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The development of special and general relativity has relied significantly on ideas of symmetry. Similarly, modern efforts to test these theories have often sought either violations or extensions of the symmetries seen, and symmetry is regularly used a tool in seeking new applications. In this Special Issue of symmetry, we explore some contemporary research related to symmetry in special and general relativity.
Lorentz symmetry  rotation invariance  StandardModel Extension  Noether’s theorem  Weyl method  Palais principle of symmetric criticality  solutions to Einstein’s equations  magnetic monopole  pulsar timing  StandardModel Extension  binary pulsars  Lorentz and CPT violation  StandardModel Extension  Dirac fermions  Dirac neutrinos  Majorana neutrinos  determinants of block matrices  lorentz violation  CPT violation  penning trap  quantum mechanics  antimatter  interferometry  gravitational waves  Lorentz violation  standardmodel extension  geodesic deviation  Lorentz violation  standard model extension  CPT violation
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This Special Issue presents research papers on various topics within many different branches of mathematics, applied mathematics, and mathematical physics. Each paper presents mathematical theories, methods, and their application based on current and recently developed symmetric polynomials. Also, each one aims to provide the full understanding of current research problems, theories, and applications on the chosen topics and includes the most recent advances made in the area of symmetric functions and polynomials.
Fubini polynomials  wtorsion Fubini polynomials  fermionic padic integrals  symmetric identities  Chebyshev polynomials  sums of finite products  hypergeometric function  Fubini polynomials  Euler numbers  symmetric identities  elementary method  computational formula  two variable qBerstein polynomial  two variable qBerstein operator  qEuler number  qEuler polynomial  Fubini polynomials  Euler numbers  congruence  elementary method  qBernoulli numbers  qBernoulli polynomials  two variable qBernstein polynomials  two variable qBernstein operators  padic integral on ?p  the degenerate gamma function  the modified degenerate gamma function  the degenerate Laplace transform  the modified degenerate Laplace transform  Fibonacci  Lucas  linear form in logarithms  continued fraction  reduction method  sums of finite products of Chebyshev polynomials of the third and fourth kinds  Hermite  generalized Laguerre  Legendre  Gegenbauer  Jacobi  thirdorder character  classical Gauss sums  rational polynomials  analytic method  recursive formula  fermionic padic qintegral on ?p  qEuler polynomials  qChanghee polynomials  symmetry group  Apostoltype Frobenius–Euler polynomials  threevariable Hermite polynomials  symmetric identities  explicit relations  operational connection  qVolkenborn integral on ?p  Bernoulli numbers and polynomials  generalized Bernoulli polynomials and numbers of arbitrary complex order  generalized Bernoulli polynomials and numbers attached to a Dirichlet character ?  Changhee polynomials  Changhee polynomials of type two  fermionic padic integral on ?p  Chebyshev polynomials of the first, second, third, and fourth kinds  sums of finite products  representation  catalan numbers  elementary and combinatorial methods  recursive sequence  convolution sums  wellposedness  stability  acoustic wave equation  perfectly matched layer  Fibonacci polynomials  Lucas polynomials  trivariate Fibonacci polynomials  trivariate Lucas polynomials  generating functions  central incomplete Bell polynomials  central complete Bell polynomials  central complete Bell numbers  Legendre polynomials  Laguerre polynomials  generalized Laguerre polynomials  Gegenbauer polynomials  hypergeometric functions 1F1 and 2F1  Euler polynomials  Bernoulli polynomials  elementary method  identity  congruence  new sequence  Catalan numbers  elementary and combinatorial methods  congruence  conjecture  fluctuation theorem  thermodynamics of information  stochastic thermodynamics  mutual information  nonequilibrium free energy  entropy production
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This book contains the successful invited submissions to a Special Issue of Symmetry on the subject of ""Graph Theory"". Although symmetry has always played an important role in Graph Theory, in recent years, this role has increased significantly in several branches of this field, including but not limited to Gromov hyperbolic graphs, the metric dimension of graphs, domination theory, and topological indices. This Special Issue includes contributions addressing new results on these topics, both from a theoretical and an applied point of view.
