Topics of papers to be published on the Neutrosophic Sets and Systems (NSS), Neutrosophic Computing and Machine Learning (NCML), Neutrosophic Knowledge (NK) international journals
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 or dependent 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, single-values, etc.;
Indeterminacy (or Neutrality), as independent or dependent 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://fs.unm.edu/eBook-Neutrosophics6.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:
Etymology
The words “neutrosophy” and “neutrosophic” were
coined/invented by F. Smarandache in his 1998 book.
Neutrosophy: A branch of philosophy, introduced by F. Smarandache in
1980, which studies the origin, nature, and scope of neutralities, as
well as their interactions with different ideational spectra.
Neutrosophy considers a proposition, theory, event, concept, or entity
<A> in relation to its opposite <antiA>, and with their
neutral <neutA>.
Neutrosophy (as dynamic of opposites and their neutrals) is an
extension of the Dialectics and Yin Yang (which are the dynamic of
opposites only).
Neutrosophy is the basis of neutrosophic set, neutrosophic logic,
neutrosophic measure, neutrosophic probability, neutrosophic statistics
etc.
Further on, Neutrosophy were extended to Collective
Neutrosophy and n-ary Collective Neutrosophy as opposition,
cooperation, or neutrality: https://fs.unm.edu/NSS/31CollectiveNeutrosophy.pdf
Neutrosophic Set is a Generalization of
Intuitionist Fuzzy Set, Inconsistent Intuitionist Fuzzy Set (Picture
Fuzzy Set, Ternary Fuzzy Set), Pythagorean Fuzzy Set (Atanassov’s
Intuitionist Fuzzy Set of second type), q-Rung Orthopair Fuzzy Set,
Spherical Fuzzy Set, and n-HyperSpherical Fuzzy Set, while
Neutrosophication is a Generalization of Regret
Theory, Grey System Theory, and Three-Ways Decision.
https://fs.unm.edu/Raspunsatan.pdf
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
3D-Neutrosophic 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
non-standard real subsets of ]-0, 1+[ with not
necessarily any connection between them.
For all engineering, technical, administrative and other practical
applications the classical unit interval [0, 1] should be used.
While
Neutrosophic Probability and Statistics are generalizations of
classical and imprecise probability and classical statistics
respectively.
The Most Important Books and Papers on the
Advancement of Neutrosophics
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 (1980-2020) hundreds of authors from tens of countries around the globe contributed papers to 15 international paradoxist anthologies: https://fs.unm.edu/a/paradoxism.htm
1995-1998 – 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 Yin-Yang ancient Chinese philosophy, the Manichaeism,
and in general of the Dualism,
https://fs.unm.edu/Neutrosophy-A-New-Branch-of-Philosophy.pdf
Towards A New Paradigm: Insights into Neutrosophic Philosophy https://fs.unm.edu/TowardANewParadigm.pdf
introduced the neutrosophic set/logic/probability/statistics;
introduces the single-valued neutrosophic set (pp. 7-8);
https://fs.unm.edu/eBook-Neutrosophics6.pdf
(online sixth edition)
The Rank
Order of the Neutrosophic Triplets (T, I, F) May Change after
Normalization
Single-Valued, Interval-Valued, Subset-Valued Neutrosophic Standard and NonStandard Set and Logic
https://fs.unm.edu/StandardNonStandardNeutrosophicSet.pdf
Indeterminacy in Neutrosophic Theories and
their Applications
https://fs.unm.edu/Indeterminacy.pdf
1998, 2019 - Extended Nonstandard Neutrosophic Logic, Set, Probability based on NonStandard Analysis
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://fs.unm.edu/NonStandardAnalysis-Imamura-proven-wrong.pdf
2002 – Introduction of corner cases of sets / probabilities /
statistics / logics, such as:
- Neutrosophic intuitionistic set (different from intuitionist fuzzy
set), neutrosophic paraconsistent set, neutrosophic faillibilist set,
neutrosophic paradoxist set, neutrosophic pseudo-paradoxist set,
neutrosophic tautological set, neutrosophic nihilist set, neutrosophic
dialetheist set, neutrosophic trivialist set;
- Neutrosophic intuitionistic probability and statistics, neutrosophic
paraconsistent probability and statistics, neutrosophic faillibilist
probability and statistics, neutrosophic paradoxist probability and
statistics, neutrosophic pseudo-paradoxist probability and statistics,
neutrosophic tautological probability and statistics, neutrosophic
nihilist probability and statistics, neutrosophic dialetheist
probability and statistics,neutrosophic trivialist probability and
statistics;
- Neutrosophic paradoxist logic (or paradoxism), neutrosophic
pseudo-paradoxist logic (or neutrosophic pseudo-paradoxism),
neutrosophic tautological logic (or neutrosophic tautologism):
https://fs.unm.edu/DefinitionsDerivedFromNeutrosophics.pdf
2003 – Introduction by Kandasamy and Smarandache of Neutrosophic
Numbers (a+bI, where I = literal indeterminacy, I2
= I, which is different from the numerical indeterminacy I =
real set),
I-Neutrosophic Algebraic Structures
and Neutrosophic Cognitive Maps
https://fs.unm.edu/NCMs.pdf
2005 - Introduction of Interval Neutrosophic Set/Logic
https://fs.unm.edu/INSL.pdf
2006 – Introduction of Degree of Dependence and Degree of
Independence
between the Neutrosophic Components T, I, F.
