Mathematics Commons^™

Collected Papers (On Physics, Artificial Intelligence, Health Issues, Decision Making, Economics, Statistics), Volume Xi, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

This eleventh volume of Collected Papers includes 90 papers comprising 988 pages on Physics, Artificial Intelligence, Health Issues, Decision Making, Economics, Statistics, written between 2001-2022 by the author alone or in collaboration with 84 co-authors from 19 countries.

Collected Papers (On Neutrosophic Theory And Applications), Volume Vi, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

This sixth volume of Collected Papers includes 74 papers comprising 974 pages on (theoretic and applied) neutrosophics, written between 2015-2021 by the author alone or in collaboration with 121 co-authors from 19 countries.

Collected Papers (On Neutrosophics, Plithogenics, Hypersoft Set, Hypergraphs, And Other Topics), Volume X, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

This tenth volume of Collected Papers includes 86 papers in English and Spanish languages comprising 972 pages, written between 2014-2022 by the author alone or in collaboration with 105 co-authors from 26 countries.

Collected Papers (Neutrosophics And Other Topics), Volume Xiv, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

This fourteenth volume of Collected Papers is an eclectic tome of 87 papers in Neutrosophics and other fields, such as mathematics, fuzzy sets, intuitionistic fuzzy sets, picture fuzzy sets, information fusion, robotics, statistics, or extenics, comprising 936 pages, published between 2008-2022 in different scientific journals or currently in press, by the author alone or in collaboration with 99 co-authors from 26 countries.

Small Tech, High Touch: A Permutation, Victor Christianto, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

In an earlier paper published in a neutrosophic math journal (IJNS), we discussed a new approach to technology, which may be called as ‘opti-realism’ or ‘pess-optimism’ as alternative to utopianism based on technocracy, which may lead the world into global techno-totalitarianism. In this article, we submit a new approach to Nature and technology, which is more modest and humble, rather than a techno-utopianism version of reality that most futurists argue for. Our proposed approach resembles more to Myer-Briggs 16 types of personality, including IJNS, IFNS etc. In our scheme, there are 8 characters of approach toward technology which can lead …

On Neutrosophic Αψ -Supra Open Sets, Mani Parimala, Muthusamy Karthika, Harish Garg, Saeid Jafari, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

Neutrosophic topological space is an extension of fuzzy topology. Neutrosophic topological space addresses each element’s membership, indeterminacy and non-membership grades. Dropping an axiom in the neutrosophic topological space produces a new topological space called neutrosophic supra topological space. Elements in this neutrosophic supra topology are neutrosophic sets. We established the neutrosophic αψ-supra open set in neutrosophic supra topological spaces in this paper. Also, we investigate the properties of the newly defined set. Neutrosophic αψ -supra continuity is introduced and studied subsequently.

Analyzing The Sustainability Of Industry Affected In Covid-19 Pandemic Scenario Using Cosine Similarity Measure Under Svpns And Pnn Model, Priyanka Majumder, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

COVID-19 outbreak is a reminder of the fact that the pandemics have happened in the past and will also occur in the future. The COVID-19 not only has affected the economy; but also it has affected the livelihood, which leads to the changes in businesses. This study aims to identify the most significant indicator (or parameter) that impacts the sustainability of industries. The study should also develop a realtime monitoring system for the sustainability of industries affected by COVID 19. In this work, the Polynomial Neural Network (PNN) and cosine similarity measure under SVPNS (Single-Valued Pentapartitioned Neutrosophic Set) environment have …

Generation Of Creative Game Scene Patterns By The Neutrosophic Genetic Cocoso Method, Aurimas Petrovas, Romualdas Bausys, Edmundas Kazimieras Zavadskas, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

Creative procedural generation requires, by its nature, a nondeterministic result. Each set of outputs has to satisfy the required criteria and, at the same time, has to show unique results to be considered creative. One of the keys to increasing nondeterminism is to use fuzzy neutrosophic sets. A combination of a CoCoSo multi-criteria decision algorithm with a genetic algorithm to generate game scenes was proposed. The algorithm satisfies the required game rules and improves the aesthetics value of the visual game scene. The proposed approach seeks to produce a creative solution which satisfies the replayability principle, when the solution is …

Introduction To Plithogenic Sociogram With Preference Representations By Plithogenic Number, Nivetha Martin, Florentin Smarandache, R. Priya

