first chapter explains how, although he shares Frege’s aim at substituting logical standards of rigor to intuitive …
Paratodo X: Una Introducción A La Lógica Formal, 2015 University at Albany, State University of New York
Paratodo X: Una Introducción A La Lógica Formal, P.D. Magnus
Philosophy Faculty Books
A translation of the logic textbook forall x (v 1.30) into Spanish. Translation by José Ángel Gascón.
Newton On Indivisibles, 2015 Universitat Pompeu Fabra
Newton On Indivisibles, Antoni Malet, Marco Panza
MPP Published Research
Though Wallis’s Arithmetica infinitorum was one of Newton’s major sources of inspiration during the first years of his mathematical education, indivisibles were not a central feature of his mathematical production.
Wallis On Indivisibles, 2015 Universitat Pompeu Fabra
Wallis On Indivisibles, Antoni Malet, Marco Panza
MPP Published Research
The present chapter is devoted, first, to discuss in detail the structure and results of Wallis’s major and most influential mathematical work, the Arithmetica Infinitorum (Wallis 1656). Next we will revise Wallis’s views on indivisibles as articulated in his answer to Hobbes’s criticism in the early 1670s. Finally, we will turn to his discussion of the proper way to understand the angle of contingence in the first half of the 1680s. As we shall see, there are marked differences in the status that indivisibles seem to enjoy in Wallis’s thought along his mathematical career. These differences correlate with the changing …
Transition To Higher Mathematics: Structure And Proof (Second Edition), 2015 University of Washington - Seattle Campus
Transition To Higher Mathematics: Structure And Proof (Second Edition), Bob A. Dumas, John E. Mccarthy
Books and Monographs
This book is written for students who have taken calculus and want to learn what “real mathematics" is. We hope you will find the material engaging and interesting, and that you will be encouraged to learn more advanced mathematics. This is the second edition of our text. It is intended for students who have taken a calculus course, and are interested in learning what higher mathematics is all about. It can be used as a textbook for an "Introduction to Proofs" course, or for self-study. Chapter 1: Preliminaries, Chapter 2: Relations, Chapter 3: Proofs, Chapter 4: Principles of Induction, Chapter …
Extensions Of Functors From Set To V-Cat, 2015 University Politehnica of Bucharest
Extensions Of Functors From Set To V-Cat, Adriana Balan, Alexander Kurz, Jirí Velebil
Engineering Faculty Articles and Research
We show that for a commutative quantale V every functor Set --> V-cat has an enriched left- Kan extension. As a consequence, coalgebras over Set are subsumed by coalgebras over V-cat. Moreover, one can build functors on V-cat by equipping Set-functors with a metric.
The Finite Embeddability Property For Some Noncommutative Knotted Varieties Of Rl And Drl, 2015 University of Denver
The Finite Embeddability Property For Some Noncommutative Knotted Varieties Of Rl And Drl, Riquelmi Salvador Cardona Fuentes
Electronic Theses and Dissertations
Residuated lattices, although originally considered in the realm of algebra providing a general setting for studying ideals in ring theory, were later shown to form algebraic models for substructural logics. The latter are non-classical logics that include intuitionistic, relevance, many-valued, and linear logic, among others. Most of the important examples of substructural logics are obtained by adding structural rules to the basic logical calculus FL. We denote by 𝖱𝖫𝑛 � the varieties of knotted residuated lattices. Examples of these knotted rules include integrality and contraction. The extension of �� by the rules corresponding to these two equations is …
Positive Fragments Of Coalgebraic Logics, 2015 University Politehnica of Bucharest
Positive Fragments Of Coalgebraic Logics, Adriana Balan, Alexander Kurz, Jirí Velebil
Engineering Faculty Articles and Research
Positive modal logic was introduced in an influential 1995 paper of Dunn as the positive fragment of standard modal logic. His completeness result consists of an axiomatization that derives all modal formulas that are valid on all Kripke frames and are built only from atomic propositions, conjunction, disjunction, box and diamond. In this paper, we provide a coalgebraic analysis of this theorem, which not only gives a conceptual proof based on duality theory, but also generalizes Dunn's result from Kripke frames to coalgebras for weak-pullback preserving functors. To facilitate this analysis we prove a number of category theoretic results on …
Approximation Of Nested Fixpoints, 2015 Chapman University
Approximation Of Nested Fixpoints, Alexander Kurz
Engineering Faculty Articles and Research
The question addressed in this paper is how to correctly approximate infinite data given by systems of simultaneous corecursive definitions. We devise a categorical framework for reasoning about regular datatypes, that is, datatypes closed under products, coproducts and fixpoints. We argue that the right methodology is on one hand coalgebraic (to deal with possible nontermination and infinite data) and on the other hand 2-categorical (to deal with parameters in a disciplined manner). We prove a coalgebraic version of Bekic lemma that allows us to reduce simultaneous fixpoints to a single fix point. Thus a possibly infinite object of interest is …