

Topics of papers to be published in Neutrosophic Sets and Systems (NSS) international journal Zadeh introduced the degree of membership/truth (T) in 1965 and defined the fuzzy set. Atanassov introduced the degree of nonmembership/falsehood (F) in 1986 and defined the intuitionistic fuzzy set. Smarandache introduced the degree of indeterminacy/neutrality (I) as independent component in 1995 (published in 1998) and he defined the neutrosophic set on three components: (T, I, F) = (Truth, Indeterminacy, Falsehood), where in general T, I, F are subsets of the interval [0, 1]; in particular T, I, F may be intervals, hesitant sets, singlevalues, etc.; Indeterminacy (or Neutrality), as independent component from the truth and from the falsehood, is the main distinction between Neutrosophic Theories and other classical and fuzzy theory or fuzzy extension theories: https://fs.unm.edu/Indeterminacy.pdf See F. Smarandache, Neutrosophy / Neutrosophic probability, set, and logic", Proquest, Michigan, USA, 1998, https://arxiv.org/ftp/math/papers/0101/0101228.pdf https://fs.unm.edu/eBookNeutrosophics6.pdf; reviewed in Zentralblatt für Mathematik (Berlin, Germany): https://zbmath.org/?q=an:01273000 and cited by Denis Howe in The Free Online Dictionary of Computing, England, 1999. Neutrosophic Set and Logic are generalizations of classical, fuzzy, and intuitionist fuzzy set and logic: https://arxiv.org/ftp/math/papers/0404/0404520.pdf https://arxiv.org/ftp/math/papers/0303/0303009.pdf Etymology Neutrosophic Logic is a general framework for unification of many existing
logics, such as fuzzy logic (especially intuitionistic fuzzy logic),
paraconsistent logic, intuitionist logic, etc. The main idea of NL is to
characterize each logical statement in a 3DNeutrosophic Space, where each
dimension of the space represents respectively the truth (T), the falsehood (F),
and the indeterminacy (I) of the statement under consideration, where T, I, F
are standard or nonstandard real subsets of ]^{}0, 1^{+}[ with not necessarily any
connection between them. 1980s  Foundation of Paradoxism that is an international movement in science and culture based on excessive use of contradictions, antitheses, oxymoron, and paradoxes [Smarandache]. During three decades (19802020) hundreds of authors from tens of countries around the globe contributed papers to 15 international paradoxist anthologies: https://fs.unm.edu/a/paradoxism.htm 19951998 – Smarandache extended the paradoxism (based on opposites) to a new branch of philosophy called Neutrosophy (based on opposites and their neutral/indeterminacies), that gave birth to many scientific branches, such as: neutrosophic logic, neutrosophic set, neutrosophic probability and statistics, neutrosophic algebraic structures, and so on with multiple applications in all fields. Neutrosophy
is also an extension of the Dialectics, the YinYang ancient
Chinese philosophy, the Manichaeism, and in general of the Dualism,
Single Valued Neutrosophic Sets https://fs.unm.edu/SingleValuedNeutrosophicSets.pdf
Indeterminacy in Neutrosophic Theories and their Applications
1998, 2019  Extended Nonstandard Neutrosophic Logic, Set, Probability based on NonStandard Analysis https://arxiv.org/ftp/arxiv/papers/1903/1903.04558.pdf https://fs.unm.edu/AdvancesOfStandardAndNonstandard.pdf
Improved
Definition of NonStandard Neutrosophic Logic and
Introduction to Neutrosophic Hyperreals (Third version),
arXiv, Cornell University, New York City, USA,
https://arxiv.org/ftp/arxiv/papers/1812/1812.02534.pdf,
2007 – The Neutrosophic Set was extended [Smarandache, 2007] to
Neutrosophic
Overset (when some neutrosophic component is > 1), since he observed that, for
example, an employee working overtime deserves a degree of membership > 1, with
respect to an employee that only works regular fulltime and whose degree of
membership = 1;
(T_{1}, T_{2},
...; I_{1}, I_{2}, ...; F_{1}, F_{2}, ...): (<A>; <neutA_{1}>, <neutA_{2}>, …, <neutA_{n}>; <antiA>) https://fs.unm.edu/LawIncludedMultipleMiddle.pdf and the Law of Included InfinitelyManyMiddles (2023) https://fs.unm.edu/NSS/LawIncludedInfinitely1.pdf (<A>; <neutA_{1}>, <neutA_{2}>, …, <neutA_{infinity}>; <antiA>)
https://fs.unm.edu/NS/NeutrosophicStatistics.htm Neutrosophic Numbers used in Neutrosophic Statistics https://fs.unm.edu/NS/AppurtenanceInclusionEquationsrevised.pdf
2015  Extension of the Analytical Hierarchy Process (AHP) to αDiscounting Method for MultiCriteria Decision Making (αD MCDC) https://fs.unm.edu/ScArt/AlphaDiscountingMethod.pdf https://fs.unm.edu/ScArt/CPIntervalAlphaDiscounting.pdf https://fs.unm.edu/ScArt/ThreeNonLinearAlpha.pdf https://fs.unm.edu/alphaDiscountingMCDMbook.pdf
2015 – (t,i,f)Neutrosophic Graphs.
