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Written and revised by D. B. A. Epstein.

Category theory. Homological algebra --- 515.14 --- Algebraic topology --- Homology theory. --- 515.14 Algebraic topology --- Cohomology theory --- Contrahomology theory --- Algebra homomorphism. --- Algebra over a field. --- Algebraic structure. --- Approximation. --- Axiom. --- Basis (linear algebra). --- CW complex. --- Cartesian product. --- Classical group. --- Coefficient. --- Cohomology operation. --- Cohomology ring. --- Cohomology. --- Commutative property. --- Complex number. --- Computation. --- Continuous function. --- Cup product. --- Cyclic group. --- Diagram (category theory). --- Dimension. --- Direct limit. --- Embedding. --- Existence theorem. --- Fibration. --- Homomorphism. --- Hopf algebra. --- Hopf invariant. --- Ideal (ring theory). --- Integer. --- Inverse limit. --- Manifold. --- Mathematics. --- Monomial. --- N-skeleton. --- Natural transformation. --- Permutation. --- Quaternion. --- Ring (mathematics). --- Scalar (physics). --- Special unitary group. --- Steenrod algebra. --- Stiefel manifold. --- Subgroup. --- Subset. --- Summation. --- Symmetric group. --- Symplectic group. --- Theorem. --- Uniqueness theorem. --- Upper and lower bounds. --- Vector field. --- Vector space. --- W0.

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This book presents a classification of all (complex)irreducible representations of a reductive group withconnected centre, over a finite field. To achieve this,the author uses etale intersection cohomology, anddetailed information on representations of Weylgroups.

512 --- Characters of groups --- Finite fields (Algebra) --- Finite groups --- Groups, Finite --- Group theory --- Modules (Algebra) --- Modular fields (Algebra) --- Algebra, Abstract --- Algebraic fields --- Galois theory --- Characters, Group --- Group characters --- Groups, Characters of --- Representations of groups --- Rings (Algebra) --- Algebra --- 512 Algebra --- Finite groups. --- Characters of groups. --- Addition. --- Algebra representation. --- Algebraic closure. --- Algebraic group. --- Algebraic variety. --- Algebraically closed field. --- Bijection. --- Borel subgroup. --- Cartan subalgebra. --- Character table. --- Character theory. --- Characteristic function (probability theory). --- Characteristic polynomial. --- Class function (algebra). --- Classical group. --- Coefficient. --- Cohomology with compact support. --- Cohomology. --- Combination. --- Complex number. --- Computation. --- Conjugacy class. --- Connected component (graph theory). --- Coxeter group. --- Cyclic group. --- Cyclotomic polynomial. --- David Kazhdan. --- Dense set. --- Derived category. --- Diagram (category theory). --- Dimension. --- Direct sum. --- Disjoint sets. --- Disjoint union. --- E6 (mathematics). --- Eigenvalues and eigenvectors. --- Endomorphism. --- Equivalence class. --- Equivalence relation. --- Existential quantification. --- Explicit formula. --- Explicit formulae (L-function). --- Fiber bundle. --- Finite field. --- Finite group. --- Fourier transform. --- Green's function. --- Group (mathematics). --- Group action. --- Group representation. --- Harish-Chandra. --- Hecke algebra. --- Identity element. --- Integer. --- Irreducible representation. --- Isomorphism class. --- Jordan decomposition. --- Line bundle. --- Linear combination. --- Local system. --- Mathematical induction. --- Maximal torus. --- Module (mathematics). --- Monodromy. --- Morphism. --- Orthonormal basis. --- P-adic number. --- Parametrization. --- Parity (mathematics). --- Partially ordered set. --- Perverse sheaf. --- Pointwise. --- Polynomial. --- Quantity. --- Rational point. --- Reductive group. --- Ree group. --- Schubert variety. --- Scientific notation. --- Semisimple Lie algebra. --- Sheaf (mathematics). --- Simple group. --- Simple module. --- Special case. --- Standard basis. --- Subset. --- Subtraction. --- Summation. --- Surjective function. --- Symmetric group. --- Tensor product. --- Theorem. --- Two-dimensional space. --- Unipotent representation. --- Vector bundle. --- Vector space. --- Verma module. --- Weil conjecture. --- Weyl group. --- Zariski 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

Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

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

Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

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