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Optimization is considered as a decision-making process for getting the most out of available resources for the best attainable results. Many real-world problems are multi-objective or multi-attribute problems that naturally involve several competing objectives that need to be optimized simultaneously, while respecting some constraints or involving selection among feasible discrete alternatives. In this Reprint of the Special Issue, 19 research papers co-authored by 88 researchers from 14 different countries explore aspects of multi-objective or multi-attribute modeling and optimization in crisp or uncertain environments by suggesting multiple-attribute decision-making (MADM) and multi-objective decision-making (MODM) approaches. The papers elaborate upon the approaches of state-of-the-art case studies in selected areas of applications related to sustainable development decision aiding in engineering and management, including construction, transportation, infrastructure development, production, and organization management.

artificial neural network --- sustainability hierarchy --- expert --- Rough Hamy aggregator --- sustainable solution --- crank–slider --- technology selection problem --- AHP --- bus pass --- optimization --- discrete time/cost trade-off --- Rough WASPAS --- hybrid multi-criteria decision making (MCDM) --- travel times --- extended Tomada de Decisão Interativa Multicritério (TODIM) --- bi-level programming --- multi-objective evolutionary algorithms --- project scheduling --- WASPAS --- port scheduling --- rehydration --- sustainable transport policy --- gold mines --- hybrid mathematical model --- sustainable developments --- straw bales --- group decision making --- contractor --- Total Interpretive Structural Modeling (TISM) --- MULTIMOORA --- building investment project --- heuristics --- cleaner production (CP) --- particle swarm optimization (PSO) --- optimization study --- critical information infrastructures --- bi-objective optimization --- dynamic analysis --- location-allocation problem --- probabilistic linguistic term sets (PLTSs) --- drying --- multiple objective optimization --- multi-objective decision-making (MODM) --- ranking --- hierarchical SWARA --- choice --- linguistic hesitant fuzzy set and Standard variance --- multiple-attribute decision-making (MADM) --- project --- sustainable energy evaluation --- emission of pollutants --- genetic algorithm --- ARAS-G --- multi-purpose system --- renewable energy --- assessment --- hospital evaluation --- bat algorithm --- multiple-criteria decision-making --- comfort of use of buildings --- energy efficiency --- healthcare facility --- conceptual framework --- hybrid expert system --- engineering --- sustainability --- verbal analysis --- sustainable energy developments --- sustainable development --- hybrid --- public transport --- water resource management --- compacted clay --- multiple criteria decision making (MCDM) --- MCDM --- particle swarm optimization algorithm --- sustainable traffic --- single-cylinder engine --- Rough BWM --- policy measures --- apple --- clay blocks --- historic buildings --- hesitant fuzzy set --- construction --- TOPSIS-GM --- roundabout --- fuzzy --- sustainable transport --- surface transport --- grey --- Multiple Attribute Decision Making (MADM) --- WSM --- ecological building --- management --- Geomean --- SWARA --- vibration suppression --- organizations --- innovation in transport --- risk --- berth-quay crane joint scheduling --- cost calculation --- multiple criteria decision aid

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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

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• 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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• 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

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Most real-world search and optimization problems naturally involve multiple criteria as objectives. Generally, symmetry, asymmetry, and anti-symmetry are basic characteristics of binary relationships used when modeling optimization problems. Moreover, the notion of symmetry has appeared in many articles about uncertainty theories that are employed in multi-criteria problems. Different solutions may produce trade-offs (conflicting scenarios) among different objectives. A better solution with respect to one objective may compromise other objectives. There are various factors that need to be considered to address the problems in multidisciplinary research, which is critical for the overall sustainability of human development and activity. In this regard, in recent decades, decision-making theory has been the subject of intense research activities due to its wide applications in different areas. The decision-making theory approach has become an important means to provide real-time solutions to uncertainty problems. Theories such as probability theory, fuzzy set theory, type-2 fuzzy set theory, rough set, and uncertainty theory, available in the existing literature, deal with such uncertainties. Nevertheless, the uncertain multi-criteria characteristics in such problems have not yet been explored in depth, and there is much left to be achieved in this direction. Hence, different mathematical models of real-life multi-criteria optimization problems can be developed in various uncertain frameworks with special emphasis on optimization problems.

