La neutrosofía es una nueva rama de la filosofía la cual estudia el origen, naturaleza y alcance de las neutralidades creada por el Profesor Florentin Smarandache. La lógica y los conjuntos neutrosóficos por su parte, constituyen una generalización de la lógica y los conjuntos difusos de Zadeh, y especialmente de la lógica intuicionista de Atanassov, con múltiples aplicaciones en el campo de la toma de decisiones, segmentación de imágenes y aprendizaje automático, por ci...

This is the second volume of the Encyclopedia of Neutrosophic Researchers, edited from materials offered by the authors who responded to the editor’s invitation. The authors are listed alphabetically, and represent the following countries: Angola, Argentina, P.R. China, Denmark, Dominican Republic, Ecuador, Egypt, India, Iraq, Iran, Jordan, South Korea, Morocco, Nigeria, Pakistan, Romania, Serbia, Syria, Turkey, S.R. Vietnam. The introduction contains an updated history...

The innovative notion of neutrosophic triplet groups, introduced by Smarandache and Ali in 2014-2016, happens to yield the anti-element and neutral element once the element is given. It is established that the neutrosophic triplet group collection forms the classical group under product for Zn, for some specific n. However the collection is not even closed under sum. These neutrosophic triplet groups are built using only modulo integers or Cayley tables. Several interest...

The first part of this book focuses on Neutrosophic Precalculus, which studies the neutrosophic functions. A Neutrosophic Function 𝑓:𝐴→𝐵 is a function which has some indeterminacy, with respect to its domain of definition, to its range, or to its relationship that associates elements in 𝐴 with elements in 𝐵. As particular cases, we present the neutrosophic exponential function and neutrosophic logarithmic function. The neutrosophic inverse function is the inverse of...

This book is part of the book-series dedicated to the advances of neutrosophic theories and their applications, started by the author in 1998. Its aim is to present the last developments in the field. This is the second extended and improved edition of Neutrosophic Perspectives (September 2017; first edition was published in June 2017). For the first time, we now introduce: — Neutrosophic Duplets and the Neutrosophic Duplet Structures; — Neutrosophic Multisets (as a...

This book is an excellent exposition of the use of Data Envelopment Analysis (DEA) to generate data analytic insights to make evidence-based decisions, to improve productivity, and to manage cost-risk and benefit-opportunity in public and private sectors. The design and the content of the book make it an up-to-date and timely reference for professionals, academics, students, and employees, in particular those involved in strategic and operational decision-making processe...

This is the first volume of the Encyclopedia of Neutrosophic Researchers, edited from materials offered by the authors who responded to my invitation. The introduction contains a short history of neutrosophics, together with links to the main papers and books. Neutrosophy considers a proposition, theory, event, concept, or entity, "A" in relation to its opposite, "Anti-A" and that which is not A, "Non-A", and that which is neither "A" nor "Anti-A", denoted by "Neut-A"...

Neutrosophic theory and applications have been expanding in all directions at an astonishing rate especially after the introduction the journal entitled “Neutrosophic Sets and Systems”. New theories, techniques, algorithms have been rapidly developed. One of the most striking trends in the neutrosophic theory is the hybridization of neutrosophic set with other potential sets such as rough set, bipolar set, soft set, hesitant fuzzy set, etc. The different hybrid structure...

Neutrosophic Over--/Under-/Off-Set and -Logic were defined for the first time by the author in 1995 and presented to various international and national conferences and seminars between 1995-2016 and first time published in 2007. They are totally different from other sets/logics/probabilities/statistics. Smarandache extended the neutrosophic set respectively to Neutrosophic Overset {when some neutrosophic component is > 1}, Neutrosophic Underset {when some neutrosophic co...

This book consists of seven chapters. In chapter one we introduced neutrosophic ideals (bi, quasi, interior, (m,n) ideals) and discussed the properties of these ideals. Moreover, we characterized regular and intra-regular AG-groupoids using these ideals. In chapter two we introduced neutrosophic minimal ideals in AG-groupoids and discussed several properties. In chapter three, we introduced different neutrosophic regularities of AG-groupoids. Further we discussed several...

