Overview of Neutrosophic and Plithogenic Theories and Applications
Prof. Dr. Florentin Smarandache, PostDocs
University of New Mexico
Mathematics, Physics and Natural Sciences Division
705 Gurley Ave., Gallup, NM 87301, USA
Email:
smarand@unm.edu
Abstract
This presentation is an Overview on the Foundation and Development of Neutrosophic
Theories and their Applications for a period of more than two decades
(19952023) since they were defined and studied, together with their applications, and links to many
opensource articles and books that the attendees can download.
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), qRung Orthopair
Fuzzy Set, Spherical Fuzzy Set, and nHyperSpherical
Fuzzy Set, while
Neutrosophication is a
Generalization of Regret Theory, Grey System Theory, and ThreeWays Decision.
https://arxiv.org/ftp/arxiv/papers/1911/1911.07333.pdf
http://fs.unm.edu/Raspunsatan.pdf
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:
http://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
http://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
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.
https://arxiv.org/ftp/math/papers/0010/0010099.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 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.
For software engineering proposals the classical unit interval [0, 1] may 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
(19802020) hundreds of authors from tens of countries around the globe
contributed papers to 15 international paradoxist anthologies:
http://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), 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,
http://fs.unm.edu/NeutrosophyANewBranchofPhilosophy.pdf
introduced the neutrosophic set/logic/probability/statistics;
introduces the singlevalued neutrosophic set (pp. 78);
https://arxiv.org/ftp/math/papers/0101/0101228.pdf (fourth edition)
http://fs.unm.edu/eBookNeutrosophics6.pdf (online
sixth edition)
1998, 2019  Introduction of Nonstandard Neutrosophic Logic, Set, Probability
https://arxiv.org/ftp/arxiv/papers/1903/1903.04558.pdf
https://fs.unm.edu/AdvancesOfStandardAndNonstandard.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 pseudoparadoxist 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
pseudoparadoxist 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 pseudoparadoxist
logic (or neutrosophic pseudoparadoxism), neutrosophic tautological logic (or
neutrosophic tautologism):
https://arxiv.org/ftp/math/papers/0301/0301340.pdf
http://fs.unm.edu/DefinitionsDerivedFromNeutrosophics.pdf
2003 – Introduction by Kandasamy and Smarandache of
Neutrosophic Numbers (a+bI, where I = literal indeterminacy, I^{2} = I,
which is different from the numerical indeterminacy I = real set),
INeutrosophic Algebraic Structures
and Neutrosophic Cognitive Maps
https://arxiv.org/ftp/math/papers/0311/0311063.pdf
http://fs.unm.edu/NCMs.pdf
2005  Introduction of Interval Neutrosophic Set/Logic
https://arxiv.org/pdf/cs/0505014.pdf
http://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
http://fs.unm.edu/eBookNeutrosophics6.pdf (p. 92)
http://fs.unm.edu/NSS/DegreeOfDependenceAndIndependence.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;
and to Neutrosophic 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 Neutrosophic 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 Neutrosophic Logic/Measure/Probability/Statistics etc. were
extended to respectively Neutrosophic Over/Under/Off Logic / Measure /
Probability / Statistics etc.
https://arxiv.org/ftp/arxiv/papers/1607/1607.00234.pdf
http://fs.unm.edu/NeutrosophicOversetUndersetOffset.pdf
http://fs.unm.edu/SVNeutrosophicOversetJMI.pdf
http://fs.unm.edu/IVNeutrosophicOversetUndersetOffset.pdf
http://fs.unm.edu/NSS/DegreesOfOverUnderOffMembership.pdf
2007 – Smarandache introduced the
Neutrosophic Tripolar Set and Neutrosophic Multipolar Set
and consequently
the Neutrosophic Tripolar Graph and Neutrosophic Multipolar Graph
http://fs.unm.edu/eBookNeutrosophics6.pdf (p. 93)
http://fs.unm.edu/IFSgeneralized.pdf
2009 – Introduction of Nnorm and Nconorm
https://arxiv.org/ftp/arxiv/papers/0901/0901.1289.pdf
http://fs.unm.edu/NnormNconorm.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://arxiv.org/ftp/arxiv/papers/1311/1311.7139.pdf
http://fs.unm.edu/NeutrosophicMeasureIntegralProbability.pdf
2013 – Smarandache Refined / Split the Neutrosophic Components (T, I, F) into Neutrosophic
SubComponents
(T_{1}, T_{2},
...; I_{1}, I_{2}, ...; F_{1}, F_{2}, ...):
https://arxiv.org/ftp/arxiv/papers/1407/1407.1041.pdf
http://fs.unm.edu/nValuedNeutrosophicLogicPiP.pdf
2014 – Introduction of the Law of Included MultipleMiddle (as extension
of the Law of Included Middle)
(<A>; <neutA_{1}>, <neutA_{2}>, …,
<neutA_{n}>; <antiA>)
http://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>)
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://arxiv.org/ftp/arxiv/papers/1406/1406.2000.pdf
http://fs.unm.edu/NeutrosophicStatistics.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
http://fs.unm.edu/alphaDiscountingMCDMbook.pdf
2015  Introduction of Neutrosophic Precalculus and Neutrosophic Calculus
https://arxiv.org/ftp/arxiv/papers/1509/1509.07723.pdf
http://fs.unm.edu/NeutrosophicPrecalculusCalculus.pdf
2015 – Refined Neutrosophic Numbers (a+ b_{1}I_{1} + b_{2}I_{2} + … + b_{n}I_{n}), where I_{1}, I_{2},
…, I_{n} are SubIndeterminacies of Indeterminacy I.