For single valued neutrosophic logic, the sum of the components is:
0 ≤ t+i+f ≤ 3 when all three components are independent;
0 ≤ t+i+f ≤ 2 when two components are dependent, while the third one is
independent from them;
0 ≤ t+i+f ≤ 1 when all three components are dependent.
When three or two of the components T, I, F are independent, one leaves
room for background
incomplete information (sum < 1), paraconsistent and contradictory
information (sum > 1), or complete information (sum = 1).
If all three components T, I, F are dependent, then similarly one
leaves room for incomplete information (sum < 1), or complete
information (sum = 1).
In general, the sum of two components x and y that vary in the unitary
interval [0, 1] is:
0 ≤ x + y ≤ 2 - d°(x, y), where d°(x, y) is the degree of dependence
between x and y, while
d°(x, y) is the degree of independence between x and y.
Degrees of Dependence and Independence between Neutrosophic Components
T, I, F are independent components, leaving room for incomplete
information (when their superior sum < 1), paraconsistent
and contradictory information (when the superior sum > 1), or complete
information (sum of components = 1).
For software engineering proposals the classical unit interval [0, 1]
is used.
https://doi.org/10.5281/zenodo.571359
https://fs.unm.edu/eBook-Neutrosophics6.pdf
(p. 92)
https://fs.unm.edu/NSS/DegreeOfDependenceAndIndependence.pdf
The Rank Order of the Neutrosophic Triplets (T, I, F) May Change after Normalization
https://fs.unm.edu/RankingOrderMayChange.pdf
2007 – The uncertain Set was extended by Smarandache in 2007 to
uncertain OverSet (when some 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 full-time and whose degree of membership = 1;
and to uncertain UnderSet (when some neutrosophic component is
< 0), since, for example, an employee making more damage than
benefit to his company deserves a degree of membership < 0, with
respect to an employee that produces benefit to the company and has the
degree of membership > 0;
and to and to uncertain OffSet (when some neutrosophic
components are off the interval [0, 1], i.e. some neutrosophic
component > 1 and some neutrosophic component < 0).
Then, similarly, the uncertain Logic/Measure/Probability/Statistics
etc. were extended to respectively uncertain Over-/Under-/Off- Logic
/ Measure / Probability / Statistics etc.
By "uncertain" we mean all types of fuzzy and fuzzy-extensions (intuitionistic fuzzy, neutrosophic, spherical fuzzy, plithogenic, etc.).
