True-False Set Is A Particular Case Of The Refined Neutrosophic Set, 2020 University of New Mexico

#### True-False Set Is A Particular Case Of The Refined Neutrosophic Set, Florentin Smarandache, Said Broumi

*Branch Mathematics and Statistics Faculty and Staff Publications*

Borzooei, Mohseni Takallo, and Jun recently proposed a new type of set, called True-False Set [1], and they claimed it is a generalization of Neutrosophic Set [2]. We prove that this assertion is untrue. Actually it’s the opposite, the True-False Set is a particular case of the Refined Neutrosophic Set.

Decision Making On Teachers’ Adaptation To Cybergogy In Saturated Interval- Valued Refined Neutrosophic Overset /Underset /Offset Environment, 2020 University of New Mexico

#### Decision Making On Teachers’ Adaptation To Cybergogy In Saturated Interval- Valued Refined Neutrosophic Overset /Underset /Offset Environment, Florentin Smarandache, Nivetha Martin, Priya R.

*Branch Mathematics and Statistics Faculty and Staff Publications*

Neutrosophic overset, neutrosophic underset and neutrosophic offset introduced by Smarandache are the special kinds of neutrosophic sets with values beyond the range [0,1] and these sets are pragmatic in nature as it represents the real life situations. This paper introduces the concept of saturated refined neutrosophic sets and extends the same to the special kinds of neutrosophic sets. The proposed concept is applied in decision making on Teacher’s adaptation to cybergogy. The decision making environment is characterized by different types of teachers, online teaching skills and various training methods. Fuzzy relation is used to match the most suitable method to …

Numerical Computations Of Vortex Formation Length In Flow Past An Elliptical Cylinder, 2020 University of Pittsburgh

#### Numerical Computations Of Vortex Formation Length In Flow Past An Elliptical Cylinder, Matthew Karlson, Bogdan Nita, Ashwin Vaidya

*Department of Mathematics Facuty Scholarship and Creative Works*

We examine two dimensional properties of vortex shedding past elliptical cylinders through numerical simulations. Specifically, we investigate the vortex formation length in the Reynolds number regime 10 to 100 for elliptical bodies of aspect ratio in the range 0.4 to 1.4. Our computations reveal that in the steady flow regime, the change in the vortex length follows a linear profile with respect to the Reynolds number, while in the unsteady regime, the time averaged vortex length decreases in an exponential manner with increasing Reynolds number. The transition in profile is used to identify the critical Reynolds number which marks the …

Length Neutrosophic Subalgebras Of Bck/Bci-Algebras, 2020 University of New Mexico

#### Length Neutrosophic Subalgebras Of Bck/Bci-Algebras, Florentin Smarandache, Young Bae Jun, Madad Khan, Seok-Zun Song

*Branch Mathematics and Statistics Faculty and Staff Publications*

the notion of (i, j, k)-length neutrosophic subalgebras in BCK/BCI-algebras is introduced, and their properties are investigated. Characterizations of length neutrosophic subalgebras are discussed by using level sets of interval neutrosophic sets. Conditions for level sets of interval neutrosophic sets to be subalgebras are provided.

On Product Of Smooth Neutrosophic Topological Spaces, 2020 University of New Mexico

#### On Product Of Smooth Neutrosophic Topological Spaces, Florentin Smarandache, Kalaivani Chandran, Swathi Sundari Sundaramoorthy, Saeid Jafari

*Branch Mathematics and Statistics Faculty and Staff Publications*

In this paper, we develop the notion of the basis for a smooth neutrosophic topology in a more natural way. As a sequel, we define the notion of symmetric neutrosophic quasi-coincident neighborhood systems and prove some interesting results that fit with the classical ones, to establish the consistency of theory developed. Finally, we define and discuss the concept of product topology, in this context, using the definition of basis.