Information technology industries --- multiple-criteria decision-making --- underground mines --- mining methods --- expert knowledge --- failure mode and effects analysis --- solar panel systems --- step-wise weight assessment ratio analysis --- grey relational analysis --- Z-number theory --- B2C e-commerce factors --- website --- MCDM --- Fuzzy AHP --- TOPSIS-Grey --- China --- IoT --- platform selection --- multi criteria decision analysis (MCDA) --- AHP --- PROMETHEE-II --- Industry 4.0 --- data envelopment analysis --- conjoint analysis --- experimental design --- criteria importance --- weight restrictions --- subjective and objective teacher efficiency --- multi-objective planning --- reverse supply chain --- robust optimization --- uncertainty --- meta-heuristic algorithm --- steel making industry --- fuzzy PIPRECIA --- fuzzy EDAS --- railway --- multi-criteria decision-making --- transport policy --- Six Sigma (6σ) --- DMAIC --- vehicle fleet --- optimization --- text mining --- Multi-Attribute Decision Making (MADM), criteria selection --- weighting --- Prospective MADM --- Latent Semantic Analysis (LSA) --- SIMUS --- decision tree --- transport plan --- Laplace’s criterion --- Hurwitz’s criterion --- q-rung orthopair fuzzy numbers --- q-rung orthopair fuzzy prioritized weighted average operator --- q-rung orthopair fuzzy prioritized weighted geometric operator --- green supply chain management --- fuzzy theory --- sustainable development --- SCOR model --- FAHP --- PROMETHEE II --- textile and garments industry --- sustainable supplier selection --- MCDA --- efficiency --- DEA --- SFA --- classification --- dimensionality reduction --- q-ROFNs --- Einstein operators --- prioritized aggregation operators --- multi-criteria group decision making --- hazardous materials --- vehicle route model (VRP) --- uncertainty theory --- chance constrained programming model --- hybrid intelligent algorithm --- linear Diophantine fuzzy set --- linear Diophantine fuzzy soft rough set --- soft rough linear Diophantine fuzzy set --- upper reduct and lower reduct --- core set --- multi-criteria decision making --- q-Rung orthopair fuzzy sets --- geometric aggregation operators based on generalized and group-generalized parameters --- water loss management --- decision making --- intuitionistic fuzzy sets --- the COMET method --- service quality --- fuzzy set --- Jensen–Shannon divergence --- shapley function --- TODIM --- port-hinterland transportation system --- bi-objective programming --- intermodal transportation --- carbon emissions --- uncertain demand --- distributionally robust --- chance constraint --- Yangtze River Economic Belt --- multi-criteria decision-analysis --- MCDA benchmark --- normalization --- entropy --- decision-making methods --- multi-criteria problems --- evolutionary algorithms --- machine learning --- fuzzy logic --- uncertain data --- consistency weights --- fuzzy preference relation (FPR) --- hesitant fuzzy preference relation (HFPR) --- Łukasiewicz consistency --- normal hesitant fuzzy preference relation (NHFPR) --- multiple criteria decision-making (MCDM) --- outsourcing provider --- DEMATEL --- CRITIC --- TOPSIS --- comparison measure --- representation --- disjoint --- multiplicative preference relation (MPR) --- group decision-making (GDM) --- incomplete fuzzy preference relation (IFPR) --- TL-consistency --- cubic m-polar fuzzy set --- Dombi’s operations --- cubic m-polar fuzzy aggregation operators with P-order (R-order) --- SIR technique --- complex networks --- social networks --- viral marketing --- information propagation --- crisp probability --- interval probability --- influence diagrams --- circuit breakers --- granular computing --- interval-valued --- intuitionistic fuzzy set --- multiple granulation --- ordered