https://fs.unm.edu/Over-Under-Off.htm
https://fs.unm.edu/NeutrosophicOversetUndersetOffset.pdf
https://fs.unm.edu/SVNeutrosophicOverset-JMI.pdf
https://fs.unm.edu/IV-Neutrosophic-Overset-Underset-Offset.pdf
https://fs.unm.edu/NSS/DegreesOf-Over-Under-Off-Membership.pdf
Operators for Uncertain Over/Under/Off-Sets/-Logics/ Probabilities/-Statistics
https://fs.unm.edu/NSS/29OperatorsUncertain.pdf
2007 – Smarandache introduced the Neutrosophic Tripolar Set and
Neutrosophic Multipolar Set
and consequently
the Neutrosophic Tripolar Graph and Neutrosophic Multipolar
Graph
https://fs.unm.edu/eBook-Neutrosophics6.pdf
(p. 93)
https://fs.unm.edu/IFS-generalized.pdf
2009 – Introduction of N-norm and N-conorm
https://fs.unm.edu/N-normN-conorm.pdf
2010 - The α-Discounting (α-DMCDM) as an
extension of AHP, TOPSIS, VIKOR, PROMETHEE, and Weighted Sum
https://fs.unm.edu/NSS/15AlphaDiscounting-MostGeneral.pdf
2013 - Development of Neutrosophic Measure and Neutrosophic
Probability
( chance that an event occurs, indeterminate chance of occurrence,
chance that the event does not occur )
https://fs.unm.edu/NeutrosophicMeasureIntegralProbability.pdf
2013 – Smarandache Refined / Split the Neutrosophic Components
(T, I, F) into Neutrosophic SubComponents
(T1,
T2, ...; I1, I2, ...; F1,
F2, ...):
https://fs.unm.edu/n-ValuedNeutrosophicLogic-PiP.pdf
2014
– Introduction of the Law of Included Multiple-Middle (as
extension of the Law of Included Middle)
(<A>; <neutA1>, <neutA2>, …, <neutAn>; <antiA>)
https://fs.unm.edu/LawIncludedMultiple-Middle.pdf
and the Law of Included Infinitely-Many-Middles (2023)
https://fs.unm.edu/NSS/LawIncludedInfinitely1.pdf
(<A>; <neutA1>, <neutA2>, …, <neutAinfinity>; <antiA>)
2014 - Development of Neutrosophic Statistics (indeterminacy
is introduced into classical statistics with respect to any data
regarding the sample / population, probability distributions / laws /
graphs / charts etc., with respect to the individuals that only
partially belong to a sample / population, and so on):
https://fs.unm.edu/NS/NeutrosophicStatistics.htm
Neutrosophic Numbers used in Neutrosophic Statistics
https://fs.unm.edu/NS/AppurtenanceInclusionEquations-revised.pdf
2010 - Extension of the Analytical Hierarchy Process (AHP), TOPSIS, VIKOR, PROMETHEE, and Weighted Sum to α-Discounting Method for Multi-Criteria
Decision Making (α-D MCDC)
https://fs.unm.edu/ScArt/AlphaDiscountingMethod.pdf
https://fs.unm.edu/ScArt/CP-IntervalAlphaDiscounting.pdf
https://fs.unm.edu/ScArt/ThreeNonLinearAlpha.pdf
https://fs.unm.edu/alpha-DiscountingMCDM-book.pdf
2015 - Introduction of Neutrosophic Precalculus and Neutrosophic
Calculus
https://fs.unm.edu/NeutrosophicPrecalculusCalculus.pdf
2015 – Refined Neutrosophic Numbers (a+ b1I1
+ b2I2 + … + bnIn), where I1,
I2, …, In are SubIndeterminacies of Indeterminacy
I.
2015 – (t,i,f)-Neutrosophic Graphs.
2015 - Thesis-AntiThesis-NeutroThesis, and NeutroSynthesis,
Neutrosophic Axiomatic System, neutrosophic dynamic systems, symbolic
neutrosophic logic, (t, i, f)-Neutrosophic Structures, I-Neutrosophic
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:
https://fs.unm.edu/SymbolicNeutrosophicTheory.pdf
2015 – Introduction of the SubIndeterminacies of the
form 
, for k 
{0, 1, 2, …, n-1}, into the ring of modulo integers Zn
- called natural neutrosophic indeterminacies (Vasantha-Smarandache)
https://fs.unm.edu/MODNeutrosophicNumbers.pdf
2015 – Introduction of Neutrosophic Crisp Set and Topology
(Salama & Smarandache)
https://fs.unm.edu/NeutrosophicCrispSetTheory.pdf
2015 - 2017
Refined Complex Neutrosophic Set
2016 - 2024 - the n-th powerset, and the
SuperHyperStructures and Neutrosophic SuperHyperStructures that are
built on it, were founded by Smarandache:
https://fs.unm.edu/NidusIdearum2-ed2.pdf
(2016, pp. 107-108).
