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The present book contains 20 articles collected from amongst the 53 total submitted manuscripts for the Special Issue “Fuzzy Sets, Fuzzy Loigic and Their Applications” of the MDPI journal Mathematics. The articles, which appear in the book in the series in which they were accepted, published in Volumes 7 (2019) and 8 (2020) of the journal, cover a wide range of topics connected to the theory and applications of fuzzy systems and their extensions and generalizations. This range includes, among others, management of the uncertainty in a fuzzy environment; fuzzy assessment methods of humanmachine performance; fuzzy graphs; fuzzy topological and convergence spaces; bipolar fuzzy relations; type2 fuzzy; and intuitionistic, intervalvalued, complex, picture, and Pythagorean fuzzy sets, soft sets and algebras, etc. The applications presented are oriented to finance, fuzzy analytic hierarchy, green supply chain industries, smart health practice, and hotel selection. This wide range of topics makes the book interesting for all those working in the wider area of Fuzzy sets and systems and of fuzzy logic and for those who have the proper mathematical background who wish to become familiar with recent advances in fuzzy mathematics, which has entered to almost all sectors of human life and activity.
fuzzy analytic hierarchy process  decisionmaking  partial consensus  posterior aggregation  fuzzy topology  fuzzy convergence  latticevalued convergence  ?convergence space  relative topologicalness  ptopologcalness  diagonal condition  neighborhood condition  fuzzy sets (FSs)  uncertainty  center of gravity (COG) defuzzification technique  triangular fuzzy numbers (TFNs)  grey numbers (GNs)  fuzzy relation equations (FRE)  grade point average (GPA) index  residuated lattice  soft set  filter  tfilter  tintsoft filter  BCK/BCIalgebra  (?,?)US set  (?,?)US subalgebra  (?,?)US (closed) ideal  (?,?)US commutative ideal  fuzzy topology  fuzzy convergence  ?convergence space  regularity  intuitionistic fuzzy set  similarity  counterintuitive  fuzzy graph  picture fuzzy graph  social network  direct product  lexicographic product  strong product  Intervalvalued complex fuzzy sets  distance measures  rotational invariance  reflectional invariance  dynamic multiple attribute decision making  fuzzy regression  interval type2 fuzzy sets  fuzzy topology  fuzzy convergence  ?convergence  diagonal condition  Lcotopological space  Ltopological space  degree of Lcontinuity  degree of Lclosedness  degree of Lopenness  performance management  green supply chain  decision making  nonlinear mathematical modeling  FMCG industries  fuzzy DEMATEL  bipolar fuzzy relation  bipolar fuzzy reflexive (resp., symmetric and transitive) relation  bipolar fuzzy equivalence relation  bipolar fuzzy partition  (a, b)level set  fuzzy logic  finance  banking  banking crisis management  fuzzy number  ?limit set  periodic point  Zadeh’s extension  smart health  fuzzy collaborative intelligence  fuzzy analytic hierarchy process  suitability  picture fuzzy numbers  interaction operations  partitioned Heronian  aggregation operators  hotel selection  Pythagorean fuzzy set  Dempster–Shafer evidence theory  basic probability assignment  medical diagnosis  intervalvalued fuzzy soft set  intervalvalued fuzzy soft topology  intervalvalued fuzzy soft point  intervalvalued fuzzy soft neighborhood  intervalvalued fuzzy soft quasineighborhood  intervalvalued fuzzy soft separation axioms
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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; nperson cooperative game; ordinary singlevalued neutrosophic (co)topology; ordinary singlevalued neutrosophic subspace; ?level; ordinary singlevalued neutrosophic neighborhood system; ordinary singlevalued 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 tnorms; De Morgan neutrosophic triples; neutrosophic residual implications; infinitely ?distributive; probabilistic neutrosophic hesitant fuzzy set; decisionmaking; Choquet integral; emarketing; Internet of Things; neutrosophic set; multicriteria decision making techniques; uncertainty modeling; neutrosophic goal programming approach; shale gas water management system.