Branch Mathematics and Statistics Faculty and Staff Publications

The theory of Plithogeny is gaining momentum in recent times as it generalizes the concepts of fuzzy, intuitionistic fuzzy, neutrosophy and other extended representations of fuzzy sets. The relativity of the comprehensive and accommodative nature of plithogenic sets in dealing with attributes shall be applied to handle the decision–making problems in the field of sociology. This paper introduces the concepts of Plithogenic Sociogram (PS) and Plithogenic Number (PN) where the former is the integration of plithogeny to the sociometric technique of sociogram and the latter is the generalization of fuzzy, intuitionistic fuzzy and neutrosophic numbers that shall be used in …

Introduction To The Special Issue On Advances In Neutrosophic And Plithogenic Sets For Engineering And Sciences: Theory, Models, And Applications, S. A. Edalatpanah, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

Recently, research on uncertainty modeling has been progressing rapidly, and many essential and breakthrough studies have already been done. There are various ways to handle these uncertainties, such as fuzzy and intuitionistic fuzzy sets. Although these concepts can take incomplete information in various real-world issues, they cannot address all types of uncertainty, such as indeterminate and inconsistent information. The neutrosophic theory founded by Florentin Smarandache in 1998 constitutes a further generalization of fuzzy set, intuitionistic fuzzy set, picture fuzzy set, Pythagorean fuzzy set, spherical fuzzy set, etc. Since then, this logic has been applied in various science and engineering domains. …

Nidus Idearum. Scilogs, Ix: Neutrosophia Perennis, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

In this ninth book of scilogs collected from my nest of ideas, one may find new and old questions and solutions, – in email messages to research colleagues, or replies, and personal notes, some handwritten on the planes to, and from international conferences, about topics on Neutrosophy and its applications, such as: Neutrosophic Bipolar Set, Linguistic Neutrosophic Set, Neutrosophic Resonance Frequency, n-ary HyperAlgebra, n-ary NeutroHyperAlgebra, n-ary AntiHyperAlgebra, Plithogenic Crisp Graph, Plithogenic Fuzzy Graph, Plithogenic Intuitionistic Fuzzy Graph, Plithogenic Neutrosophic Graph, Plithogenic Real Number Graph, Plithogenic Complex Number Graph, Plithogenic Neutrosophic Number Graph, and many more.

Exchanging ideas with: Tareq Al-Shami, …

Nidus Idearum. Scilogs, X: Via Neutrosophica, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

In this tenth book of scilogs – called via neutrosophica (the neutrosophic way) –, one may find new and old questions and solutions, referring mostly to topics on NEUTROSOPHY, but also MULTISPACE, with miscellaneous addition of topics on Physics, Mathematics, or Sociology – email messages to research colleagues, or replies, notes about authors, articles, or books, spontaneous ideas, and so on.

Exchanging ideas with A. Elhassouny, Junhui Kim, Jeong Gon Lee, Kul Hur, Hojjatollah Farahani, W. B. Vasantha Kandasamy, Said Broumi, Mumtaz Ali, Mohamed Abdel-Basset, Ozen Ozer, Madad Khan, Gheorghe Săvoiu, John Mordeson, Adesina Agboola, Waldyr Rodrigues, Ajay Sharma, Stephen …

Sparse Domination Of The Martingale Transform, Michael Scott Kutzler

Mathematics & Statistics ETDs

Linear operators are of huge importance in modern harmonic analysis. Many operators can be dominated by finitely many sparse operators. The main result in this thesis is showing a toy operator, namely the Martingale Transform is dominated by a single sparse operator. Sparse operators are based on a sparse family which is simply a subset of a dyadic grid. We also show the A2 conjecture for the Martingale Transform which follows from the sparse domination of the Martingale Transform and the A2 conjecture for sparse operators.

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Multiple Baseline Interrupted Time Series: Describing Changes In New Mexico Medicaid Behavioral Health Home Patients’ Care, Jessica Reno

Mathematics & Statistics ETDs

In 2016, the CareLink New Mexico behavioral health homes program began enrolling Medicaid recipients with the goal of increasing care coordination, improving access to services, and decreasing long-term costs of care for adults with serious mental illness (SMI) and children with severe emotional disturbance (SED). To evaluate these aims, a retrospective interrupted time series study using Medicaid claims data was designed. First, a comparable subset of non-enrolled individuals was selected from the pool of Medicaid recipients with SMI or SED using propensity score matching. Then, segmented regression was applied to three outcomes: total Medicaid charges, number of outpatient behavioral health …

Optimal Transport Driven Bayesian Inversion With Application To Signal Processing, Elijah F. Perez

Mathematics & Statistics ETDs

This paper will outline a Debiased Sinkhorn Divergence driven Bayesian inversion framework. Conventionally, a Gaussian Driven Bayesian framework is used when performing Bayesian inversion. A major issue with this Gaussian framework is that the Gaussian likelihood, driven by the L2 norm, is not affected by phase shift in a given signal. This issue has been addressed in [1] using a Wasserstein framework. However, the Wasserstein framework still has an issue because it assumes statistical independence when multidimensional signals are analyzed. This assumption of statistical independence cannot always be made when analyzing signals where multiple detectors are recording one event, say …