Metric dimension  basis  resolving set  gear graph  generalized gear graph  Devaney chaos  hypercyclicity  topological transitivity  topologically mixing  disjointness  connectivity  topological indices  cuprite  atom bond connectivity index  Zagreb indices  geometric arithmetic index  general Randi? index  titanium difluoride  direct product of graphs  geodesics  Gromov hyperbolicity  bipartite graphs  alphaboron nanotube  resolving set  metric basis  metric dimension  distinguishing number  functigraph  complete graph  graph operators  gromov hyperbolicity  geodesics  topological indices  polycyclic aromatic hydrocarbons  resolving set  domination  secure resolving set and secure resolving domination  harmonic index  harmonic polynomial  inverse degree index  products of graphs  algorithm  general randi? index  atombond connectivity ABC index  geometricarithmetic GA index  HexDerived Cage networks  dominating set  binary locatingdomination number  rotationallysymmetric convex polytopes  ILP models
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Researches and investigations involving the theory and applications of integral transforms and operational calculus are remarkably widespread in many diverse areas of the mathematical, physical, chemical, engineering and statistical sciences.
highly oscillatory  convolution quadrature rule  volterra integral equation  Bessel kernel  convergence  higher order Schwarzian derivatives  Janowski starlike function  Janowski convex function  bound on derivatives  tangent numbers  tangent polynomials  Carlitztype qtangent numbers  Carlitztype qtangent polynomials  (p,q)analogue of tangent numbers and polynomials  (p,q)analogue of tangent zeta function  symmetric identities  zeros  Lommel functions  univalent functions  starlike functions  convex functions  inclusion relationships  analytic function  Hankel determinant  exponential function  upper bound  nonlinear boundary value problems  fractionalorder differential equations  RiemannStieltjes functional integral  LiouvilleCaputo fractional derivative  infinitepoint boundary conditions  advanced and deviated arguments  existence of at least one solution  Fredholm integral equation  Schauder fixed point theorem  Hölder condition  generalized Kuramoto–Sivashinsky equation  modified Kudryashov method  exact solutions  Maple graphs  analytic function  Hadamard product (convolution)  partial sum  Srivastava–Tomovski generalization of Mittag–Leffler function  subordination  differential equation  differential inclusion  Liouville–Caputotype fractional derivative  fractional integral  existence  fixed point  Bernoulli spiral  Grandi curves  Chebyshev polynomials  pseudoChebyshev polynomials  orthogonality property  symmetric  encryption  password  hash  cryptography  PBKDF  q–Bleimann–Butzer–Hahn operators  (p,q)integers  (p,q)Bernstein operators  (p,q)Bleimann–Butzer–Hahn operators  modulus of continuity  rate of approximation  Kfunctional  HurwitzLerch zeta function  generalized functions  analytic number theory  ?generalized HurwitzLerch zeta functions  derivative properties  series representation  basic hypergeometric functions  generating functions  qpolynomials  analytic functions  Mittag–Leffler functions  starlike functions  convex functions  Hardy space  vibrating string equation  initial conditions  spectral decomposition  regular solution  the uniqueness of the solution  the existence of a solution  analytic  ?convex function  starlike function  stronglystarlike function  subordination  q Sheffer–Appell polynomials  generating relations  determinant definition  recurrence relation  q Hermite–Bernoulli polynomials  q Hermite–Euler polynomials  q Hermite–Genocchi polynomials  Volterra integral equations  highly oscillatory Bessel kernel  Hermite interpolation  direct Hermite collocation method  piecewise Hermite collocation method  differential operator  qhypergeometric functions  meromorphic function  Mittag–Leffler function  Hadamard product  differential subordination  starlike functions  Bell numbers  radius estimate  (p, q)integers  Dunkl analogue  generating functions  generalization of exponential function  Szász operator  modulus of continuity  function spaces and their duals  distributions  tempered distributions  Schwartz testing function space  generalized functions  distribution space  wavelet transform of generalized functions  Fourier transform  analytic function  subordination  Dziok–Srivastava operator  nonlinear boundary value problem  nonlocal  multipoint  multistrip  existence  Ulam stability  functions of bounded boundary and bounded radius rotations  subordination  functions with positive real part  uniformly starlike and convex functions  analytic functions  univalent