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:
https://arxiv.org/ftp/arxiv/papers/1512/1512.00047.pdf
http://fs.unm.edu/SymbolicNeutrosophicTheory.pdf
2015 – Introduction of the SubIndeterminacies of the form
, for k
{0, 1, 2, …, n1}, into the ring of modulo integers Z_{n}  called natural neutrosophic indeterminacies (VasanthaSmarandache)
http://fs.unm.edu/MODNeutrosophicNumbers.pdf
2015 – Introduction of Neutrosophic Crisp Set and Topology (Salama & Smarandache)
http://fs.unm.edu/NeutrosophicCrispSetTheory.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)
http://fs.unm.edu/NeutrosophicMultisets.htm
2016 – Introduction of Neutrosophic Triplet Structures and mvalued refined neutrosophic triplet structures [Smarandache  Ali]
http://fs.unm.edu/NeutrosophicTriplets.htm
2016 – Introduction of Neutrosophic Duplet Structures
http://fs.unm.edu/NeutrosophicDuplets.htm
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):
http://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):
http://fs.unm.edu/neutrosophicevolutionPP4913.pdf
https://fs.unm.edu/V/NeutrosophicEvolution.mp4
https://fs.unm.edu/NeutrosophicEvolution.pdf
2017  Introduction by F. Smarandache of Plithogeny (as generalization of
YinYang, 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://arxiv.org/ftp/arxiv/papers/1808/1808.03948.pdf
http://fs.unm.edu/Plithogeny.pdf
2017  Enunciation of the Law that: It Is Easier to Break
from Inside than from Outside a Neutrosophic Dynamic System (Smarandache
 Vatuiu):
http://fs.unm.edu/EasierMaiUsor.pdf
2018  2023

Introduction of new types of soft sets:
HyperSoft Set, IndetermSoft Set,
IndetermHyperSoft Set, SuperHyperSoft Set, TreeSoft Set:
http://fs.unm.edu/TSS/NewTypesSoftSetsImproved.pdf
http://fs.unm.edu/TSS/SuperHyperSoftSet.pdf
https://fs.unm.edu/NSS/IndetermSoftIndetermHyperSoft38.pdf
(with IndetermSoft Operators acting on IndetermSoft Algebra)
http://fs.unm.edu/TSS/
2018 – Introduction to Neutrosophic Psychology (Neutropsyche, Refined
Neutrosophic Memory: conscious, aconscious, unconscious, Neutropsychic
Personality, Eros / Aoristos / Thanatos, Neutropsychic Crisp Personality):
http://fs.unm.edu/NeutropsychicPersonalityed3.pdf
2019  Theory of Spiral Neutrosophic Human Evolution (Smarandache  Vatuiu):
http://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]:
http://fs.unm.edu/Neutrosociology.pdf
2019  Refined Neutrosophic Crisp Set
http://fs.unm.edu/RefinedNeutrosophicCrispSet.pdf
20192022 
Introduction of new types of topologies: Refined Neutrosophic Topology,
Refined Neutrosophic Crisp Topology, NeutroTopology, AntiTopology,
SuperHyperTopology, and Neutrosophic SuperHyperTopology:
http://fs.unm.edu/NSS/NewTypesTopologiesImproved14.pdf
http://fs.unm.edu/TT/
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:
http://fs.unm.edu/NA/NeutroAlgebra.htm
http://fs.unm.edu/NA/NeutroAlgebra.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
NeutroAxiom
results from the partial negation of one or more axioms [and no
total negation of no axiom] from
any geometric axiomatic system.