Plithogenic Cubic Sets, 2020 University of New Mexico

#### Plithogenic Cubic Sets, Florentin Smarandache, S.P. Priyadharshini, F. Nirmala Irudayam

*Branch Mathematics and Statistics Faculty and Staff Publications*

In this article, using the concepts of cubic set and plithogenic set, the ideas of plithogenic fuzzy cubic set, plithogenic intuitionistic fuzzy cubic set, plithogenic neutrosophic cubic set are introduced and its corresponding internal and external cubic sets are discussed with examples.

A Novel Approach For Assessing The Reliability Of Data Contained In A Single Valued Neutrosophic Number And Its Application In Multiple Criteria Decision Making, 2020 University of New Mexico

#### A Novel Approach For Assessing The Reliability Of Data Contained In A Single Valued Neutrosophic Number And Its Application In Multiple Criteria Decision Making, Florentin Smarandache, Dragisa Stanujkic, Darjan Karabasevic, Gabrijela Popovic

*Branch Mathematics and Statistics Faculty and Staff Publications*

Multiple criteria decision making is one of the many areas where neutrosophic sets have been applied to solve various problems so far.

Alternative Cichoń Diagrams And Forcing Axioms Compatible With Ch, 2020 The Graduate Center, City University of New York

#### Alternative Cichoń Diagrams And Forcing Axioms Compatible With Ch, Corey B. Switzer

*Dissertations, Theses, and Capstone Projects*

This dissertation surveys several topics in the general areas of iterated forcing, infinite combinatorics and set theory of the reals. There are two parts. In the first half I consider alternative versions of the Cichoń diagram. First I show that for a wide variety of reduction concepts there is a Cichoń diagram for effective cardinal characteristics relativized to that reduction. As an application I investigate in detail the Cichoń diagram for degrees of constructibility relative to a fixed inner model of ZFC. Then I study generalizations of cardinal characteristics to the space of functions from Baire space to Baire space. …

A Review Of Fuzzy Soft Topological Spaces, Intuitionistic Fuzzy Soft Topological Spaces And Neutrosophic Soft Topological Spaces, 2020 University of New Mexico

#### A Review Of Fuzzy Soft Topological Spaces, Intuitionistic Fuzzy Soft Topological Spaces And Neutrosophic Soft Topological Spaces, Florentin Smarandache, M. Parimala, M. Karthika

*Branch Mathematics and Statistics Faculty and Staff Publications*

The notion of fuzzy sets initiated to overcome the uncertainty of an object. Fuzzy topological space, intuitionistic fuzzy sets in topological structure space, vagueness in topological structure space, rough sets in topological space, theory of hesitancy and neutrosophic topological space, etc. are the extension of fuzzy sets. Soft set is a family of parameters which is also a set. Fuzzy soft topological space, intuitionistic fuzzy soft and neutrosophic soft topological space are obtained by incorporating soft sets with various topological structures. This motivates to write a review and study on various soft set concepts. This paper shows the detailed review …

A General Model Of Neutrosophic Ideals In Bck/Bci-Algebras Based On Neutrosophic Points, 2020 University of New Mexico

#### A General Model Of Neutrosophic Ideals In Bck/Bci-Algebras Based On Neutrosophic Points, Florentin Smarandache, Hashem Bordbar, Rajab Ali Borzooei, Young Bae Jun

*Branch Mathematics and Statistics Faculty and Staff Publications*

More general form of (∈, ∈∨q)-neutrosophic ideal is introduced, and their properties are investigated.

The Polar Form Of A Neutrosophic Complex Number, 2020 University of New Mexico

#### The Polar Form Of A Neutrosophic Complex Number, Florentin Smarandache, Riad K. Al-Hamido, Mayas Ismail

*Branch Mathematics and Statistics Faculty and Staff Publications*

In this paper, we will define the exponential form of a neutrosophic complex number. We have proven some characteristics and theories, including the conjugate of the exponential form of a neutrosophic complex number, division of the exponential form of a neutrosophic complex numbers, multiplication of the exponential form of a neutrosophic complex numbers. In addition, we have given the method of changing from the exponential to the algebraic form of a complex number.