Applications Of Evidence Theory To High-Consequence Systems Safety, Christina Marie Deffenbaugh

Mathematics & Statistics ETDs

Issues linked to abnormal environments (like high-consequence systems safety, e.g., nuclear weapon components, bridges, apartment buildings, etc.) may have insufficient information to use either classical statistical methods or Bayesian approaches for calculating associated probabilistic risks, so there is often a requirement for another method that can deal with a low-information situation to obtain a risk assessment. Belief/plausibility measures of uncertainty from A. P. Dempster and G. Shafer’s Evidence Theory is one such method. This thesis has two goals. First, a brief discussion on belief/plausibility measures as an application of Evidence Theory will familiarize the audience with its history and how …

The Encyclopedia Of Neutrosophic Researchers - 4th Volume (2021), Florentin Smarandache, Maykel Leyva-Vazquez

Branch Mathematics and Statistics Faculty and Staff Publications

Este es el cuarto volumen de la Enciclopedia de Investigadores Neutróficos, editados a partir de materiales ofrecidos por los autores que respondieron a la invitación del editor. Los autores se enumeran alfabéticamente. La introducción contiene una breve historia de la neutrosófica, y en especial se su impacto en Latinoamérica junto con enlaces a los principales artículos y libros. Los conjuntos neutrosóficos, la lógica neutrosófica, la probabilidad neutrosófica, la estadística neutrosófica, el precálculo neutrosófico, el cálculo neutrosófico, la psicología neutrosófica, la sociología neutrosófica etc., están ganando una atención significativa en resolver muchos problemas de la vida real que implican incertidumbre, imprecisión, …

Theory And Application Of Hypersoft Set, Florentin Smarandache, Muhammad Saeed, Muhammad Saqlain, Mohamed Abdel-Baset

Branch Mathematics and Statistics Faculty and Staff Publications

Aims and Scope Florentin Smarandache generalize the soft set to the hypersoft set by transforming the function �� into a multi-argument function. This extension reveals that the hypersoft set with neutrosophic, intuitionistic, and fuzzy set theory will be very helpful to construct a connection between alternatives and attributes. Also, the hypersoft set will reduce the complexity of the case study. The Book “Theory and Application of Hypersoft Set” focuses on theories, methods, algorithms for decision making and also applications involving neutrosophic, intuitionistic, and fuzzy information. Our goal is to develop a strong relationship with the MCDM solving techniques and to …

Solving Neutrosophic Linear Equations Systems Using Symbolic Computation (Resolucion De Sistemas De Ecuaciones Lineales Neutrosóficas Mediante Computación Simbólica), Maykel Leyva-Vazquez, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

In this paper, we apply the concept of neutrosophic numbers to solve a systems of neutrophic linear equations using symbolic computation. Also, we utilize Jupyter, which is supported in Google Colaboratory for performing symbolic computation. The sympy library of Python is used to perform the process of neutrosophic computation. Systems of neutrosophic linear equations are solved through symbolic computation in Python. A case study was developed for the determination of vehicular traffic with indeterminacy. This king of computation opens new ways to deal with indeterminacy in real-world problems.

Indeterminacy In Neutrosophic Theories And Their Applications, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

Indeterminacy makes the main distinction between fuzzy / intuitionistic fuzzy (and other extensions of fuzzy) set / logic vs. neutrosophic set / logic, and between classical probability and neutrosophic probability. Also, between classical statistics vs. neutrosophic and plithogenic statistics, between classical algebraic structures vs. neutrosophic algebrais structures, between crisp numbers vs. neutrosophic numbers. We present a broad definition of indeterminacy, various types of indeterminacies, and many practical applications.

Techno-Art Of Selariu Supermathematics Functions, Vol. Iii, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

The name of supermathematics (SM) was coined by the late mathematician Prof. em. Dr. doc. eng. Gheorghe Silaş who, at the presentation of the first works in this field, at the First National Conference of Vibrations in Machine Construction, Timişoara, 1978, entitled “EXCENTRIC CIRCULAR FUNCTIONS” declared: “Young man, you didn't just discover some new functions, but a new mathematics, a supermathematics”. Then, at my age of 40, I was as happy as I was when a teenager. And I found, with great satisfaction, that he might be right! In 1978! In 2000, after 22 years, he offered me to write …

A Review On Electroculture, Magneticulture And Laserculture To Boostplant Growth, Victor Christianto, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

While several reviews on potential applications of electroculture are available, in this survey, we discuss these issues from history, starting from earliest experiments by Ross. And in the last section, we discuss possible application of laserculture, another form of potential improvement. It is our hope that what we present here may be found useful for improving agricultural performance in many countries, as well as reducing dependence on fertilizer.