http://fs.unm.edu/NSS/NeutroGeometryAntiGeometry31.pdf
http://fs.unm.edu/NG/
20192022  Extension of HyperGraph to SuperHyperGraph
and Neutrosophic SuperHyperGraph
http://fs.unm.edu/NSS/nSuperHyperGraph.pdf
2020  Introduction to Neutrosophic
Genetics:
http://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:
http://fs.unm.edu/NSS/NeutroGeometryAntiGeometry31.pdf
Real Examples of NeutroGeometry
and AntiGeometry:
http://fs.unm.edu/NSS/ExamplesNeutroGeometryAntiGeometry35.pdf
2021  Introduction of Plithogenic Logic as a generalization of
MultiVariate Logic
http://fs.unm.edu/NSS/IntroductionPlithogenicLogic1.pdf
2021  Introduction of Plithogenic Probability and Statistics as
generalizations of MultiVariate
Probability and Statistics respectively
http://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)
http://fs.unm.edu/NSS/AlgebraicNeutrosophicEuclideanGeometry10.pdf
2022  SuperHyperAlgebra & Neutrosophic SuperHyperAlgebra
http://fs.unm.edu/SuperHyperAlgebra.pdf
2022  SuperHyperFunction, SuperHyperTopology
http://fs.unm.edu/NSS/SuperHyperFunction37.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
http://fs.unm.edu/NSS/SymbolicPlithogenicAlgebraic39.pdf
2023  Foundation of Neutrosophic
Cryptology (MerkepciAbobalaAllouf)
http://fs.unm.edu/NeutrosophicCryptography1.pdf
http://fs.unm.edu/NeutrosophicCryptography2.pdf
http://fs.unm.edu/NSS/2OnANovelSecurityScheme.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;
http://fs.unm.edu/BibliometricNeutrosophy.pdf ]
Important
Neutrosophic Researchers:
There are about 7,000 neutrosophic researchers, within 89
countries around the globe, that have produced about 4,000 publications and
tenths of PhD and MSc theses, within
more than two decades. Many neutrosophic researchers got specialized into
various fields of neutrosophics:
Xiaohong Zhang &
Yingcang Ma (neutrosophic triplet
and quadruple algebraic structures), Yanhui Guo (neutrosophic image processing),
Jun Ye & Peide Liu &
Jianqiang Wang (neutrosophic
optimization),
Xindong Peng & Jingguo Dai (neutrosophic bibliometrics),
Jianqiang
Wang, Guiwu Wei,
Donghai Liu, Xiaohong Chen, Dan Peng, Jiongmei Mo, HanLiang
Huang, Victor Chang, Hongjun Guan, Shuang Guan, Aiwu Zhao, WenHua Cui, Xiaofei
Yang, Xin Zhou, G.L. Tang, W.L. Liu, Wen Jiang, Zihan Zhang, Xinyang Deng,
Changxing Fan, Sheng Feng, En Fan, Keli Hu,
Xingsen Li, Xin Zhou, Ping Li;
Rajab
Ali Borzooei & Young Bae Jun (neutrosophic BCK/BCIalgebras), Arsham Borumand
Saeid (neutrosophic structures), Saied Jafari (neutrosophic topology), Maikel LeyvaVazquez (neutrosophic cognitive
maps);
Amira S. Ashour, Muhammad Aslam (neutrosophic statistics), Nguyen
Xuan Thao (neutrosophic similarity measures), Le Hoang Son, Vakkas Ulucay &
Memet Sahin (neutrosophic quadruple structures), Irfan Deli,
Madad Khan (neutrosophic algebraic structures),
Said Broumi & Muhammad Akram
(neutrosophic graphs), Mohamed AbdelBaset (neutrosophic
linear and nonlinear programming), Ahmed Mostafa Khalil,
Ahmed Salama (neutrosophic crisp topology),
etc.
Neutrosophic 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/NSS2/index.php/111/submissions
International Journal of Neutrosophic Science (IJNS, in SCOPUS):
http://americaspg.com/journals/show/21
Neutrosophic Systems with Applications (NSWA):
https://nswajournal.org/index.php/nswa
Neutrosophic Computing and Machine Learning (NCML), in
Spanish:
http://fs.unm.edu/NCML/
Neutrosophic
Knowledge (NK), in English and Arabic:
http://fs.unm.edu/NK/
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:
http://fs.unm.edu/neutrosophy.htm
http://fs.unm.edu/NSS/Articles.htm
http://fs.unm.edu/CR/CRArticles.htm
http://fs.unm.edu/NCML/Articles.htm
http://fs.unm.edu/NK/Articles.htm