An Expanded Model Of Unmatter From Neutrosophic Logic Perspective: Towards Matter-Spirit Unity View, 2020 University of New Mexico

#### An Expanded Model Of Unmatter From Neutrosophic Logic Perspective: Towards Matter-Spirit Unity View, Florentin Smarandache, Victor Christianto, Robert Neil Boyd

*Branch Mathematics and Statistics Faculty and Staff Publications*

In Neutrosophic Logic, a basic assertion is that there are variations of about everything that we can measure; the variations surround three parameters called T, I, F (truth, indeterminacy, falsehood) which can take a range of values. A previous paper in IJNS, 2020 shortly reviews the links among aether and matter creation from the perspective of Neutrosophic Logic. In any case, matter creation process in nature stays a major puzzle for physicists, scientists and other science analysts. To this issue neutrosophic logic offers an answer: "unmatter." This paper examines an extended model of unmatter, to incorporate issue soul solidarity. So, …

Reconstructability Analysis & Its Occam Implementation, 2020 Portland State University

#### Reconstructability Analysis & Its Occam Implementation, Martin Zwick

*Systems Science Faculty Publications and Presentations*

This talk will describe Reconstructability Analysis (RA), a probabilistic graphical 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, resembles and partially overlaps Bayesian networks (BN) and log-linear techniques, but also has some unique capabilities. (A paper explaining the relationship between RA and BN will be given in this special session.) RA is designed for exploratory modeling although it can also be used for confirmatory hypothesis testing. In RA modeling, one either predicts some DV from a set of IVs …

Joint Lattice Of Reconstructability Analysis And Bayesian Network General Graphs, 2020 Portland State University

#### Joint Lattice Of Reconstructability Analysis And Bayesian Network General Graphs, Marcus Harris, Martin Zwick

*Systems Science Faculty Publications and Presentations*

This paper integrates the structures considered in Reconstructability Analysis (RA) and those considered in Bayesian Networks (BN) into a joint lattice of probabilistic graphical models. This integration and associated lattice visualizations are done in this paper for four variables, but the approach can easily be expanded to more variables. The work builds on the RA work of Klir (1985), Krippendorff (1986), and Zwick (2001), and the BN work of Pearl (1985, 1987, 1988, 2000), Verma (1990), Heckerman (1994), Chickering (1995), Andersson (1997), and others. The RA four variable lattice and the BN four variable lattice partially overlap: there are ten …

Plithogenic Cognitive Maps In Decision Making, 2020 University of New Mexico

#### Plithogenic Cognitive Maps In Decision Making, Florentin Smarandache, Nivetha Martin

*Branch Mathematics and Statistics Faculty and Staff Publications*

Plithogenic sets introduced by Smarandache (2018) have disclosed new research vistas and this paper introduces the novel concept of plithogenic cognitive maps (PCM) and its applications in decision making. The new approach of defining instantaneous state neutrosophic vector with the confinement of indeterminacy to (0,1] is proposed to quantify the degree of indeterminacy. The resultant vector is obtained by applying instantaneous state vector through the connection matrix together with plithogenic operators comprising the contradiction degrees. The connection matrix is represented as fuzzy matrix and neutrosophic matrix and the resultant vector is determined by applying plithogenic fuzzy operators and plithogenic neutrosophic …

C# Application To Deal With Neutrosophic G(Alpha)-Closed Sets In Neutrosophic Topology, 2020 Kongunadu Arts and Science College

#### C# Application To Deal With Neutrosophic G(Alpha)-Closed Sets In Neutrosophic Topology, S. Saranya, M. Vigneshwaran, S. Jafari

*Applications and Applied Mathematics: An International Journal (AAM)*

In this paper, we have developed a C# Application for finding the values of the complement, union, intersection and the inclusion of any two neutrosophic sets in the neutrosophic field by using .NET Framework, Microsoft Visual Studio and C# Programming Language. In addition to this, the system can find neutrosophic topology, neutrosophic alpha-closed sets and neutrosophic g(alpha)-closed sets in each resultant screens. Also, this computer-based application produces the complement values of each neutrosophic closed sets.

