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Algebraic Structures of Neutrosophic Triplets, Neutrosophic Duplets, or Neutrosophic Multisets

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ISBN: 9783038973843 Year: Volume: 1 Pages: 478 DOI: 10.3390/books978-3-03897-385-0 Language: eng
Publisher: MDPI - Multidisciplinary Digital Publishing Institute
Subject: Science (General) --- Mathematics
Added to DOAB on : 2019-04-05 10:34:31
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Abstract

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.

Keywords

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

Algebraic Structures of Neutrosophic Triplets, Neutrosophic Duplets, or Neutrosophic Multisets

Authors: --- ---
ISBN: 9783038974758 Year: Volume: 2 Pages: 450 DOI: 10.3390/books978-3-03897-476-5 Language: eng
Publisher: MDPI - Multidisciplinary Digital Publishing Institute
Subject: Science (General) --- Mathematics
Added to DOAB on : 2019-04-05 10:34:31
License:

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Export citation

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Abstract

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.

Keywords

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

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