singlevalued neutrosophic soft number and its operations  SVN soft weighted arithmetic averaging operator  SVN soft weighted geometric averaging operator  decisionmaking  optimization solution  sampling plan  producer’s risk’  consumer’s risk  sample size  decision making  neutrosophic set  Qneutrosophic set  Qneutrosophic soft set  soft set  Neutrosophic compound orthogonal neural network  Neutrosophic number  Neutrosophic function  Function approximation  triangular neutrosophic cubic fuzzy number  Einstein tnorm  arithmetic averaging operator  Multiattribute decision making  numerical application  neutrosophic statistical interval method  classical statistics  fuzzy logic  producer’s risk  consumer’s risk  neutrosophic cubic weighted geometric operator (NCWG)  neutrosophic cubic ordered weighted geometric operator (NCOWG)  neutrosophic cubic Einstein weighted geometric operator (NCEWG)  neutrosophic cubic Einstein ordered weighted geometric operator (NCEOWG)  multiattribute decision making  singlevalued neutrosophic set  aggregation  TOPSIS  singlevalued neutrosophic linguistic set  distance measure  combined weighted average  MAGDM  lowcarbon supplier selection  weighted geometric operator  weighted average operator  neutrosophic cubic sets  multiattribute decisionmaking (MADM)  neutrosophic cubic hybrid weighted arithmetic and geometric aggregation operator (NCHWAGA)  neutrosophic sets  cubic sets  soft sets  neutrosophic cubic soft sets  neutrosophic cubic soft expert system  multicriteria decisionmaking  neutrosophic extended triplet group  generalized neutrosophic extended triplet group  quasicompletely regular semigroup  clifford semigroup  prostate cancer  neutrosophic statistics  dietary fat level  neutrosophic regression  neutrosophic correlation  single valued neutrosophic sets  logarithmic operational laws  logarithmic aggregation operators  MCGDM problems  complex neutrosophic set  complex neutrosophic soft expert set  fuzzy parameterized single valued neutrosophic soft expert set  single valued neutrosophic set  soft expert set  decision making  membership function  neutrosophic set  neutrosophic soft rough  relations  rough set approximation  soft set  neutrosophic time series  triangular neutrosophic number  neutrosophic logical relationship  neutrosophic logical relationship groups  smart port  simplified neutrosophic set  singlevalued neutrosophic set  exponential similarity measure  port evaluation  nonstandard analysis  extended nonstandard analysis  open and closed monads to the left/right  pierced and unpierced binads  MoBiNad set  infinitesimals  infinities  nonstandard reals  standard reals  nonstandard neutrosophic lattices of first type (as poset) and second type (as algebraic structure), nonstandard neutrosophic logic  extended nonstandard neutrosophic logic  nonstandard arithmetic operations  nonstandard unit interval  nonstandard neutrosophic infimum  nonstandard neutrosophic supremum  intuitionistic fuzzy parameters  uncertainty modeling  neutrosophic goal programming approach  shale gas water management system  emarketing  Internet of Things  neutrsophic set  multicriteria decision making techniques  probabilistic neutrosophic hesitant fuzzy set (PNHFS)  decisionmaking  Choquet integral  neutrosophic extended triplet group  neutrosophic quadruple numbers  neutrosophic set  BNHWA aggregation operator  BNHOWA aggregation operator  BNHHA aggregation operator  score function  accuracy function  certainty function  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  neutrosophic sets  neutrosophic triangular norms  residuated lattices  representable neutrosophic tnorms  De Morgan neutrosophic triples  neutrosophic residual implications  infinitely ?distributive  visual tracking  neutrosophic weight  objectness  weighted multiple instance learning  supply chain sustainability metrics  plithogeny  aggregation operations  neutrosophic set  quality function deployment  multigranulation neutrosophic rough set  nondual  two universes  multiattribute group decision making  neutrosophic extended triplet group  neutrosophic quadruple numbers  refined neutrosophic numbers  refined neutrosophic quadruple numbers  neutrosophic set  fuzzy numbers  neutrosophic numbers  neutrosophic symmetric scenarios  performance indicators  financial assets  simplified neutrosophic hesitant fuzzy set  multiattribute decisionmaking  maximizing deviation  TOPSIS  single valued neutrosophic set  covering  symmetric relation  graph representation  matrix representation  paper defect diagnosis  ordinary single valued neutrosophic (co)topology  ordinary single valued neutrosophic subspace  ?level  ordinary single valued neutrosophic neighborhood system  ordinary single valued neutrosophic base  ordinary single valued neutrosophic subbase  neutrosophic offset  uninorm  neutrosophic offuninorm  neutrosophic offnorm  neutrosophic offconorm  implicator  prospector  nperson cooperative game  hypergroup  semihypergroup  neutrosophic extended triplet group  neutrosophic extended triplet semihypergroup (NETsemihypergroup)  NEThypergroup  neutrosophic rings  neutrosophic quadruple rings  idempotents  neutrosophic extended triplet group  neutrosophic set
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Entropies and entropylike quantities play an increasing role in modern nonlinear data analysis. Fields that benefit from this application range from biosignal analysis to econophysics and engineering. This issue is a collection of papers touching on different aspects of entropy measures in data analysis, as well as theoretical and computational analyses. The relevant topics include the difficulty to achieve adequate application of entropy measures and the acceptable parameter choices for those entropy measures, entropybased coupling, and similarity analysis, along with the utilization of entropy measures as features in automatic learning and classification. Various real data applications are given.
