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This Special Issue contains eight original papers with a high impact in various domains of set-valued analysis. Set-valued analysis has made remarkable progress in the last 70 years, enriching itself continuously with new concepts, important results, and special applications. Different problems arising in the theory of control, economics, game theory, decision making, nonlinear programming, biomathematics, and statistics have strengthened the theoretical base and the specific techniques of set-valued analysis. The consistency of its theoretical approach and the multitude of its applications have transformed set-valued analysis into a reference field of modern mathematics, which attracts an impressive number of researchers.

gauge multivalued integral --- scalarly defined multivalued integral --- decomposition of a multifunction --- Kuelbs–Steadman space --- Henstock–Kurzweil integrable function --- vector measure --- dense embedding --- completely continuous embedding --- Köthe space --- Banach lattice --- fractional differential inclusion --- maximal monotone operator --- Riemann–Liouville integral --- absolutely continuous in variation --- Vladimirov pseudo-distance --- fuzzy measure space --- fuzzy integration --- t-norm --- Chebyshev’s inequality --- Hölder’s inequality --- periodic boundary value inclusion --- Stieltjes derivative --- Stieltjes integrals --- Bohnenblust–Karlin fixed-point theorem --- regulated function --- solution set --- discontinuous function --- impulsive problem with variable times --- Riemann-Lebesgue integral --- interval valued (set) multifunction --- non-additive set function --- image processing --- b-metric space --- Hβ-Hausdorff–Pompeiu b-metric --- multi-valued fractal --- iterated multifunction system --- integral inclusion

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This Special Issue contains eight original papers with a high impact in various domains of set-valued analysis. Set-valued analysis has made remarkable progress in the last 70 years, enriching itself continuously with new concepts, important results, and special applications. Different problems arising in the theory of control, economics, game theory, decision making, nonlinear programming, biomathematics, and statistics have strengthened the theoretical base and the specific techniques of set-valued analysis. The consistency of its theoretical approach and the multitude of its applications have transformed set-valued analysis into a reference field of modern mathematics, which attracts an impressive number of researchers.

Research & information: general --- Mathematics & science --- gauge multivalued integral --- scalarly defined multivalued integral --- decomposition of a multifunction --- Kuelbs–Steadman space --- Henstock–Kurzweil integrable function --- vector measure --- dense embedding --- completely continuous embedding --- Köthe space --- Banach lattice --- fractional differential inclusion --- maximal monotone operator --- Riemann–Liouville integral --- absolutely continuous in variation --- Vladimirov pseudo-distance --- fuzzy measure space --- fuzzy integration --- t-norm --- Chebyshev’s inequality --- Hölder’s inequality --- periodic boundary value inclusion --- Stieltjes derivative --- Stieltjes integrals --- Bohnenblust–Karlin fixed-point theorem --- regulated function --- solution set --- discontinuous function --- impulsive problem with variable times --- Riemann-Lebesgue integral --- interval valued (set) multifunction --- non-additive set function --- image processing --- b-metric space --- Hβ-Hausdorff–Pompeiu b-metric --- multi-valued fractal --- iterated multifunction system --- integral inclusion

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The present book contains the 24 total articles accepted and published in the Special Issue “Fuzzy Sets, Fuzzy Logic and Their Applications, 2020” of the MDPI Mathematics journal, which covers a wide range of topics connected to the theory and applications of fuzzy sets and systems of fuzzy logic and their extensions/generalizations. These topics include, among others, elements from fuzzy graphs; fuzzy numbers; fuzzy equations; fuzzy linear spaces; intuitionistic fuzzy sets; soft sets; type-2 fuzzy sets, bipolar fuzzy sets, plithogenic sets, fuzzy decision making, fuzzy governance, fuzzy models in mathematics of finance, a philosophical treatise on the connection of the scientific reasoning with fuzzy logic, etc. It is hoped that the book will be interesting and useful for those working in the area of fuzzy sets, fuzzy systems and fuzzy logic, as well as for those with the proper mathematical background and willing to become familiar with recent advances in fuzzy mathematics, which has become prevalent in almost all sectors of the human life and activity.

Research & information: general --- Mathematics & science --- bipolar gradation of openness --- bipolar gradation of closedness --- bipolar fuzzy topology --- bipolar gradation preserving map --- fuzzy collaborative forecasting --- dynamic random access memory --- partial consensus --- fuzzy intersection --- fuzzy linear system --- fuzzy number --- fuzzy number vector --- embedding method --- inductive and deductive reasoning --- fuzzy logic (FL) --- scientific method --- probability and statistics --- Bayesian probabilities --- fuzzy implication --- ordering property --- least fuzzy negation --- t-conditionality --- neutrosophic set --- plithogenic set --- fuzzy set --- entropy --- similarity measure --- information measure --- Hyers-Ulam stability --- pexider type functional equation --- intuitionistic fuzzy normed spaces --- alternative fixed point theorem --- interval-valued fuzzy competition graph --- interval-valued fuzzy p competition graph --- interval-valued fuzzy neighbourhood graph --- interval-valued m-step fuzzy competition graph --- homomorphism of graph products --- max-min algebra --- fuzzy max-T algebra --- Łukasiewicz triangular norm --- max-Łukasiewicz algebra --- parametric solvability --- soft set --- fuzzy soft set --- multi-fuzzy set --- multi-fuzzy soft set --- ℒℳℱ?? --- similarity measure of ℒℳℱ?? --- site selection --- shopping mall site selection --- linguistic terms for fuzzy variable --- fuzzy AHP --- fuzzy TOPSIS --- octahedron set --- i-octahedron subgroupoid --- i-octahedron ideal --- i-sup-property, i-octahedron subgroup --- i-octahedron subring --- interval matrix --- interval eigenvector --- strong interval eigenvector --- fuzzy nonlinear systems --- fuzzy arithmetic --- fuzzy calculus --- multidimensional fuzzy arithmetic --- RDM fuzzy arithmetic --- fuzzy parametric form --- fuzzy measures --- monotone measures --- product spaces --- Schauder fixed point theorem --- fuzzy normed linear space --- t-norm --- measure of non-compactness --- fuzzy logic connectives --- law of importation --- α-migrativity --- distance measure --- fuzzy differential equations --- fuzzy difference equations --- mixed continuous-discrete model --- strongly generalized Hukuhara differentiability --- time value of money --- GEFS --- SEFS --- fuzzy relations: fuzzy sets --- max–min composition --- min–max composition --- monotone statistical parameters --- fuzzy statistics --- FAHP --- FTOPSIS --- FCOPRAS --- hexagonal fuzzy number --- governance --- fuzzy logic --- management system --- type-2 fuzzy set --- fuzzification --- type-reduction --- defuzzification --- B-spline surface model function

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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