Symbolic (or Literal) Neutrosophic Theory is referring to the use of abstract symbols (i.e. the letters T, I, F, or their refined indexed letters Tj, Ik, Fl) in neutrosophics. In the first chapter we extend the dialectical triad thesis-antithesis-synthesis (dynamics of and , to get a synthesis) to the neutrosophic tetrad thesis-antithesis-neutrothesis-neutrosynthesis (dynamics of , , and , in order to get a neutrosynthesis). In the second chapter we introduce the ne...

In this book authors for the first time have made a through study of neutrosophic graphs. This study reveals that these neutrosophic graphs give a new dimension to graph theory. The important feature of this book is it contains over 200 neutrosophic graphs to provide better understanding of this concepts. Further these graphs happen to behave in a unique way inmost cases, for even the edge colouring problem is different from the classical one. Several directions and dime...

Since the world is full of indeterminacy, the Neutrosophics found their place into contemporary research. We now introduce for the first time the notions of Neutrosophic Crisp Sets and Neutrosophic Topology on Crisp Sets. We develop the 2012 notion of Neutrosophic Topological Spaces and give many practical examples. Neutrosophic Science means development and applications of Neutrosophic Logic / Set / Measure / Integral / Probability etc. and their applications in any fie...

In this book authors build algebraic structures on fuzzy unit semi open square UF = {(a, b) | a, b ε [0, 1)} and on the fuzzy neutrosophic unit semi open square UN = {a + bI | a, b ε [0, 1)}. This study is new and we define, develop and describe several interesting and innovative theories about them. We cannot build ring on UN or UF. We have only pseudo rings of infinite order. We also build pseudo semirings using these semi open unit squares. We construct vector spaces,...

Neutrosophic Theory means Neutrosophy applied in many fields in order to solve problems related to indeterminacy. Neutrosophy considers every entity together with its opposite or negation , and with their spectrum of neutralities in between them (i.e. entities supporting neither nor ). Where , which of course depends on , can be indeterminacy, neutrality, tie (game), unknown, vagueness, contradiction, ignorance, incompleteness, imprecision, etc. Hence, in one hand,...

Although the neutrosophic statistics has been defined since 1996, and published in the 1998 book Neutrosophy. / Neutrosophic Probability, Set, and Logic, it has not been developed since now. A similar fate had the neutrosophic probability that, except a few sporadic articles published in the meantime, it was barely developed in the 2013 book “Introduction to Neutrosophic Measure, Neutrosophic Integral, and Neutrosophic Probability”. Neutrosophic Statistics is an exten...

Here for the first time we introduce the semi open square using modulo integers. Authors introduce several algebraic structures on them. These squares under addition modulo ‘n’ is a group and however under product × this semi open square is only a semigroup as under × the square has infinite number of zero divisors. Apart from + and × we define min and max operation on this square. Under min and max operation this semi real open square is a semiring. We define the new...

In a similar way as passing from Euclidean Geometry to Non-Euclidean Geometry, we can pass from Subluminal Physics to Superluminal Physics, and further to Instantaneous Physics (instantaneous traveling). In the lights of two consecutive successful CERN experiments with superluminal particles in the Fall of 2011, we believe these two new fields of research should begin developing. A physical law has a form in Newtonian physics, another form in the Relativity Theory, and d...

This book is a collection of articles, notes, reviews, blogs and abstracts on Physics. Some are published for the first time here, some were previously published in journals, and revised here. We approach a novel form of plasma, Unmatter Plasma. The electron-positron beam plasma was generated in the laboratory in the beginning of 2015. This experimental fact shows that unmatter, a new form of matter that is formed by matter and antimatter bind together (mathematically pr...

In this book, the contributors argue on actual reasons why Hilbert’s axiomatic program to unify gravitation theory and electromagnetism failed completely. An outline of plausible resolution of this problem is given here, based on: a) Gödel’s incompleteness theorem, b) Newton’s aether stream model. Also, a calculation of receding Moon from Earth based on such a matter creation hypothesis is given. More experiments and observations are called to verify this new hypothesis,...