experiment of design  empirical mode decomposition  signal analysis  similarity indices  synchronization analysis  auditory attention  entropy measure  linear discriminant analysis (LDA)  support vector machine (SVM)  auditory attention classifier  electroencephalography (EEG)  vague entropy  distance induced vague entropy  distance  complex fuzzy set  complex vague soft set  entropy, entropy visualization  entropy balance equation  Shannontype relations  multivariate analysis  machine learning evaluation  data transformation  sample entropy  treadmill walking  center of pressure displacement  dualtasking  analog circuit  fault diagnosis  cross wavelet transform  Tsallis entropy  parametric tdistributed stochastic neighbor embedding  support vector machine  information transfer  Chinese stock sectors  effective transfer entropy  market crash  system coupling  crossvisibility graphs  image entropy  geodesic distance  DempsterShafer evidence theory  uncertainty of basic probability assignment  belief entropy  plausibility transformation  weighted Hartley entropy  Shannon entropy  learning  information  novelty detection  nonprobabilistic entropy  learning systems  permutation entropy  embedded dimension  short time records  signal classification  relevance analysis  global optimization  metaheuristic  firefly algorithm  crossentropy method  coevolution  symbolic analysis  ordinal patterns  Permutation entropy  conditional entropy of ordinal patterns  KolmogorovSinai entropy  algorithmic complexity  information entropy  particle size distribution  selfsimilar measure  simulation  data analysis  entropy  entropy measures  automatic learning
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Neutrosophy (1995) is a new branch of philosophy that studies triads of the form (,
generalized aggregation operators  interval neutrosophic set (INS)  multiattribute decision making (MADM)  Choquet integral  fuzzy measure  clustering algorithm  neutrosophic association rule  data mining  neutrosophic sets  big data  analytic hierarchy process (AHP)  SWOT analysis  multicriteria decisionmaking (MCDM) techniques  neutrosophic set theory  neutrosophic clustering  image segmentation  neutrosophic cmeans 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  decisionmaking trial and evaluation laboratory (DEMATEL)  intervalvalued neutrosophic set  extended ELECTRE III  symmetry  single valued neutrosophic set (SVNS)  neutrosophic multiset (NM)  single valued neutrosophic multiset (SVNM)  cosine measure  multiple attribute decisionmaking  LNGPBM operator  LNGWPBM operator  Linguistic neutrosophic sets  generalized partitioned Bonferroni mean operator  multiple attribute group decisionmaking (MAGDM)  pseudoBCI algebra  hesitant fuzzy set  neutrosophic set  filter  action learning  school administrator  SVM  neutrosophic classification  neutrosophic set  soft set  totally dependentneutrosophic set  totally dependentneutrosophic soft set  generalized De Morgan algebra  complex neutrosophic set  complex neutrosophic graph  fuzzy graph  matrix representation  neutrosophic triplet groups  semigroup  semineutrosophic triplets  classical group of neutrosophic triplets  Ssemigroup 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  multicriteria decisionmaking  neutrosophy  DSmT  decisionmaking 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  singlevalued neutrosophic multisets  medical diagnosis  probabilistic rough sets over two universes  threeway decisions  similarity measures  neutrosophic cubic set  decisionmaking  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  2inglevalued neutrosophic set  Technique for Order Preference by Similarity to an Ideal Solution (TOPSIS)  integrated weight  maximizing deviation  multiattribute decisionmaking (MADM)  neutrosophic triplet set (NTS)  partial metric spaces (PMS)  fixed point theory (FPT)  neutrosophic triplet  quasi neutrosophic triplet loop  quasi neutrosophic triplet group  BEalgebra  CIalgebra  fuzzy time series  forecasting  twofactor fuzzy logical relationship  multivalued neutrosophic set  Hamming distance  neutrosophic set  prioritized operator  Muirhead mean  multicriteria decisionmaking  aggregation operators  dual aggregation operators  neutrosophic triplet group (NTG)  NTsubgroup  homomorphism theorem  weak commutative neutrosophic triplet group  neutrosophic rough set  MGNRS  dual domains  inclusion relation  decisionmaking  neutromonomorphism  neutroepimorphism  neutroautomorphism  fundamental neutrohomomorphism theorem  first neutroisomorphism theorem  and second neutroisomorphism theorem  linear and nonlinear neutrosophic number  deneutrosophication 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  multicriteria group decisionmaking  power aggregation operator  extended TOPSIS method  probabilistic singlevalued (interval) neutrosophic hesitant fuzzy set  multiattribute decision making  aggregation operator  quasigroup  loop  BCIalgebra  BolMoufang  quasi neutrosophic loops  Fenyves identities  Gmetric  neutrosophic Gmetric  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  multiattribute decision making (MADM)  multiple attribute group decision making (MAGDM)  2tuple 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  Qlinguistic neutrosophic variable set  