functions  starlike and qstarlike functions  qderivative (or qdifference) operator  sufficient conditions  distortion theorems  Janowski functions  analytic number theory  ?generalized Hurwitz–Lerch zeta functions  derivative properties  recurrence relations  integral representations  Mellin transform  natural transform  Adomian decomposition method  Caputo fractional derivative  generalized mittagleffler function  analytic functions  Hadamard product  starlike functions  qderivative (or qdifference) operator  Hankel determinant  qstarlike functions  fuzzy volterra integrodifferential equations  fuzzy general linear method  fuzzy differential equations  generalized Hukuhara differentiability  spectrum symmetry  DCT  MFCC  audio features  anuran calls  analytic functions  convex functions  starlike functions  strongly convex functions  strongly starlike functions  uniformly convex functions  Struve functions  truncatedexponential polynomials  monomiality principle  generating functions  Apostoltype polynomials and Apostoltype numbers  Bernoulli, Euler and Genocchi polynomials  Bernoulli, Euler, and Genocchi numbers  operational methods  summation formulas  symmetric identities  Euler numbers and polynomials  qEuler numbers and polynomials  HurwitzEuler eta function  multiple HurwitzEuler eta function  higher order qEuler numbers and polynomials  (p, q)Euler numbers and polynomials of higher order  symmetric identities  symmetry of the zero
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The present book contains 14 papers published in the Special Issue “Differential Geometry” of the journal Mathematics. They represent a selection of the 30 submissions. This book covers a variety of both classical and modern topics in differential geometry. We mention properties of both rectifying and affine curves, the geometry of hypersurfaces, angles in Minkowski planes, Euclidean submanifolds, differential operators and harmonic forms on Riemannian manifolds, complex manifolds, contact manifolds (in particular, Sasakian and transSasakian manifolds), curvature invariants, and statistical manifolds and their submanifolds (in particular, Hessian manifolds). We wish to mention that among the authors, there are both wellknown geometers and young researchers. The authors are from countries with a tradition in differential geometry: Belgium, China, Greece, Japan, Korea, Poland, Romania, Spain, Turkey, and United States of America. Many of these papers were already cited by other researchers in their articles. This book is useful for specialists in differential geometry, operator theory, physics, and information geometry as well as graduate students in mathematics.
Euclidean submanifold  position vector field  concurrent vector field  concircular vector field  rectifying submanifold  Tsubmanifolds  constant ratio submanifolds  Ricci soliton  Kähler–Einstein metrics  compact complex surfaces  pinching of the curvatures  statistical manifolds  Hessian manifolds  Hessian sectional curvature  scalar curvature  Ricci curvature  Minkowski plane  Minkowskian length  Minkowskian angle  Minkowskian pseudoangle  L2harmonic forms  Hodge–Laplacian  manifold with singularity  L2Stokes theorem  capacity  kth generalized Tanaka–Webster connection  nonflat complex space form  real hypersurface  lie derivative  shape operator  conical surface  developable surface  generalized 1type Gauss map  cylindrical hypersurface  inextensible flow  lightlike surface  ruled surface  Darboux frame  CBochner tensor  generalized normalized ?Casorati curvature  Sasakian manifold  slant  invariant  antiinvariant  transSasakian 3manifold  Reeb flow symmetry  Ricci operator  Sasakian statistical manifold  conjugate connection  Casorati curvature  framed rectifying curves  singular points  framed helices  centrodes  circular rectifying curves  statistical structure  affine hypersurface  affine sphere  conjugate symmetric statistical structure  sectional ?curvature  complete connection  symplectic curves  circular helices  symplectic curvatures  Frenet frame
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Engineering mathematics is a branch of applied mathematics where mathematical methods and techniques are implemented for solving problems related to the engineering and industry. It also represents a multidisciplinary approach where theoretical and practical aspects are deeply merged with the aim at obtaining optimized solutions. In line with that, the present Special Issue, 'Engineering Mathematics in Ship Design', is focused, in particular, with the use of this sort of engineering science in the design of ships and vessels. Articles are welcome when applied science or computation science in ship design represent the core of the discussion.
