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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

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The authors offer an introduction to mathematical analysis with applications in economic theory & econometrics.

Economics, Mathematical. --- Mathematical analysis. --- Econometrics. --- Approximation. --- Axiom of choice. --- Banach space. --- Bijection. --- Bounded function. --- Budget set. --- Calculation. --- Cardinality. --- Cauchy sequence. --- Central limit theorem. --- Combination. --- Compact space. --- Complete metric space. --- Concave function. --- Conditional expectation. --- Continuous function (set theory). --- Continuous function. --- Contraction mapping. --- Contradiction. --- Convex analysis. --- Convex set. --- Countable set. --- Dense set. --- Differentiable function. --- Dimension (vector space). --- Dimension. --- Division by zero. --- Dynamic programming. --- Empty set. --- Equation. --- Equivalence class. --- Estimator. --- Existential quantification. --- Finite set. --- Fixed-point theorem. --- Function (mathematics). --- Hahn–Banach theorem. --- Independence (probability theory). --- Indicator function. --- Inequality (mathematics). --- Infimum and supremum. --- Intermediate value theorem. --- Karush–Kuhn–Tucker conditions. --- Law of large numbers. --- Lebesgue measure. --- Limit of a sequence. --- Limit superior and limit inferior. --- Linear algebra. --- Linear function. --- Linear map. --- Linear subspace. --- Loss function. --- Markov chain. --- Mathematical optimization. --- Mathematics. --- Maximal element. --- Measurable function. --- Measure (mathematics). --- Metric space. --- Monotonic function. --- Normed vector space. --- Null set. --- Open set. --- Optimization problem. --- Parameter. --- Pareto efficiency. --- Partially ordered set. --- Preference (economics). --- Preference relation. --- Probability distribution. --- Probability space. --- Probability theory. --- Probability. --- Quantity. --- Random variable. --- Rational number. --- Real number. --- Scientific notation. --- Sequence. --- Set (mathematics). --- Simple function. --- Special case. --- Stochastic process. --- Stone–Weierstrass theorem. --- Subsequence. --- Subset. --- Summation. --- Surjective function. --- Theorem. --- Topological space. --- Topology. --- Uncountable set. --- Uniform continuity. --- Uniform distribution (discrete). --- Union (set theory). --- Upper and lower bounds. --- Utility. --- Variable (mathematics). --- Vector space. --- Zorn's lemma.