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

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

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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