vector similarity measure  cosine measure  Dice measure  Jaccard measure  decision making  inclusion relation  neutrosophic rough set  multiattribute group decisionmaking (MAGDM)  multigranulation neutrosophic rough set (MNRS)  two universes  single valued trapezoidal neutrosophic number  multicriteria group decision making  possibility degree  power aggregation operators  LAsemihypergroups  neutrosophic triplet set  neutrohomomorphism  algorithm  decision making  expert set  generalized neutrosophic set  neutrosophic sets  Qneutrosophic  soft sets  simplified neutrosophic sets (SNSs)  interval number  dependent degree  multicriteria group decisionmaking (MCGDM)  computability  oracle Turing machines  neutrosophic sets  neutrosophic logic  recursive enumerability  oracle computation  criterion functions  neutrosophic computation  neutrosophic logic  quantum computation  computation  logic
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Neutrosophy (1995) is a new branch of philosophy that studies triads of the form (,
generalized aggregation operators  interval neutrosophic set (INS)  multiattribute decision making (MADM)  Choquet integral  fuzzy measure  clustering algorithm  neutrosophic association rule  data mining  neutrosophic sets  big data  analytic hierarchy process (AHP)  SWOT analysis  multicriteria decisionmaking (MCDM) techniques  neutrosophic set theory  neutrosophic clustering  image segmentation  neutrosophic cmeans 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  decisionmaking trial and evaluation laboratory (DEMATEL)  intervalvalued neutrosophic set  extended ELECTRE III  symmetry  single valued neutrosophic set (SVNS)  neutrosophic multiset (NM)  single valued neutrosophic multiset (SVNM)  cosine measure  multiple attribute decisionmaking  LNGPBM operator  LNGWPBM operator  Linguistic neutrosophic sets  generalized partitioned Bonferroni mean operator  multiple attribute group decisionmaking (MAGDM)  pseudoBCI algebra  hesitant fuzzy set  neutrosophic set  filter  action learning  school administrator  SVM  neutrosophic classification  neutrosophic set  soft set  totally dependentneutrosophic set  totally dependentneutrosophic soft set  generalized De Morgan algebra  complex neutrosophic set  complex neutrosophic graph  fuzzy graph  matrix representation  neutrosophic triplet groups  semigroup  semineutrosophic triplets  classical group of neutrosophic triplets  Ssemigroup 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  multicriteria decisionmaking  neutrosophy  DSmT  decisionmaking 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  singlevalued neutrosophic multisets  medical diagnosis  probabilistic rough sets over two universes  threeway decisions  similarity measures  neutrosophic cubic set  decisionmaking  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  2inglevalued neutrosophic set  Technique for Order Preference by Similarity to an Ideal Solution (TOPSIS)  integrated weight  maximizing deviation  multiattribute decisionmaking (MADM)  neutrosophic triplet set (NTS)  partial metric spaces (PMS)  fixed point theory (FPT)  neutrosophic triplet  quasi neutrosophic triplet loop  quasi neutrosophic triplet group  BEalgebra  CIalgebra  fuzzy time series  forecasting  twofactor fuzzy logical relationship  multivalued neutrosophic set  Hamming distance  neutrosophic set  prioritized operator  Muirhead mean  multicriteria decisionmaking  aggregation operators  dual aggregation operators  neutrosophic triplet group (NTG)  NTsubgroup  homomorphism theorem  weak commutative neutrosophic triplet group  neutrosophic rough set  MGNRS  dual domains  inclusion relation  decisionmaking  neutromonomorphism  neutroepimorphism  neutroautomorphism  fundamental neutrohomomorphism theorem  first neutroisomorphism theorem  and second neutroisomorphism theorem  linear and nonlinear neutrosophic number  deneutrosophication 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  multicriteria group decisionmaking  power aggregation operator  extended TOPSIS method  probabilistic singlevalued (interval) neutrosophic hesitant fuzzy set  multiattribute decision making  aggregation operator  quasigroup  loop  BCIalgebra  BolMoufang  quasi neutrosophic loops  Fenyves identities  Gmetric  neutrosophic Gmetric  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  multiattribute decision making (MADM)  multiple attribute group decision making (MAGDM)  2tuple 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  Qlinguistic neutrosophic variable set  vector similarity measure  cosine measure  Dice measure  Jaccard measure  decision making  inclusion relation  neutrosophic rough set  multiattribute group decisionmaking (MAGDM)  multigranulation neutrosophic rough set (MNRS)  two universes  single valued trapezoidal neutrosophic number  multicriteria group decision making  possibility degree  power aggregation operators  LAsemihypergroups  neutrosophic triplet set  neutrohomomorphism  algorithm  decision making  expert set  generalized neutrosophic set  neutrosophic sets  Qneutrosophic  soft sets  simplified neutrosophic sets (SNSs)  interval number  dependent degree  multicriteria group decisionmaking (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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