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Some of the most beautiful studies in Mathematics are related to Symmetry and Geometry. For this reason, we select here some contributions about such aspects and Discrete Geometry. As we know, Symmetry in a system means invariance of its elements under conditions of transformations. When we consider network structures, symmetry means invariance of adjacency of nodes under the permutations of node set. The graph isomorphism is an equivalence relation on the set of graphs. Therefore, it partitions the class of all graphs into equivalence classes. The underlying idea of isomorphism is that some objects have the same structure if we omit the individual character of their components. A set of graphs isomorphic to each other is denominated as an isomorphism class of graphs. The automorphism of a graph will be an isomorphism from G onto itself. The family of all automorphisms of a graph G is a permutation group.
strongly regular graph  automorphism group  orbit matrix  binary polyhedral group  icosahedron  dodecahedron  600cell  Electric multiple unit trains  highlevel maintenance planning  time window  0–1 programming model  particle swarm algorithm  fixed point  splitquaternion  quadratic polynomial  splitoctonion  neutrosophic set  neutrosophic rough set  pessimistic (optimistic) multigranulation neutrosophic approximation operators  complete lattice  rough set  matroid  operator  attribute reduction  graded rough sets  rough intuitionistic fuzzy sets  dominance relation  logical conjunction operation  logical disjunction operation  multigranulation  planar point set  convex polygon  disjoint holes  fuzzy logic  pseudoBCI algebra  quasimaximal element  KGunion  quasialternating BCKalgebra  quality function deployment  engineering characteristics  group decision making  2tuple  metro station  emergency routes  graph partitioning  graph clustering  invariant measures  partition comparison  finite automorphism groups  graph automorphisms  Fuzzy sets  ring  normed space  fuzzy normed ring  fuzzy normed ideal  fuzzy implication  quantum Balgebra  qfilter  quotient algebra  basic implication algebra  Detour–Harary index  maximum  unicyclic  bicyclic  cacti  threeway decisions  intuitionistic fuzzy sets  multigranulation rough intuitionistic fuzzy sets  granularity importance degree  complexity  Chebyshev polynomials  gear graph  pyramid graphs  edge detection  Laplacian operation  regularization  parameter selection  performance evaluation  aggregation operator  triangular norm  ?convex set  atombond connectivity index  geometric arithmetic index  line graph  generalized bridge molecular graph  graceful labeling  edge graceful labeling  edge even graceful labeling  polar grid graph  graph  good drawing  crossing number  join product  cyclic permutation  nonlinear  synchronized  linear discrete  chaotic system  algorithm  generalized permanental polynomial  coefficient  copermanental  isoperimetric number  random graph  intersection graph  social network  Abel–Grassmann’s groupoid (AGgroupoid)  Abel–Grassmann’s group (AGgroup)  involution AGgroup  commutative group  filter  graceful labeling  edge even graceful labeling  cylinder grid graph  selective maintenance  multistate system  human reliability  optimization  genetic algorithm  hypernearring  multitransformation  embedding  distance matrix (spectrum)  distance signlees Laplacian matrix (spectrum)  (generalized) distance matrix  spectral radius  transmission regular graph  graph  good drawing  crossing number  join product  cyclic permutation  cyclic associative groupoid (CAgroupoid)  cancellative  variant CAgroupoids  decomposition theorem  construction methods
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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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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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