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This book contains 37 papers by 73 renowned experts from 13 countries around the world, on following topics: neutrosophic set; neutrosophic rings; neutrosophic quadruple rings; idempotents; neutrosophic extended triplet group; hypergroup; semihypergroup; neutrosophic extended triplet group; neutrosophic extended triplet semihypergroup and hypergroup; neutrosophic offset; uninorm; neutrosophic offuninorm and offnorm; neutrosophic offconorm; implicator; prospector; n-person cooperative game; ordinary single-valued neutrosophic (co)topology; ordinary single-valued neutrosophic subspace; ?-level; ordinary single-valued neutrosophic neighborhood system; ordinary single-valued neutrosophic base and subbase; fuzzy numbers; neutrosophic numbers; neutrosophic symmetric scenarios; performance indicators; financial assets; neutrosophic extended triplet group; neutrosophic quadruple numbers; refined neutrosophic numbers; refined neutrosophic quadruple numbers; multigranulation neutrosophic rough set; nondual; two universes; multiattribute group decision making; nonstandard analysis; extended nonstandard analysis; monad; binad; left monad closed to the right; right monad closed to the left; pierced binad; unpierced binad; nonstandard neutrosophic mobinad set; neutrosophic topology; nonstandard neutrosophic topology; visual tracking; neutrosophic weight; objectness; weighted multiple instance learning; neutrosophic triangular norms; residuated lattices; representable neutrosophic t-norms; De Morgan neutrosophic triples; neutrosophic residual implications; infinitely ?-distributive; probabilistic neutrosophic hesitant fuzzy set; decision-making; Choquet integral; e-marketing; Internet of Things; neutrosophic set; multicriteria decision making techniques; uncertainty modeling; neutrosophic goal programming approach; shale gas water management system.

nonstandard neutrosophic supremum --- classical statistics --- complex neutrosophic set --- neutrosophic offnorm --- neutrosophic extended triplet group --- multi-attribute decision-making (MADM) --- neutrosophic time series --- refined neutrosophic quadruple numbers --- BNHHA aggregation operator --- neutrosophic offconorm --- monad --- matrix representation --- left monad closed to the right --- implicator --- neutrsophic set --- neutrosophic correlation --- neutrosophic cubic sets --- decision-making --- MoBiNad set --- open and closed monads to the left/right --- distance measure --- De Morgan neutrosophic triples --- group decision making --- financial assets --- soft expert set --- uninorm --- multi-attribute group decision making --- sampling plan --- cubic sets --- neutrosophic cubic ordered weighted geometric operator (NCOWG) --- shale gas water management system --- weighted average operator --- aggregation operations --- quality function deployment --- Einstein t-norm --- neutrosophic rings --- non-standard neutrosophic topology --- BNHWA aggregation operator --- hypergroup --- triangular neutrosophic cubic fuzzy number --- pierced and unpierced binads --- numerical application --- neutrosophic cubic weighted geometric operator (NCWG) --- relations --- extended nonstandard analysis --- arithmetic averaging operator --- nonstandard reals --- Choquet integral --- Function approximation --- neutrosophic triangular norms --- weighted geometric operator --- neutrosophic regression --- optimization solution --- ordinary single valued neutrosophic neighborhood system --- smart port --- neutrosophic topology --- multi-criteria decision making techniques --- low-carbon supplier selection --- producer’s risk --- quasi-completely regular semigroup --- score function --- MAGDM --- multicriteria decision-making --- neutrosophic soft rough --- NET-hypergroup --- refined neutrosophic numbers --- neutrosophic logical relationship groups --- combined weighted average --- TOPSIS --- neutrosophic logical relationship --- logarithmic aggregation operators --- non-standard analysis --- multi-attribute decision-making --- neutrosophic extended triplet semihypergroup (NET-semihypergroup) --- aggregation --- nonstandard neutrosophic logic --- symmetric relation --- uncertainty modeling --- single valued neutrosophic sets --- BNHOWA aggregation operator --- ordinary single valued neutrosophic subspace --- generalized neutrosophic extended triplet group --- multi-attribute decision making --- ordinary single valued