Logic and Foundations Commons^™

Fuzzy Semi-S-Irresolute Continuous Mappings In Šostak’S Fuzzy Topological Spaces, B. Vijayalakshmi, J. Praba, M. Saraswathi, A. Vadivel

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, the concepts of fuzzy semi-S-irresolute open map, fuzzy semi-S-irresolute closed map and fuzzy semi-S-irresolute homeomorphism to the fuzzy topological spaces in Šostak’s sense are introduced and studied. Some of their characteristic properties are considered. Also a comparison between these new types of functions are established by giving examples.

New Notions From (R; S)-Generalized Fuzzy E-Open Sets, A. Vadivel, P. Periyasamy, V. Chandrasekar, G. Saravanakumar

Applications and Applied Mathematics: An International Journal (AAM)

The present article discuss (r; s)-generalized fuzzy e-border, (r; s)-generalized fuzzy e-exterior and (r; s)-generalized fuzzy e-frontier in double fuzzy topologies. Furthermore, some characterizations of generalized double fuzzy e-continuous, generalized double fuzzy e-open, generalized double fuzzy e-closed and generalized double fuzzy e-closure-irresolute functions are studied and investigated. Moreover, the interrelations among the new concepts are discussed with some necessary examples.

Modest Automorphisms Of Presburger Arithmetic, Simon Heller

Dissertations, Theses, and Capstone Projects

It is interesting to consider whether a structure can be expanded by an automorphism so that one obtains a nice description of the expanded structure's first-order properties. In this dissertation, we study some such expansions of models of Presburger arithmetic. Building on some of the work of Harnik (1986) and Llewellyn-Jones (2001), in Chapter 2 we use a back-and-forth construction to obtain two automorphisms of sufficiently saturated models of Presburger arithmetic. These constructions are done first in the quotient of the Presburger structure by the integers (which is a divisible ordered abelian group with some added structure), and then lifted …

A Hybrid Plithogenic Decision-Making Approach With Quality Function Deployment For Selecting Supply Chain Sustainability Metrics, Florentin Smarandache, Mohamed Abdel-Basset, Rehab Mohamed, Abd El-Nasser H. Zaied

Branch Mathematics and Statistics Faculty and Staff Publications

Supply chain sustainability has become one of the most attractive decision management topics. There are many articles that have focused on this field presenting many different points of view. This research is centred on the evaluation of supply chain sustainability based on two critical dimensions. The first is the importance of evaluation metrics based on economic, environmental and social aspects, and the second is the degree of difficulty of information gathering. This paper aims to increase the accuracy of the evaluation. The proposed method is a combination of quality function deployment (QFD) with plithogenic aggregation operations. The aggregation operation is …

Cubic Interior Ideals In Semigroups, G. Muhiuddin

Applications and Applied Mathematics: An International Journal (AAM)

In this paper we apply the cubic set theory to interior ideals of a semigroup. The notion of cubic interior ideals is introduced, and related properties are investigated. Characterizations of (cubic) interior ideals are established, and conditions for a semigroup to be left (right) simple are provided.

Computable Reducibility Of Equivalence Relations, Marcello Gianni Krakoff

Boise State University Theses and Dissertations

Computable reducibility of equivalence relations is a tool to compare the complexity of equivalence relations on natural numbers. Its use is important to those doing Borel equivalence relation theory, computability theory, and computable structure theory. In this thesis, we compare many naturally occurring equivalence relations with respect to computable reducibility. We will then define a jump operator on equivalence relations and study proprieties of this operation and its iteration. We will then apply this new jump operation by studying its effect on the isomorphism relations of well-founded computable trees.

Formally Verifying Peano Arithmetic, Morgan Sinclaire

Boise State University Theses and Dissertations

This work is concerned with implementing Gentzen’s consistency proof in the Coq theorem prover.

In Chapter 1, we summarize the basic philosophical, historical, and mathematical background behind this theorem. This includes the philosophical motivation for attempting to prove the consistency of Peano arithmetic, which traces itself from the first attempted axiomatizations of mathematics to the maturation of Hilbert’s program. We introduce many of the basic concepts in mathematical logic along the way: first-order logic (FOL), Peano arithmetic (PA), primitive recursive arithmetic (PRA), Gödel's 2nd Incompleteness theorem, and the ordinals below ε₀.

In …

Extension Of Soft Set To Hypersoft Set, And Then To Plithogenic Hypersoft Set, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

In this paper, we generalize the soft set tothe hypersoft set by transforming the function F into a multi-attribute function. Then we introduce the hybrids of Crisp, Fuzzy, Intuitionistic Fuzzy, Neutrosophic, and Plithogenic Hypersoft Set.

Experience Of A Noyce-Student Learning Assistant In An Inquiry-Based Learning Class, Melissa Riley

UNO Student Research and Creative Activity Fair

This presentation refers to an undergraduate course called introduction to abstract mathematics at the University of Nebraska at Omaha. During the academic year 2017-2018, undergraduate, mathematics student Melissa Riley was a Noyce-student learning assistant for the Inquiry Based Learning (IBL) section of the course. She assisted the faculty-in-charge with all aspects of the course. These included: materials preparation, class organization, teamwork, class leading, presentations, and tutoring. This presentation shall address some examples of how the IBL approach can be used in this type of class including: the structure of the course, the activities and tasks performed by the students, learning …

Extending Set Functors To Generalised Metric Spaces, Adriana Balan, Alexander Kurz, Jiří Velebil

Mathematics, Physics, and Computer Science Faculty Articles and Research

For a commutative quantale V, the category V-cat can be perceived as a category of generalised metric spaces and non-expanding maps. We show that any type constructor T (formalised as an endofunctor on sets) can be extended in a canonical way to a type constructor T_V on V-cat. The proof yields methods of explicitly calculating the extension in concrete examples, which cover well-known notions such as the Pompeiu-Hausdorff metric as well as new ones.