F. Smarandache, HyperUncertain,
SuperUncertain, and SuperHyperUncertain
Sets/Logics/Probabilities/Statistics, Critical Review, 10-19, Vol. XIV,
2017:
https://fs.unm.edu/CR/
2016 - 2018 - Neutrosophic Quantum Computer
https://fs.unm.edu/NeutrosophicQuantumComputer.pdf
Neutrosophic Logic Based Quantum Computing
https://fs.unm.edu/neut/NeutrosophicLogicBasedQuantum.pdf
2016 - Addition, Multiplication, Scalar Multiplication, Power, Subtraction, and Division of Neutrosophic Triplets (T, I, F)
https://fs.unm.edu/CR/SubstractionAndDivision.pdf
2016 – Introduction of Neutrosophic Multisets (as
generalization of classical multisets)
https://fs.unm.edu/NeutrosophicMultisets.htm
2016 – Introduction of Neutrosophic Triplet Structures and
m-valued refined neutrosophic triplet structures [Smarandache - Ali]
https://fs.unm.edu/NeutrosophicTriplets.htm
2016 – Introduction of Neutrosophic Duplet Structures
https://fs.unm.edu/NeutrosophicDuplets.htm
2017 - 2020 - Neutrosophic Score, Accuracy, and Certainty Functions form a total order relationship on the set of (single-valued, interval-valued, and in general subset-valued) neutrosophic triplets (T, I, F); and these functions are used in MCDM (Multi-Criteria 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/neutrosophic-evolution-PP-49-13.pdf
https://fs.unm.edu/V/NeutrosophicEvolution.mp4
https://fs.unm.edu/NeutrosophicEvolution.pdf
2017 - Introduction by F. Smarandache of Plithogeny (as
generalization of Yin-Yang, Manichaeism, Dialectics, Dualism, and
Neutrosophy), and Plithogenic Set / Plithogenic Logic as generalization of MultiVariate
Logic /
Plithogenic Probability and Plithogenic
Statistics as generalizations of MultiVariate Probability and Statistics (as generalization of fuzzy, intuitionistic fuzzy,
neutrosophic set/logic/probability/statistics):
https://fs.unm.edu/Plithogeny.pdf
Plithogeny
is a
generalization of Dialectics (dynamics of one type of opposites:
<A> and
<antiA>),
and of Neutrosophy (dynamics of one type of opposites and their
neutrals:
<A> and
<antiA> and
<neutA>),
since Plithogeny studies: the dynamics of many types of opposites
and
their
neutrals ( <A> and
<anti-A> and
<neut-A>;
<B> and
<anti-B> and <neut-B>; etc.) and many
non-opposites
( <C>,
<D>,
etc.) all together.
2017 - Enunciation of the Law that: It Is Easier to Break from
Inside than from Outside a Neutrosophic Dynamic System (Smarandache
- Vatuiu):
https://fs.unm.edu/EasierMaiUsor.pdf
2018 - 2024 - Introduction of six new types of soft sets: HyperSoft Set, IndetermSoft Set, IndetermHyperSoft Set, SuperHyperSoft Set, TreeSoft Set, ForestSoft Set:
https://fs.unm.edu/TSS/NewTypesSoftSets-Improved.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):
https://fs.unm.edu/NeutropsychicPersonality-ed3.pdf
2019
- Theory of Spiral Neutrosophic Human Evolution (Smarandache -
Vatuiu):
https://fs.unm.edu/SpiralNeutrosophicEvolution.pdf
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]:
https://fs.unm.edu/Neutrosociology.pdf
2019 - Refined Neutrosophic Crisp Set
https://fs.unm.edu/RefinedNeutrosophicCrispSet.pdf
2019-2024 - 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}.