neutrosophic base --- nonstandard arithmetic operations --- pierced binad --- MCGDM problems --- simplified neutrosophic set --- residuated lattices --- Neutrosophic compound orthogonal neural network --- rough set approximation --- single-valued neutrosophic linguistic set --- binad --- multi-granulation neutrosophic rough set --- single valued neutrosophic set --- infinitesimals --- standard reals --- soft set --- non-standard neutrosophic mobinad set --- certainty function --- neutrosophic weight --- two universes --- sample size --- n-person cooperative game --- paper defect diagnosis --- performance indicators --- semihypergroup --- logarithmic operational laws --- right monad closed to the left --- idempotents --- unpierced binad --- neutrosophic cubic hybrid weighted arithmetic and geometric aggregation operator (NCHWAGA) --- neutrosophic symmetric scenarios --- extended nonstandard neutrosophic logic --- neutrosophic statistics --- neutrosophic goal programming approach --- neutrosophic offset --- neutrosophic statistical interval method --- weighted multiple instance learning --- neutrosophic cubic Einstein ordered weighted geometric operator (NCEOWG) --- fuzzy parameterized single valued neutrosophic soft expert set --- single-valued neutrosophic soft number and its operations --- Internet of Things --- extended non-standard analysis --- dietary fat level --- soft sets --- visual tracking --- neutrosophic offuninorm --- neutrosophic cubic Einstein weighted geometric operator (NCEWG) --- ordinary single valued neutrosophic subbase --- membership function --- non-dual --- SVN soft weighted arithmetic averaging operator --- Q-neutrosophic set --- neutrosophic sets --- fuzzy numbers --- intuitionistic fuzzy parameters --- producer’s risk’ --- graph representation --- exponential similarity measure --- infinities --- maximizing deviation --- Multi-attribute decision making --- SVN soft weighted geometric averaging operator --- objectness --- Q-neutrosophic soft set --- accuracy function --- consumer’s risk --- decision making --- Neutrosophic number --- clifford semigroup --- neutrosophic numbers --- neutrosophic residual implications --- nonstandard neutrosophic lattices of first type (as poset) and second type (as algebraic structure) --- covering --- e-marketing --- nonstandard analysis --- neutrosophic quadruple rings --- complex neutrosophic soft expert set --- single-valued neutrosophic set --- neutrosophic cubic soft expert system --- neutrosophic cubic soft sets --- triangular neutrosophic number --- supply chain sustainability metrics --- neutrosophic quadruple numbers --- ?-level --- nonstandard neutrosophic infimum --- infinitely ?-distributive --- plithogeny --- neutrosophic set --- fuzzy logic --- prospector --- Neutrosophic function --- representable neutrosophic t-norms --- probabilistic neutrosophic hesitant fuzzy set (PNHFS) --- prostate cancer --- nonstandard unit interval --- port evaluation --- simplified neutrosophic hesitant fuzzy set --- ordinary single valued neutrosophic (co)topology

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Neutrosophy (1995) is a new branch of philosophy that studies triads of the form (, , ), where is an entity {i.e. element, concept, idea, theory, logical proposition, etc.}, is the opposite of , while is the neutral (or indeterminate) between them, i.e., neither nor .Based on neutrosophy, the neutrosophic triplets were founded, which have a similar form (x, neut(x), anti(x)), that satisfy several axioms, for each element x in a given set.This collective book presents original research papers by many neutrosophic researchers from around the world, that report on the state-of-the-art and recent advancements of neutrosophic triplets, neutrosophic duplets, neutrosophic multisets and their algebraic structures – that have been defined recently in 2016 but have gained interest from world researchers. Connections between classical algebraic structures and neutrosophic triplet / duplet / multiset structures are also studied. And numerous neutrosophic applications in various fields, such as: multi-criteria decision making, image segmentation, medical diagnosis, fault diagnosis, clustering data, neutrosophic probability, human resource management, strategic planning, forecasting model, multi-granulation, supplier selection problems, typhoon disaster evaluation, skin lesson detection, mining algorithm for big data analysis, etc.