information system --- multiple-criteria decision-making --- underground mines --- mining methods --- expert knowledge --- failure mode and effects analysis --- solar panel systems --- step-wise weight assessment ratio analysis --- grey relational analysis --- Z-number theory --- B2C e-commerce factors --- website --- MCDM --- Fuzzy AHP --- TOPSIS-Grey --- China --- IoT --- platform selection --- multi criteria decision analysis (MCDA) --- AHP --- PROMETHEE-II --- Industry 4.0 --- data envelopment analysis --- conjoint analysis --- experimental design --- criteria importance --- weight restrictions --- subjective and objective teacher efficiency --- multi-objective planning --- reverse supply chain --- robust optimization --- uncertainty --- meta-heuristic algorithm --- steel making industry --- fuzzy PIPRECIA --- fuzzy EDAS --- railway --- multi-criteria decision-making --- transport policy --- Six Sigma (6σ) --- DMAIC --- vehicle fleet --- optimization --- text mining --- Multi-Attribute Decision Making (MADM), criteria selection --- weighting --- Prospective MADM --- Latent Semantic Analysis (LSA) --- SIMUS --- decision tree --- transport plan --- Laplace’s criterion --- Hurwitz’s criterion --- q-rung orthopair fuzzy numbers --- q-rung orthopair fuzzy prioritized weighted average operator --- q-rung orthopair fuzzy prioritized weighted geometric operator --- green supply chain management --- fuzzy theory --- sustainable development --- SCOR model --- FAHP --- PROMETHEE II --- textile and garments industry --- sustainable supplier selection --- MCDA --- efficiency --- DEA --- SFA --- classification --- dimensionality reduction --- q-ROFNs --- Einstein operators --- prioritized aggregation operators --- multi-criteria group decision making --- hazardous materials --- vehicle route model (VRP) --- uncertainty theory --- chance constrained programming model --- hybrid intelligent algorithm --- linear Diophantine fuzzy set --- linear Diophantine fuzzy soft rough set --- soft rough linear Diophantine fuzzy set --- upper reduct and lower reduct --- core set --- multi-criteria decision making --- q-Rung orthopair fuzzy sets --- geometric aggregation operators based on generalized and group-generalized parameters --- water loss management --- decision making --- intuitionistic fuzzy sets --- the COMET method --- service quality --- fuzzy set --- Jensen–Shannon divergence --- shapley function --- TODIM --- port-hinterland transportation system --- bi-objective programming --- intermodal transportation --- carbon emissions --- uncertain demand --- distributionally robust --- chance constraint --- Yangtze River Economic Belt --- multi-criteria decision-analysis --- MCDA benchmark --- normalization --- entropy --- decision-making methods --- multi-criteria problems --- evolutionary algorithms --- machine learning --- fuzzy logic --- uncertain data --- consistency weights --- fuzzy preference relation (FPR) --- hesitant fuzzy preference relation (HFPR) --- Łukasiewicz consistency --- normal hesitant fuzzy preference relation (NHFPR) --- multiple criteria decision-making (MCDM) --- outsourcing provider --- DEMATEL --- CRITIC --- TOPSIS --- comparison measure --- representation --- disjoint --- multiplicative preference relation (MPR) --- group decision-making (GDM) --- incomplete fuzzy preference relation (IFPR) --- TL-consistency --- cubic m-polar fuzzy set --- Dombi’s operations --- cubic m-polar fuzzy aggregation operators with P-order (R-order) --- SIR technique --- complex networks --- social networks --- viral marketing --- information propagation --- crisp probability --- interval probability --- influence diagrams --- circuit breakers --- granular computing --- interval-valued --- intuitionistic fuzzy set --- multiple granulation --- ordered information system