Conceptually, this allows us to to solve the same recursive domain equation X ≅ TX in different categories (such as sets and metric spaces) and …

Special Issue: New Types Of Neutrosophic Set/Logic/Probability, Neutrosophic Over-/Under-/ Off-Set, Neutrosophic Refined Set, And Their Extension To Plithogenic Set/Logic/ Probability, With Applications, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

No abstract provided.

Special Subset Vertex Multisubgraphs For Multi Networks, Florentin Smarandache, W.B. Vasantha Kandasamy, Ilanthenral K

Branch Mathematics and Statistics Faculty and Staff Publications

In this book authors study special type of subset vertex multi subgraphs; these multi subgraphs can be directed or otherwise. Another special feature of these subset vertex multigraphs is that we are aware of the elements in each vertex set and how it affects the structure of both subset vertex multisubgraphs and edge multisubgraphs. It is pertinent to record at this juncture that certain ego centric directed multistar graphs become empty on the removal of one edge, there by theorising the importance, and giving certain postulates how to safely form ego centric multi networks. Given any subset vertex multigraph we …

A Short Remark On Gödel Incompleteness Theorem And Its Self-Referential Paradox From Neutrosophic Logic Perspective, Florentin Smarandache, Victor Christianto

Branch Mathematics and Statistics Faculty and Staff Publications

It is known from history of mathematics, that Gödel submitted his two incompleteness theorems, which can be considered as one of hallmarks of modern mathematics in 20th century. Here we argue that Gödel incompleteness theorem and its self-referential paradox have not only put Hilbert’s axiomatic program into question, but he also opened up the problem deep inside the then popular Aristotelian Logic. Although there were some attempts to go beyond Aristotelian binary logic, including by Lukasiewicz’s three-valued logic, here we argue that the problem of self-referential paradox can be seen as reconcilable and solvable from Neutrosophic Logic perspective. Motivation of …

Special Issue: Algebraic Structures Of Neutrosophic Triplets, Neutrosophic Duplets, Or Neutrosophic Multisets, Vol. Ii, Florentin Smarandache, Xiaohong Zhang, Mumtaz Ali

Branch Mathematics and Statistics Faculty and Staff Publications

No abstract provided.

Plithogenic Fuzzy Whole Hypersoft Set, Construction Of Operators And Their Application In Frequency Matrix Multi Attribute Decision Making Technique, Florentin Smarandache, Shazia Rana, Madiha Qayyum, Muhammad Saeed, Bakhtawar Ali Khan

Branch Mathematics and Statistics Faculty and Staff Publications

In this paper, initially a matrix representation of Plithogenic Hypersoft Set (PHSS) is introduced and then with the help of this matrix some local operators for Plithogenic Fuzzy Hypersoft set (PFHSS) are developed. These local operators are used to generalize PFHSS to Plithogenic Fuzzy Whole Hypersoft set (PFWHSS). The generalized PFWHSS set is hybridization of Fuzzy Hypersoft set (which represent multiattributes and their subattributes as a combined whole membership i.e. case of having an exterior view of the event) and the Plithogenic Fuzzy Hypersoft set (in which multi attributes and their subattributes are represented with individual memberships case of having …

A Bipolar Fuzzy Extension Of The Multimoora Method, Florentin Smarandache, Dragisa Stanujkic, Darjan Karabasevic, Edmundas Kazimieras Zavadskas, Willem Brauer

Branch Mathematics and Statistics Faculty and Staff Publications

The aim of this paper is to make a proposal for a new extension of the MULTIMOORA method extended to deal with bipolar fuzzy sets. Bipolar fuzzy sets are proposed as an extension of classical fuzzy sets in order to enable solving a particular class of decision-making problems. Unlike other extensions of the fuzzy set of theory, bipolar fuzzy sets introduce a positive membership function, which denotes the satisfaction degree of the element x to the property corresponding to the bipolar-valued fuzzy set, and the negative membership function, which denotes the degree of the satisfaction of the element x to …

Historia De Las Teorías Neutrosóficas Y Sus Aplicaciones (Actualizado), Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

Historia de las Teorías Neutrosóficas y sus Aplicaciones (actualizado)

Tripleta De Estructura Neutrosófica Y Tripleta De Estructura Neutrosófica Extendida, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

En el presente estudio se realiza una revisión de las tripletas de estructura neutrosófica y tripleta de estructura neutrosófica extendida, con el fin de introducir nuevos conceptos a emplear en trabajos futuros.

Grado De Dependencia E Independencia De Los (Sub) Componentes De Conjuntos Borrosos Y Neutrosóficos, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

La introducción del grado de dependencia (y en consecuencia el grado de independencia) entre los componentes del conjunto difuso, y también entre los componentes del conjunto neutrosófico, se introduce por primera vez en la quinta edición del libro de Neutrosofía en el año 2006, basado en los elementos descritos en dicha edición del libro, se comienza a conocer conceptos de conjuntos neutrosóficos de los componentes borrosos así como los grados de dependencia e independencia, Por tal motivo el objetivo del presente trabajo es extender el conjunto neutrosófico refinado, teniendo en cuenta la grado de dependencia o independencia de los subcomponentes …