similarity measure --- generalized partitioned Bonferroni mean operator --- normal distribution --- school administrator --- complex neutrosophic set --- expert set --- neutrosophic classification --- multi-attribute decision-making (MADM) --- multi-criteria decision-making (MCDM) techniques --- criterion functions --- matrix representation --- possibility degree --- quantum computation --- typhoon disaster evaluation --- NT-subgroup --- generalized neutrosophic ideal --- three-way decisions --- decision-making --- G-metric --- multiple attribute group decision-making (MAGDM) --- SVM --- semi-neutrosophic triplets --- LA-semihypergroups --- power operator --- fuzzy graph --- neutrosophic cubic graphs --- LNGPBM operator --- neutrosophic c-means clustering --- (commutative) ideal --- region growing --- clustering algorithm --- Neutrosophic cubic sets --- forecasting --- vector similarity measure --- totally dependent-neutrosophic soft set --- Fenyves identities --- TODIM model --- similarity measures --- CI-algebra --- Dice measure --- de-neutrosophication methods --- DSmT --- semigroup --- VIKOR model --- multigranulation neutrosophic rough set (MNRS) --- simplified neutrosophic linguistic numbers --- Technique for Order Preference by Similarity to an Ideal Solution (TOPSIS) --- multi-criteria group decision making --- multi-attribute group decision-making (MAGDM) --- exponential operational laws of interval neutrosophic numbers --- simplified neutrosophic weighted averaging operator --- neutro-epimorphism --- Choquet integral --- fixed point theory (FPT) --- computability --- neutrosophic triplet set --- interval-valued neutrosophic set --- simplified neutrosophic sets (SNSs) --- totally dependent-neutrosophic set --- Maclaurin symmetric mean --- recursive enumerability --- loop --- photovoltaic plan --- intersection --- neutrosophic bipolar fuzzy set --- big data --- inclusion relation --- dual aggregation operators --- Hamming distance --- neutro-automorphism --- neutrosophic set theory --- multiple attribute decision-making --- multicriteria decision-making --- pseudo primitive elements --- medical diagnosis --- neutrosophic G-metric --- bipolar fuzzy set --- NC power dual MM operator (NCPDMM) operator --- neutrosophic sets (NSs) --- emerging technology commercialization --- neutrosophic triplet groups --- probabilistic rough sets over two universes --- neutrosophic triplet set (NTS) --- neutrosophic triplet cosets --- MM operator --- TOPSIS --- cloud model --- extended ELECTRE III --- extended TOPSIS method --- 2ingle-valued neutrosophic set --- dual domains --- probabilistic single-valued (interval) neutrosophic hesitant fuzzy set --- Jaccard measure --- data mining --- BE-algebra --- neutrosophic soft set --- aggregation operators --- image segmentation --- multiple attribute decision making (MADM) --- neutrosophic duplets --- fundamental neutro-homomorphism theorem --- neutro-homomorphism --- power aggregation operator --- linear and non-linear neutrosophic number --- multi-attribute decision making --- first neutro-isomorphism theorem --- MCGDM problems --- neutrosophic bipolar fuzzy weighted averaging operator --- Bonferroni mean --- analytic hierarchy process (AHP) --- quasigroup --- action learning --- weak commutative neutrosophic triplet group --- generalized aggregation operators --- single valued neutrosophic multiset (SVNM) --- sustainable supplier selection problems (SSSPs) --- LNGWPBM operator --- skin cancer --- oracle computation --- fault diagnosis --- interval valued neutrosophic support soft sets --- neutrosophic triplet normal subgroups --- soft set --- multi-criteria decision-making --- neutrosophic triplet --- generalized group --- neutrosophic multiset (NM) --- two universes --- algorithm --- multi-attribute decision making (MADM) --- PA operator --- BCI-algebra --- neutrosophic triplet group (NTG) --- single valued trapezoidal neutrosophic number --- quasi neutrosophic triplet loop --- neutrosophy --- complex neutrosophic graph --- S-semigroup of neutrosophic triplets --- and second neutro-isomorphism theorem --- MADM --- dermoscopy --- linguistic neutrosophic sets --- defuzzification --- construction project --- potential evaluation --- neutrosophic big data --- decision-making algorithms --- neutosophic extended triplet subgroups --- applications of neutrosophic cubic graphs --- fuzzy time series --- TFNNs VIKOR method --- two-factor fuzzy logical relationship --- oracle Turing machines --- grasp type --- interval neutrosophic sets --- multi-criteria group decision-making --- interval neutrosophic weighted exponential aggregation (INWEA) operator --- power aggregation operators --- neutrosophic triplet group --- MGNRS --- 2-tuple linguistic neutrosophic sets (2TLNSs) --- computation --- filter --- multi-valued neutrosophic set --- integrated weight --- Bol-Moufang --- prioritized operator --- interval number --- logic --- pseudo-BCI algebra --- interval neutrosophic set (INS) --- neutrosophic rough set --- soft sets --- Q-neutrosophic --- Linguistic neutrosophic sets --- fuzzy measure --- homomorphism theorem --- commutative generalized neutrosophic ideal --- neutrosophic association rule --- shopping mall --- dependent degree --- Q-linguistic neutrosophic variable set --- quasi neutrosophic loops --- symmetry --- neutrosophic sets --- neutrosophic logic --- neutrosophic cubic set --- complement --- robotic dexterous hands --- neutro-monomorphism --- group --- analytic network process --- Muirhead mean --- maximizing deviation --- classical group of neutrosophic triplets --- neutrosophic triplet quotient groups --- generalized neutrosophic set --- multi-criteria group decision-making (MCGDM) --- support soft sets --- decision making --- generalized De Morgan algebra --- multiple attribute group decision making (MAGDM) --- single-valued neutrosophic multisets --- 2TLNNs TODIM method --- membership --- grasping configurations --- single valued neutrosophic set (SVNS) --- multiple attribute decision making problem --- SWOT analysis --- neutrosophic clustering --- hesitant fuzzy set --- interval neutrosophic numbers (INNs) --- quasi neutrosophic triplet group --- triangular fuzzy neutrosophic sets (TFNSs) --- interdependency of criteria --- aggregation operator --- cosine measure --- neutrosophic set --- neutrosophic computation --- decision-making trial and evaluation laboratory (DEMATEL) --- partial metric spaces (PMS) --- NCPMM operator --- clustering --- similarity measure --- generalized partitioned Bonferroni mean operator --- normal distribution --- school administrator --- complex neutrosophic set --- expert set --- neutrosophic classification --- multi-attribute decision-making (MADM) --- multi-criteria decision-making (MCDM) techniques --- criterion functions --- matrix representation --- possibility degree --- quantum computation --- typhoon disaster evaluation --- NT-subgroup --- generalized neutrosophic ideal --- three-way decisions --- decision-making --- G-metric --- multiple attribute group decision-making (MAGDM) --- SVM --- semi-neutrosophic triplets --- LA-semihypergroups --- power operator --- fuzzy graph --- neutrosophic cubic graphs --- LNGPBM operator --- neutrosophic c-means clustering --- (commutative) ideal --- region growing --- clustering algorithm --- Neutrosophic cubic sets --- forecasting --- vector similarity measure --- totally dependent-neutrosophic soft set --- Fenyves identities --- TODIM model --- similarity measures --- CI-algebra --- Dice measure --- de-neutrosophication methods --- DSmT --- semigroup --- VIKOR model --- multigranulation neutrosophic rough set (MNRS) --- simplified neutrosophic linguistic numbers --- Technique for Order Preference by Similarity to an Ideal Solution (TOPSIS) --- multi-criteria group decision making --- multi-attribute group decision-making (MAGDM) --- exponential operational laws of interval neutrosophic numbers --- simplified neutrosophic weighted averaging operator --- neutro-epimorphism --- Choquet integral --- fixed point theory (FPT) --- computability --- neutrosophic triplet set --- interval-valued neutrosophic set --- simplified neutrosophic sets (SNSs) --- totally dependent-neutrosophic set --- Maclaurin symmetric mean --- recursive enumerability --- loop --- photovoltaic plan --- intersection --- neutrosophic bipolar fuzzy set --- big data --- inclusion relation --- dual aggregation operators --- Hamming distance --- neutro-automorphism --- neutrosophic set theory --- multiple attribute decision-making --- multicriteria decision-making --- pseudo primitive elements --- medical diagnosis --- neutrosophic