2015  ThesisAntiThesisNeutroThesis, and NeutroSynthesis, Neutrosophic
Axiomatic System, neutrosophic dynamic systems, symbolic neutrosophic logic, (t,
i, f)Neutrosophic Structures, INeutrosophic Structures, Refined Literal
Indeterminacy, Quadruple Neutrosophic Algebraic Structures, Multiplication Law
of SubIndeterminacies, and Neutrosophic Quadruple Numbers of the form a + bT +
cI + dF, where T, I, F are literal neutrosophic components, and a, b, c, d are
real or complex numbers: 2016  Addition, Multiplication, Scalar Multiplication, Power, Subtraction, and Division of Neutrosophic Triplets (T, I, F) https://fs.unm.edu/CR/SubstractionAndDivision.pdf
2017  2020  Neutrosophic Score, Accuracy, and Certainty Functions form a total order relationship on the set of (singlevalued, intervalvalued, and in general subsetvalued) neutrosophic triplets (T, I, F); and these functions are used in MCDM (MultiCriteria Decision Making): https://fs.unm.edu/NSS/TheScoreAccuracyAndCertainty1.pdf
2017  In biology Smarandache introduced the Theory of Neutrosophic Evolution:
Degrees of Evolution, Indeterminacy or Neutrality, and Involution (as
extension of
Darwin's Theory of Evolution): https://fs.unm.edu/V/NeutrosophicEvolution.mp4
https://fs.unm.edu/NeutrosophicEvolution.pdf
2017  Enunciation of the Law that: It Is Easier to Break
from Inside than from Outside a Neutrosophic Dynamic System (Smarandache
 Vatuiu):
2018  2023  Introduction of new types of soft sets: HyperSoft Set, IndetermSoft Set, IndetermHyperSoft Set, SuperHyperSoft Set, TreeSoft Set: https://fs.unm.edu/TSS/NewTypesSoftSetsImproved.pdf https://fs.unm.edu/TSS/SuperHyperSoftSet.pdf https://fs.unm.edu/NSS/IndetermSoftIndetermHyperSoft38.pdf (with IndetermSoft Operators acting on IndetermSoft Algebra)
2018 – Introduction to Neutrosophic Psychology (Neutropsyche, Refined
Neutrosophic Memory: conscious, aconscious, unconscious, Neutropsychic
Personality, Eros / Aoristos / Thanatos, Neutropsychic Crisp Personality):
2019  Introduction to Neutrosophic Sociology (NeutroSociology) [neutrosophic
concept, or (T, I, F)concept, is a concept that is T% true, I% indeterminate,
and F% false]: 2019  Refined Neutrosophic Crisp Set https://fs.unm.edu/RefinedNeutrosophicCrispSet.pdf 20192024  Introduction of sixteen new types of topologies: NonStandard Topology, Largest Extended NonStandard Real Topology, Neutrosophic Triplet Weak/Strong Topologies, Neutrosophic Extended Triplet Weak/Strong Topologies, Neutrosophic Duplet Topology, Neutrosophic Extended Duplet Topology, Neutrosophic MultiSet Topology, NonStandard Neutrosophic Topology, NeutroTopology, AntiTopology, Refined Neutrosophic Topology, Refined Neutrosophic Crisp Topology, SuperHyperTopology, and Neutrosophic SuperHyperTopology: https://fs.unm.edu/TT/RevolutionaryTopologies.pdf 2019  Generalization of the classical Algebraic Structures to NeutroAlgebraic Structures (or NeutroAlgebras) {whose operations and axioms are partially true, partially indeterminate, and partially false} as extensions of Partial Algebra, and to AntiAlgebraic Structures (or AntiAlgebras) {whose operations and axioms are totally false}.