https://fs.unm.edu/NA/NeutroAlgebra.htm
https://fs.unm.edu/NA/NeutroAlgebra.pdf
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
In 2019 he proposed the Infinitesimally Punctured Wave [ https://fs.unm.edu/IPW/ ], Infinitesimally Punctured Surface, Infinitesimally Punctured Space, and in general Infinitesimally Punctured Quantum Physics — in which a quantum object is visualized as an aggregation of infinitely many infinitesimally spaced particles. When these particles are densely packed, the ensemble appears as a continuous wave, surface, or space respectively; but when a measurement isolates a single constituent, particle-like behavior emerges. The model is situated alongside established alternative interpretations (e.g., de Broglie–Bohm pilot wave theory, wave packet descriptions) and linked to Neutrosophic Quantum Theory, which supplies a logical framework for handling indeterminacy. By offering a concrete visual metaphor, the punctured wave/surface/space/manifold picture aims to bridge the discrete continuous divide and stimulate further discussion on the foundations of quantum physics/mechanics [ https://fs.unm.edu/NSS/39Infinitesimally.pdf, https://fs.unm.edu/NSS/6InfinitesimallyPunctured.pdf ].The ‘infinitesimal distance’ (which is virtual and theoretical) was later extended by him to the 'finitesimally distance' that is a very tiny real distance (which is practical), allowing a wave to be ‘broken’ in a real sense at any point: https://fs.unm.edu/IPW/IPW-to-FPW.pdf.
2021: As alternatives and generalizations of the Non-Euclidean Geometries he introduced in 2021 the
NeutroGeometry & AntiGeometry.
While the Non-Euclidean 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/
2019-2022 - Extension of HyperGraph to SuperHyperGraph and Neutrosophic SuperHyperGraph
https://fs.unm.edu/NSS/n-SuperHyperGraph.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 Non-Euclidean Geometries, Smarandache introduced in
2021 the NeutroGeometry & AntiGeometry. While the Non-Euclidean 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 AH-Isometry f(x+yI) = f(x) + I[f(x+y) - f(x)], where I = literal Indeterminacy,
and x, y are real numbers,
and foundation of the Neutrosophic Euclidean Geometry (by Abobala & Hatip)
https://fs.unm.edu/NSS/AlgebraicNeutrosophicEuclideanGeometry10.pdf
and extension to n-Refined AH-Isometry (Smarandache & Abobala, 2024)
https://fs.unm.edu/NSS/RefinedLiteral21.pdf
and m-variables n-refined AH-Isometry (Smarandache, Ghadimi, Rezaei, 2024)
https://fs.unm.edu/m-variables-n-refined-AH-Isometry.pdf
2016 - 2022 SuperHyperAlgebra & Neutrosophic SuperHyperAlgebra
https://fs.unm.edu/SuperHyperAlgebra.pdf
2019 - Infinitesimally Punctured Wave as an Interpretation of
Wave-Particle Duality. The punctured
wave/surface/space picture
aims to bridge the discrete continuous divide, and stimulate further discussion on the foundations of quantum physics/mechanics.
The
‘infinitesimal distance’ (which is virtual and theoretical) was later
extended by him to the 'finitesimally distance' that is a very tiny real distance (which is practical),
allowing a wave to be ‘broken’ in a real sense at any point: https://fs.unm.edu/IPW/IPW-to-FPW.pdf ]:
https://fs.unm.edu/NSS/39Infinitesimally.pdf
https://fs.unm.edu/NSS/6InfinitesimallyPunctured.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 a0 + a1P1 + a2P2 + ... + anPn where the multiplication Pi·Pj is based on the prevalence order and absorbance law https://fs.unm.edu/NSS/SymbolicPlithogenicAlgebraic39.pdf
2023 - Foundation of Neutrosophic Cryptology (Merkepci-Abobala-Allouf)
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,
& Neutrosophic Numbers used in Neutrosophic Statistics
https://fs.unm.edu/NS/AppurtenanceInclusionEquations-revised.pdf
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/NSS/PartialLocality13.pdf
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 - Upside-Down Logics: Falsification of the Truth & Truthification of the False
https://fs.unm.edu/Upside-DownLogics.pdf
2024 - Partial Falsifiability of Fuzzy and Fuzzy-Extension Hypotheses
https://fs.unm.edu/ScArt/NoteOnPartialFalsifiability.pdf
2024 - Neutrosophic (and fuzzy-extensions) TwoFold Algebra
https://fs.unm.edu/NeutrosophicTwoFoldAlgebra.pdf
2025 - Neutrosophic Quantum Theory:Partial Entanglement, Partial Effect of the Observer, and Teleportation https://fs.unm.edu/NSS/1QuantumTheory.pdf
Neutrosophic Magnetic Field – An Introduction
https://fs.unm.edu/NSS/2MagneticField.pdf
Applications in:
Artificial Intelligence, Information Systems, Computer Science,
Cybernetics, Theory Methods, Mathematical Algebraic Structures, Applied
Mathematics, Automation, Control Systems, Big Data, Engineering,
Electrical, Electronic, Philosophy, Social Science, Psychology,
Biology, Biomedical, Genetics, Engineering, Medical Informatics,
Operational Research, Management Science, Imaging Science, Photographic
Technology, Instruments, Instrumentation, Physics, Optics, Economics,
Mechanics, Neurosciences, Radiology Nuclear, Medicine, Medical Imaging,
Interdisciplinary Applications, Multidisciplinary Sciences etc.