G-metric --- bipolar fuzzy set --- NC power dual MM operator (NCPDMM) operator --- neutrosophic sets (NSs) --- emerging technology commercialization --- neutrosophic triplet groups --- probabilistic rough sets over two universes --- neutrosophic triplet set (NTS) --- neutrosophic triplet cosets --- MM operator --- TOPSIS --- cloud model --- extended ELECTRE III --- extended TOPSIS method --- 2ingle-valued neutrosophic set --- dual domains --- probabilistic single-valued (interval) neutrosophic hesitant fuzzy set --- Jaccard measure --- data mining --- BE-algebra --- neutrosophic soft set --- aggregation operators --- image segmentation --- multiple attribute decision making (MADM) --- neutrosophic duplets --- fundamental neutro-homomorphism theorem --- neutro-homomorphism --- power aggregation operator --- linear and non-linear neutrosophic number --- multi-attribute decision making --- first neutro-isomorphism theorem --- MCGDM problems --- neutrosophic bipolar fuzzy weighted averaging operator --- Bonferroni mean --- analytic hierarchy process (AHP) --- quasigroup --- action learning --- weak commutative neutrosophic triplet group --- generalized aggregation operators --- single valued neutrosophic multiset (SVNM) --- sustainable supplier selection problems (SSSPs) --- LNGWPBM operator --- skin cancer --- oracle computation --- fault diagnosis --- interval valued neutrosophic support soft sets --- neutrosophic triplet normal subgroups --- soft set --- multi-criteria decision-making --- neutrosophic triplet --- generalized group --- neutrosophic multiset (NM) --- two universes --- algorithm --- multi-attribute decision making (MADM) --- PA operator --- BCI-algebra --- neutrosophic triplet group (NTG) --- single valued trapezoidal neutrosophic number --- quasi neutrosophic triplet loop --- neutrosophy --- complex neutrosophic graph --- S-semigroup of neutrosophic triplets --- and second neutro-isomorphism theorem --- MADM --- dermoscopy --- linguistic neutrosophic sets --- defuzzification --- construction project --- potential evaluation --- neutrosophic big data --- decision-making algorithms --- neutosophic extended triplet subgroups --- applications of neutrosophic cubic graphs --- fuzzy time series --- TFNNs VIKOR method --- two-factor fuzzy logical relationship --- oracle Turing machines --- grasp type --- interval neutrosophic sets --- multi-criteria group decision-making --- interval neutrosophic weighted exponential aggregation (INWEA) operator --- power aggregation operators --- neutrosophic triplet group --- MGNRS --- 2-tuple linguistic neutrosophic sets (2TLNSs) --- computation --- filter --- multi-valued neutrosophic set --- integrated weight --- Bol-Moufang --- prioritized operator --- interval number --- logic --- pseudo-BCI algebra --- interval neutrosophic set (INS) --- neutrosophic rough set --- soft sets --- Q-neutrosophic --- Linguistic neutrosophic sets --- fuzzy measure --- homomorphism theorem --- commutative generalized neutrosophic ideal --- neutrosophic association rule --- shopping mall --- dependent degree --- Q-linguistic neutrosophic variable set --- quasi neutrosophic loops --- symmetry --- neutrosophic sets --- neutrosophic logic --- neutrosophic cubic set --- complement --- robotic dexterous hands --- neutro-monomorphism --- group --- analytic network process --- Muirhead mean --- maximizing deviation --- classical group of neutrosophic triplets --- neutrosophic triplet quotient groups --- generalized neutrosophic set --- multi-criteria group decision-making (MCGDM) --- support soft sets --- decision making --- generalized De Morgan algebra --- multiple attribute group decision making (MAGDM) --- single-valued neutrosophic multisets --- 2TLNNs TODIM method --- membership --- grasping configurations --- single valued neutrosophic set (SVNS) --- multiple attribute decision making problem --- SWOT analysis --- neutrosophic clustering --- hesitant fuzzy set --- interval neutrosophic numbers (INNs) --- quasi neutrosophic triplet group --- triangular fuzzy neutrosophic sets (TFNSs) --- interdependency of criteria --- aggregation operator --- cosine measure --- neutrosophic set --- neutrosophic computation --- decision-making trial and evaluation laboratory (DEMATEL) --- partial metric spaces (PMS) --- NCPMM operator --- clustering