roll motion  roll damping  CFD  harmonic excitation  singlestepped planing hulls  symmetric 2D + T theory  hydrodynamic forces  towing tank tests  piezoelectric sensor  damaged sensor  impact traction  LeadZirconiumTitanium (PZT)  fracture mechanics  marine industry  water entry  hydroelasticity  cavitation  FSI  SPH  slamming  plate  stiffeners  constructal design  finite element method  deflection  numerical simulation  stiffened plate  constitutive model  finite element  fluidstructure interaction  ship design  stateoftheart  fixed pitch propeller  controllable pitch propeller  lowspeed Diesel engine  selection  optimisation  modelling  coanda effect  turbulence model  computational fluid dynamic  finite volume method  H.O.M.E.R. nozzle  numerical model  SHIPMOVE  MMG Model  external forces  marine transport  environmental management system  balanced scorecard  ISO 14001  ISO 9126  ISO 14598  AHP method  MCDM method  n/a
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In 1978, Fred Hoyle proposed that interstellar comets carrying several viruses landed on Earth as part of the panspermia hypotheses. With respect to life, the origin of homochirality on Earth has been the greatest mystery because life cannot exist without molecular asymmetry. Many scientists have proposed several possible hypotheses to answer this longstanding LD question. Previously, Martin Gardner raised the question about mirror symmetry and broken mirror symmetry in terms of the homochirality question in his monographs (1964 and 1990). Possible scenarios for the LD issue can be categorized into (i) Earth and exoterrestrial origins, (ii) bychance and necessity mechanisms, and (iii) mirrorsymmetrical and nonmirrorsymmetrical forces as physical and chemical origins. These scenarios should involve further great amplification mechanisms, enabling a pure L or Dworld.
chirogenesis  enantiomorphism  nepheline  magmatic flow  etch figures  origin of life  biological homochirality  deracemization  superhighvelocity impact  plasma reactor  absolute asymmetric synthesis  amino acids  origin of life  amino acid handedness  nucleus–molecular coupling  chirality  circularly polarized luminescence  circular dichroism  symmetry breaking  parity violation  weak neutral current  tunneling  Z0 boson  homochirality  precision measurement  homochirality  circularly polarized light  asymmetric reaction  polymer  ?strand  hidden chirality  twofold helix  multipoint approximation  tiltchirality  high dimensional chirality  spin polarized electrons  homochirality  magnetism  prebiotic  environmental chirality  C1 and C2symmetric catalysts  chiral field (memory)  racemic field  Viedma ripening effect  Wallach’s rule  heat capacity  metalorganic framework  triethylenediamine (DABCO) molecules  racemate  Salam hypothesis  homochirality  parity violation  neutrinos  gravitation  enantiomer selfdisproportionation  SDE  achiral stationary phase  homochiral and heterochiral aggregates  chiral separation  chirality  genesis of life chirality  asymmetric autocatalysis  homochirality  chirality  asymmetric synthesis  Soai reaction  biological homochirality  enantioselective reaction  autocatalysis  origin of life  replicators  bioorganic homochirality  circularly polarized photon  spinpolarized lepton  parity violation in the weak interaction  symmetry breaking  assemblies  supramolecular chirality  homochirality  selfassembly  vortex  lipid  supramolecular assembly  symmetry breaking  homochirality
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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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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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