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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 --- 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
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Information management is a common paradigm in modern decision-making. A wide range of decision-making techniques have been proposed in the literature to model complex business and engineering processes. In this Special Issue, 16 selected and peer-reviewed original research articles contribute to business information management in various current real-world problems by proposing crisp or uncertain multiple-criteria decision-making (MCDM) models and techniques, mostly including multi-attribute decision-making (MADM) approaches, in addition to a single paper proposing an interactive multi-objective decision-making (MODM) approach. Particular attention is devoted to information aggregation operators; 65% of papers dealt with this item. The topics of this Special Issue gained attention in Europe and Asia. A total of 48 authors from seven countries contributed to this Issue. The papers are mainly concentrated in three application areas: supplier selection and rational order allocation, the evaluation and selection of goods or facilities, and personnel selection/partner selection. A number of new approaches are proposed that are expected to attract great interest from the research community.

multiple attribute decision making --- maximizing deviation model --- interval multiplicative preference relations --- rough sets --- queuing systems --- fuzzy EDAS --- nonnegative normal neutrosophic number --- single-valued linguistic neutrosophic interval linguistic number --- order allocation --- multi-attribute decision-making (MADM) --- multi-criteria decision-making --- Pythagorean uncertain linguistic variable --- neutrosophic sets --- supplier --- green supplier --- trust interval --- ANFIS --- reliable group decision-making --- multiple criteria decision-making --- adaptive neuro-fuzzy inference system (ANFIS) --- multi-attribute group decision-making --- Pythagorean fuzzy set --- Muirhead mean --- subcontractor evaluation --- fuzzy sets --- group decision-making --- score function --- supplier selection --- unbalanced linguistic set --- projection model --- multiple criteria group decision-making --- warehouse --- multi-hesitant fuzzy sets --- Dombi operations --- interaction operational laws --- decision making --- MCDM --- multiple criteria decision making (MCDM) --- rough ANP --- MADM --- multiple attributes decision-making --- interactive approach --- weighted aggregation operator --- logistics --- rough analytical hierarchical process (AHP) --- linguistic cubic variable --- multiobjective optimization --- aggregation operators --- bi-directional projection model --- rough boundary interval --- prioritized average operator --- binary discernibility matrices --- Einstein operations --- hesitant probabilistic fuzzy Einstein aggregation operators --- multiple-criteria decision-making (MCDM) --- aggregation operator --- linguistic cubic variable Dombi weighted arithmetic average (LCVDWAA) operator --- linguistic cubic variable Dombi weighted geometric average (LCVDWGA) operator --- multi-attribute decision making --- trapezoidal fuzzy number --- rough number --- evidence theory --- uncertain group decision-making support systems --- desirability function --- deterministic finite automata --- rough weighted aggregated sum product assessment (WASPAS) --- hesitant probabilistic fuzzy element (HPFE) --- multiple attribute decision making (MADM).

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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 --- n/a --- 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