Neutroalgebra Theory, Vol. I, Florentin Smarandache, Memet Şahin, Derya Bakbak, Vakkas Uluçay, Abdullah Kargın

Branch Mathematics and Statistics Faculty and Staff Publications

In general, in any field of knowledge, with respect to any structure, one has the following neutrosophic triplet . They were introduced by Smarandache in 2019 and 2020.

1) A classical Structure is a structure whose all elements are characterized by the same given Relationships and Attributes and Laws.

2) A NeutroStructure is a structure that has at least one NeutroRelation or one NeutroAttribute or one NeutroLaw, and no AntiRelation and no AntiAttribute and no AntiLaw.

3) An AntiStructure is a structure that has at least one AntiRelation or one AntiAttribute or one AntiLaw.

As a particular case, in the …

Neutrosophic Dynamic Set, A. A. Salama, K. F. Alhasan, H. A. Elagamy, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

In this paper, we introduced the concept of the dynamic set according to modern logic, is neutrosophic logic. We study the neutrosophic dynamic set according to time and random variable depended on dynamic set. Neutrosophic dynamic is a dynamic analysis of a sequence of data through of time. It used in many problems in life such as a mathematical statistic, philosophy, medicine, engineering. Some examples and notes are presented.

Comments On “A New Combination Of Evidence Based On Compromise” By K. Yamada, Jean Dezert, Arnaud Martin, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

Yamada (2008) presents an interesting new model of combination of evidence called combination by compromise based on previous works published in Yamada (2006b,a). In the theory of belief functions, one of the most important problems is the one of reassigning the conflicting belief mass, as highlighted by the famous Zadeh’s example, see Zadeh (1979). To date, many combination rules have been developed, proposing a solution to this problem.

Neutrosophic Sets And Systems, Vol. 41, 2021, Florentin Smarandache, Mohamed Abdel-Basset, Said Broumi

Neutrosophic Sets and Systems

No abstract provided.

Eureka Moment As Divine Spark In The Light Of Direct Experience With The Spirit And Nature, Victor Christianto, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

In the ancient world, the Greeks believed that all great insights came from one of nine muses, divine sisters who brought inspiration to mere mortals. In the modern world, few people still believe in the muses, but we all still love to hear stories of sudden inspiration. Like Newton and the apple, or Archimedes and the bathtub (both another type of myth), we’re eager to hear and to share stories about flashes of insight. But what does it take to be actually creative? How to have such a flash insight? Turns out, there is real science behind "aha moments." We …

Structure, Neutrostructure, And Antistructure In Science, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

In any science, a classical Theorem, defined on a given space, is a statement that is 100% true (i.e. true for all elements of the space). To prove that a classical theorem is false, it is sufficient to get a single counter-example where the statement is false. Therefore, the classical sciences do not leave room for partial truth of a theorem (or a statement). But, in our world and in our everyday life, we have many more examples of statements that are only partially true, than statements that are totally true. The NeutroTheorem and AntiTheorem are generalizations and alternatives of …

Introduction To Neutrosophic Genetics, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

Neutrosophic Genetics is the study of genetics using neutrosophic logic, set, probability, statistics, measure and other neutrosophic tools and procedures. In this paper, based on the Neutrosophic Theory of Evolution (that includes degrees of Evolution, Neutrality (or Indeterminacy), and Involution) – as extension of Darwin’s Theory of Evolution, we show the applicability of neutrosophy in genetics, and we present within the frame of neutrosophic genetics the following concepts: neutrosophic mutation, neutrosophic speciation, and neutrosophic coevolution.

An Analysis Of Growth Of The Community Integration Psychological Score In An Ethnically Diverse Population Experiencing Homelessness In A Permanent Supportive Housing Program Using Hierarchical Mixed Modeling, Leah Hollis Puglisi

Mathematics & Statistics ETDs

Hierarchical models are becoming increasingly common in epidemiological and psychological research. When analyzing data from such studies, the nested structure of the data must be taken into account. Mixed modeling in conjunction with hierarchical mixed modeling allows researchers to ask broad questions about the population of interest. Modeling under restricted maximum likelihood estimation (REML), as opposed to full maximum likelihood estimation (ML), increases the accuracy of estimates for the random effects in the model. We use hierarchical mixed modeling under REML estimation to analyze which factors increase “community integration”, a concept and a construct developed and used in the mental …