11638nam 2202989z- 450 991034684580332120210211(CKB)4920000000095182(oapen)https://directory.doabooks.org/handle/20.500.12854/40632(oapen)doab40632(EXLCZ)99492000000009518220202102d2019 |y 0engurmn|---annantxtrdacontentcrdamediacrrdacarrierAlgebraic Structures of Neutrosophic Triplets, Neutrosophic Duplets, or Neutrosophic MultisetsMDPI - Multidisciplinary Digital Publishing Institute20191 online resource (478 p.)3-03897-384-X Neutrosophy (1995) is a new branch of philosophy that studies triads of the form (<A>, <neutA>, <antiA>), where <A> is an entity {i.e. element, concept, idea, theory, logical proposition, etc.}, <antiA> is the opposite of <A>, while <neutA> is the neutral (or indeterminate) between them, i.e., neither <A> nor <antiA>.Based on neutrosophy, the neutrosophic triplets were founded, which have a similar form (x, neut(x), anti(x)), that satisfy several axioms, for each element x in a given set.This collective book presents original research papers by many neutrosophic researchers from around the world, that report on the state-of-the-art and recent advancements of neutrosophic triplets, neutrosophic duplets, neutrosophic multisets and their algebraic structures - that have been defined recently in 2016 but have gained interest from world researchers. Connections between classical algebraic structures and neutrosophic triplet / duplet / multiset structures are also studied. And numerous neutrosophic applications in various fields, such as: multi-criteria decision making, image segmentation, medical diagnosis, fault diagnosis, clustering data, neutrosophic probability, human resource management, strategic planning, forecasting model, multi-granulation, supplier selection problems, typhoon disaster evaluation, skin lesson detection, mining algorithm for big data analysis, etc.(commutative) ideal2-tuple linguistic neutrosophic sets (2TLNSs)2ingle-valued neutrosophic set2TLNNs TODIM methodaction learningaggregation operatoraggregation operatorsalgorithmanalytic hierarchy process (AHP)analytic network processand second neutro-isomorphism theoremapplications of neutrosophic cubic graphsBCI-algebraBE-algebrabig databipolar fuzzy setBol-MoufangBonferroni meanChoquet integralCI-algebraclassical group of neutrosophic tripletscloud modelclusteringclustering algorithmcommutative generalized neutrosophic idealcomplementcomplex neutrosophic graphcomplex neutrosophic setcomputabilitycomputationconstruction projectcosine measurecriterion functionsdata miningde-neutrosophication methodsdecision makingdecision-makingdecision-making algorithmsdecision-making trial and evaluation laboratory (DEMATEL)defuzzificationdependent degreedermoscopyDice measureDSmTdual aggregation operatorsdual domainsemerging technology commercializationexpert setexponential operational laws of interval neutrosophic numbersextended ELECTRE IIIextended TOPSIS methodfault diagnosisFenyves identitiesfilterfirst neutro-isomorphism theoremfixed point theory (FPT)forecastingfundamental neutro-homomorphism theoremfuzzy graphfuzzy measurefuzzy time seriesG-metricgeneralized aggregation operatorsgeneralized De Morgan algebrageneralized groupgeneralized neutrosophic idealgeneralized neutrosophic setgeneralized partitioned Bonferroni mean operatorgrasp typegrasping configurationsgroupHamming distancehesitant fuzzy sethomomorphism theoremimage segmentationinclusion relationintegrated weightinterdependency of criteriaintersectioninterval neutrosophic numbers (INNs)interval neutrosophic set (INS)interval neutrosophic setsinterval neutrosophic weighted exponential aggregation (INWEA) operatorinterval numberinterval valued neutrosophic support soft setsinterval-valued neutrosophic setJaccard measureLA-semihypergroupslinear and non-linear neutrosophic numberlinguistic neutrosophic setsLinguistic neutrosophic setsLNGPBM operatorLNGWPBM operatorlogicloopMaclaurin symmetric meanMADMmatrix representationmaximizing deviationMCGDM problemsmedical diagnosismembershipMGNRSMM operatorMuirhead meanmulti-attribute decision makingmulti-attribute decision making (MADM)multi-attribute decision-making (MADM)multi-attribute group decision-making (MAGDM)multi-criteria decision-makingmulti-criteria decision-making (MCDM) techniquesmulti-criteria group decision makingmulti-criteria group decision-makingmulti-criteria group decision-making (MCGDM)multi-valued neutrosophic setmulticriteria decision-makingmultigranulation neutrosophic rough set (MNRS)multiple attribute decision making (MADM)multiple attribute decision making problemmultiple attribute decision-makingmultiple attribute group decision making (MAGDM)multiple attribute group decision-making (MAGDM)NC power dual MM operator (NCPDMM) operatorNCPMM operatorneutosophic extended triplet subgroupsneutro-automorphismneutro-epimorphismneutro-homomorphismneutro-monomorphismneutrosophic association ruleneutrosophic big dataneutrosophic bipolar fuzzy setneutrosophic bipolar fuzzy weighted averaging operatorneutrosophic c-means clusteringneutrosophic classificationneutrosophic clusteringneutrosophic computationneutrosophic cubic graphsneutrosophic cubic setNeutrosophic cubic setsneutrosophic dupletsneutrosophic G-metricneutrosophic logicneutrosophic multiset (NM)neutrosophic rough setneutrosophic setneutrosophic set theoryneutrosophic setsneutrosophic sets (NSs)neutrosophic soft setneutrosophic tripletneutrosophic triplet cosetsneutrosophic triplet groupneutrosophic triplet group (NTG)neutrosophic triplet groupsneutrosophic triplet normal subgroupsneutrosophic triplet quotient groupsneutrosophic triplet setneutrosophic triplet set (NTS)neutrosophynormal distributionNT-subgrouporacle computationoracle Turing machinesPA operatorpartial metric spaces (PMS)photovoltaic planpossibility degreepotential evaluationpower aggregation operatorpower aggregation operatorspower operatorprioritized operatorprobabilistic rough sets over two universesprobabilistic single-valued (interval) neutrosophic hesitant fuzzy setpseudo primitive elementspseudo-BCI algebraQ-linguistic neutrosophic variable setQ-neutrosophicquantum computationquasi neutrosophic loopsquasi neutrosophic triplet groupquasi neutrosophic triplet loopquasigrouprecursive enumerabilityregion growingrobotic dexterous handsS-semigroup of neutrosophic tripletsschool administratorsemi-neutrosophic tripletssemigroupshopping mallsimilarity measuresimilarity measuressimplified neutrosophic linguistic numberssimplified neutrosophic sets (SNSs)simplified neutrosophic weighted averaging operatorsingle valued neutrosophic multiset (SVNM)single valued neutrosophic set (SVNS)single valued trapezoidal neutrosophic numbersingle-valued neutrosophic multisetsskin cancersoft setsoft setssupport soft setssustainable supplier selection problems (SSSPs)SVMSWOT analysissymmetryTechnique for Order Preference by Similarity to an Ideal Solution (TOPSIS)TFNNs VIKOR methodthree-way decisionsTODIM modelTOPSIStotally dependent-neutrosophic settotally dependent-neutrosophic soft settriangular fuzzy neutrosophic sets (TFNSs)two universestwo-factor fuzzy logical relationshiptyphoon disaster evaluationvector similarity measureVIKOR modelweak commutative neutrosophic triplet groupAli Muhammad Mumtaz1431970Smarandache FlorentinauthZhang XiaohongauthBOOK9910346845803321Algebraic Structures of Neutrosophic Triplets, Neutrosophic Duplets, or Neutrosophic Multisets3575046UNINA