And, in general, he extended any classical Structure, in no matter what field of knowledge, to a NeutroStructure and an AntiStructure: https://fs.unm.edu/NA/NeutroStructure.pdf
As alternatives and generalizations of the NonEuclidean Geometries he introduced in 2021 the NeutroGeometry & AntiGeometry. While the NonEuclidean Geometries resulted from the total negation of only one specific axiom (Euclid’s Fifth Postulate), the AntiGeometry results from the total negation of any axiom and even of more axioms from any geometric axiomatic system (Euclid’s, Hilbert’s, etc.), and the NeutroGeometry results from the partial negation of one or more axioms [and no total negation of no axiom] from any geometric axiomatic system. https://fs.unm.edu/NSS/NeutroGeometryAntiGeometry31.pdf https://fs.unm.edu/NG/
20192022  Extension of HyperGraph to SuperHyperGraph and Neutrosophic SuperHyperGraph https://fs.unm.edu/NSS/nSuperHyperGraph.pdf
2020  Introduction to Neutrosophic Genetics: https://fs.unm.edu/NeutrosophicGenetics.pdf
2021  Introduction to Neutrosophic Number Theory (Abobala) https://fs.unm.edu/NSS/FoundationsOfNeutrosophicNumberTheory10.pdf
2021  As alternatives and generalizations of the NonEuclidean Geometries, Smarandache introduced in 2021 the NeutroGeometry & AntiGeometry. While the NonEuclidean Geometries resulted from the total negation of only one specific axiom (Euclid’s Fifth Postulate), the AntiGeometry results from the total negation of any axiom and even of more axioms from any geometric axiomatic system (Euclid’s, Hilbert’s, etc.), and the NeutroGeometry results from the partial negation of one or more axioms [and no total negation of no axiom] from any geometric axiomatic system: https://fs.unm.edu/NSS/NeutroGeometryAntiGeometry31.pdf Real Examples of NeutroGeometry and AntiGeometry: https://fs.unm.edu/NSS/ExamplesNeutroGeometryAntiGeometry35.pdf
2021  Introduction of Plithogenic Logic as a generalization of MultiVariate Logic https://fs.unm.edu/NSS/IntroductionPlithogenicLogic1.pdf 2021  Introduction of Plithogenic Probability and Statistics as generalizations of MultiVariate Probability and Statistics respectively https://fs.unm.edu/NSS/PlithogenicProbabilityStatistics20.pdf 2021  Introduction of the AHIsometry f(x+yI) = f(x) + I[f(x+y)  f(x)] and foundation of the Neutrosophic Euclidean Geometry (by Abobala & Hatip) https://fs.unm.edu/NSS/AlgebraicNeutrosophicEuclideanGeometry10.pdf and extension to nRefined AHIsometry (Smarandache & Abobala, 2024) https://fs.unm.edu/NSS/RefinedLiteral21.pdf 2016  2022 SuperHyperAlgebra & Neutrosophic SuperHyperAlgebra https://fs.unm.edu/SuperHyperAlgebra.pdf 2022  SuperHyperFunction, SuperHyperTopology https://fs.unm.edu/NSS/SuperHyperFunction37.pdf 2022  2023 Neutrosophic Operational Research (Smarandache  Jdid) https://fs.unm.edu/NeutrosophicOperationsResearch.pdf 2023  Symbolic Plithogenic Algebraic Structures built on the set of Symbolic Plithogenic Numbers of the form a_{0} + a_{1}P_{1} + a_{2}P_{2} + ... + a_{n}P_{n }where the multiplication P_{i}·P_{j }is based on the prevalence order and absorbance law https://fs.unm.edu/NSS/SymbolicPlithogenicAlgebraic39.pdf 2023  Foundation of Neutrosophic Cryptology (MerkepciAbobalaAllouf) https://fs.unm.edu/NeutrosophicCryptography1.pdf https://fs.unm.edu/NeutrosophicCryptography2.pdf
https://fs.unm.edu/NSS/ 2023  The MultiNeutrosophic Set (a neutrosophic set whose elements' degrees T, I, F are evaluated by multiple sources): https://fs.unm.edu/NSS/MultiNeutrosophicSet.pdf 2023  The MultiAlist System of Thought (an open dynamic system of many opposites, with their neutralities or indeterminacies, formed by elements from many systems): https://fs.unm.edu/NSS/MultiAlistSystemOfThought.pdf
2023  Appurtenance Equation,
Inclusion Equation, https://fs.unm.edu/NS/AppurtenanceInclusionEquationsrevised.pdf 2024  SuperHyperStructure and Neutrosophic SuperHyperStructure 2024  Zarathustra & Neutrosophy https://fs.unm.edu/Zoroastrianism.pdf The Principles of (Partial Locality, Partial Indeterminacy, Partial NonLocality) and (Multi Locality, Multi Indeterminacy, Multi NonLocality) https://fs.unm.edu/nss8/index.php/111/article/view/4858/2043 Neutrosophy Transcends Binary Oppositions in Mythology and Folklore https://fs.unm.edu/NSS/NeutrosophyTranscendsBinary4.pdf Neutrosophy means: Common Parts to Uncommon Things and Uncommon Parts to Common Things https://fs.unm.edu/NSS/NeutroMeans1.pdf 2024  UpsideDown Logics: Falsification of the Truth & Truthification of the False https://fs.unm.edu/UpsideDownLogics.pdf 2024  Neutrosophic (and fuzzyextensions) TwoFold Algebra https://fs.unm.edu/NeutrosophicTwoFoldAlgebra.pdf
Applications in: Important Neutrosophic Researchers: There are about 7,500 neutrosophic researchers, within 90 countries around the globe, that have produced about 4,000 articles and books, and over 70 PhD and MSc theses, within more than two decades. Many neutrosophic researchers got specialized into various fields of neutrosophics, plithogenics, NeutroAlgebra and AntiAlgebra, NeutroGeometry and AntiGeometry, new types of topologies, new types of soft sets, SuperHyperStructures, etc.