Ideal Theory In Bck/Bci-Algebras In The Frame Of Hesitant Fuzzy Set Theory, 2020 University of Tabuk

#### Ideal Theory In Bck/Bci-Algebras In The Frame Of Hesitant Fuzzy Set Theory, G. Muhiuddin, Habib Harizavi, Young Bae Jun

*Applications and Applied Mathematics: An International Journal (AAM)*

Several generalizations and extensions of fuzzy sets have been introduced in the literature, for example, Atanassov’s intuitionistic fuzzy sets, type 2 fuzzy sets and fuzzy multisets, etc. Using the Torra’s hesitant fuzzy sets, the notions of Sup-hesitant fuzzy ideals in BCK/BCI-algebras are introduced, and its properties are investigated. Relations between Sup-hesitant fuzzy subalgebras and Sup-hesitant fuzzy ideals are displayed, and characterizations of Sup-hesitant fuzzy ideals are discussed.

Some Operations Over Pythagorean Fuzzy Matrices Based On Hamacher Operations, 2020 Annamalai University

#### Some Operations Over Pythagorean Fuzzy Matrices Based On Hamacher Operations, I. Silambarasan, S. Sriram

*Applications and Applied Mathematics: An International Journal (AAM)*

Pythagorean fuzzy matrix is a powerful tool for describing the vague concepts more precisely. The Pythagorean fuzzy matrix based models provide more flexibility in handling the human judgment information as compared to other fuzzy models. The objective of this paper is to apply the concept of intuitionistic fuzzy matrices to Pythagorean fuzzy matrices. In this paper, we briefly introduce the Pythagorean fuzzy matrices and some theorems and examples are applied to illustrate the performance of the proposed methods. Then we define the Hamacher scalar multiplication (n._{h}A) and Hamacher exponentiation (A^^{h}n) operations on Pythagorean fuzzy matrices and …

On The Qualitative Analysis Of Volterra Iddes With Infinite Delay, 2020 Van Yuzuncu Yil University

#### On The Qualitative Analysis Of Volterra Iddes With Infinite Delay, Osman Tunç, Erdal Korkmaz, Özkan Atan

*Applications and Applied Mathematics: An International Journal (AAM)*

This investigation deals with a nonlinear Volterra integro-differential equation with infinite retardation (IDDE).We will prove three new results on the stability, uniformly stability (US) and square integrability (SI) of solutions of that IDDE. The proofs of theorems rely on the use of an appropriate Lyapunov-Krasovskii functional (LKF). By the outcomes of this paper, we generalize and obtain some former results in mathematical literature under weaker conditions.

Derivable Single Valued Neutrosophic Graphs Based On Km-Fuzzy Metric, 2020 University of New Mexico

#### Derivable Single Valued Neutrosophic Graphs Based On Km-Fuzzy Metric, Florentin Smarandache, Mohammad Hamidi

*Branch Mathematics and Statistics Faculty and Staff Publications*

In this paper we consider the concept of KM-fuzzy metric spaces and we introduce a novel concept of KM-single valued neutrosophic metric graphs based on KM-fuzzy metric spaces. Then we investigate the finite KM-fuzzy metric spaces with respect to KM-fuzzy metrics and we construct the KMfuzzy metric spaces on any given non-empty sets. We try to extend the concept of KM-fuzzy metric spaces to a larger class of KM-fuzzy metric spaces such as union and product of KM-fuzzy metric spaces and in this regard we investigate the class of products of KM-single valued neutrosophic metric graphs. In the final, we …