[ Xindong Peng and Jingguo Dai, A bibliometric analysis of neutrosophic
set: two decades review from 1998 to 2017, Artificial Intelligence
Review, Springer, 18 August 2018; https://fs.unm.edu/BibliometricNeutrosophy.pdf
]
Neutrosophic and Plithogenic 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.
Encyclopedia of Neutrosophic Researchers
The authors who have published or presented papers on neutrosophics and
are not included in the Encyclopedia of Neutrosophic Researchers (ENR),
vols. 1 - 6:
http://fs.unm.edu/EncyclopediaNeutrosophicResearchers.pdf
http://fs.unm.edu/EncyclopediaNeutrosophicResearchers2.pdf
http://fs.unm.edu/EncyclopediaNeutrosophicResearchers3.pdf
http://fs.unm.edu/EncyclopediaNeutrosophicResearchers4.pdf
http://fs.unm.edu/EncyclopediaNeutrosophicResearchers5.pdf
http://fs.unm.edu/EncyclopediaNeutrosophicResearchers6.pdf
are pleased to send their CV, photo, and List of Neutrosophic Publications to smarand@unm.edu in order to be included into the next volume of ENR
References
University of New Mexico (USA) web sites:
https://fs.unm.edu/ScienceLibrary.htm (Science Library)
https://fs.unm.edu/neutrosophy.htm
https://fs.unm.edu/NSS/Articles.htmhttps://fs.unm.edu/CR/CR-Articles.htm
https://fs.unm.edu/NCML/Articles.htm (Spanish)
https://fs.unm.edu/NK/Articles.htm (Arabic, Turkish, French)
Journals:
Neutrosophic Sets and Systems (NSS) international journal started in 2013 and it is indexed by Scopus, Web of Science (ESCI), DOAJ, Index Copernicus, Redalyc - Universidad Autonoma del Estado de Mexico (IberoAmerica), Publons, CNKI (Beijing, China), Chinese Baidu Scholar, etc. ( http://fs.unm.edu/NSS/ ).
Submit papers on neutrosophic set/logic/probability/statistics etc. and their applications through our OJS system: http://fs.unm.edu/nss8/index.php/111/Neutrosophic Optimization and Intelligent Systems (NOIS)
https://sciencesforce.com/index.php/nois
Plithogenic Logic and Computation (PLC)
https://sciencesforce.com/index.php/plc
HyperSoft Set Methods in Engineering (HSSE)
https://sciencesforce.com/index.php/hsse
Information Sciences with Applications (ISWA)
https://sciencesforce.com/index.php/iswa
Neutrosophic Systems And Application (NSWA)
https://sciencesforce.com/index.php/mawa/index
Uncertainty Discourse and Applications (UDA)
https://uda-journal.com/journalAbout 88 PostDoctorals, PhD DISSERTATIONS, and MSc. THESES on NEUTROSOPHICS AND THEIR APPLICATIONS,
from 27 countries: India, Pakistan, Taiwan, Ecuador, Cuba, USA, Malawi, Egypt, Portugal, Syria, Iran, Lithuania, Turkey, China, Algeria, Morocco, Nigeria, Colombia, Netherlands, Spain, New Zealand, Brasil, Georgia, Mexico, Romania, Australia.