TY - BOOK ID - 133881019 TI - Algebraic Structures of Neutrosophic Triplets, Neutrosophic Duplets, or Neutrosophic Multisets. AU - Ali, Muhammad Mumtaz AU - Smarandache, Florentin AU - Zhang, Xiaohong PY - 2019 PB - MDPI - Multidisciplinary Digital Publishing Institute, DB - UniCat KW - similarity measure KW - generalized partitioned Bonferroni mean operator KW - normal distribution KW - school administrator KW - complex neutrosophic set KW - expert set KW - neutrosophic classification KW - multi-attribute decision-making (MADM) KW - multi-criteria decision-making (MCDM) techniques KW - criterion functions KW - matrix representation KW - possibility degree KW - quantum computation KW - typhoon disaster evaluation KW - NT-subgroup KW - generalized neutrosophic ideal KW - three-way decisions KW - decision-making KW - G-metric KW - multiple attribute group decision-making (MAGDM) KW - SVM KW - semi-neutrosophic triplets KW - LA-semihypergroups KW - power operator KW - fuzzy graph KW - neutrosophic cubic graphs KW - LNGPBM operator KW - neutrosophic c-means clustering KW - (commutative) ideal KW - region growing KW - clustering algorithm KW - Neutrosophic cubic sets KW - forecasting KW - vector similarity measure KW - totally dependent-neutrosophic soft set KW - Fenyves identities KW - TODIM model KW - similarity measures KW - CI-algebra KW - Dice measure KW - de-neutrosophication methods KW - DSmT KW - semigroup KW - VIKOR model KW - multigranulation neutrosophic rough set (MNRS) KW - simplified neutrosophic linguistic numbers KW - Technique for Order Preference by Similarity to an Ideal Solution (TOPSIS) KW - multi-criteria group decision making KW - multi-attribute group decision-making (MAGDM) KW - exponential operational laws of interval neutrosophic numbers KW - simplified neutrosophic weighted averaging operator KW - neutro-epimorphism KW - Choquet integral KW - fixed point theory (FPT) KW - computability KW - neutrosophic triplet set KW - interval-valued neutrosophic set KW - simplified neutrosophic sets (SNSs) KW - totally dependent-neutrosophic set KW - Maclaurin symmetric mean KW - recursive enumerability KW - loop KW - photovoltaic plan KW - intersection KW - neutrosophic bipolar fuzzy set KW - big data KW - inclusion relation KW - dual aggregation operators KW - Hamming distance KW - neutro-automorphism KW - neutrosophic set theory KW - multiple attribute decision-making KW - multicriteria decision-making KW - pseudo primitive elements KW - medical diagnosis KW - neutrosophic G-metric KW - bipolar fuzzy set KW - NC power dual MM operator (NCPDMM) operator KW - neutrosophic sets (NSs) KW - emerging technology commercialization KW - neutrosophic triplet groups KW - probabilistic rough sets over two universes KW - neutrosophic triplet set (NTS) KW - neutrosophic triplet cosets KW - MM operator KW - TOPSIS KW - cloud model KW - extended ELECTRE III KW - extended TOPSIS method KW - 2ingle-valued neutrosophic set KW - dual domains KW - probabilistic single-valued (interval) neutrosophic hesitant fuzzy set KW - Jaccard measure KW - data mining KW - BE-algebra KW - neutrosophic soft set KW - aggregation operators KW - image segmentation KW - multiple attribute decision making (MADM) KW - neutrosophic duplets KW - fundamental neutro-homomorphism theorem KW - neutro-homomorphism KW - power aggregation operator KW - linear and non-linear neutrosophic number KW - multi-attribute decision making KW - first neutro-isomorphism theorem KW - MCGDM problems KW - neutrosophic bipolar fuzzy weighted averaging operator KW - Bonferroni mean KW - analytic hierarchy process (AHP) KW - quasigroup KW - action learning KW - weak commutative neutrosophic triplet group KW - generalized aggregation operators KW - single valued neutrosophic multiset (SVNM) KW - sustainable supplier selection problems (SSSPs) KW - LNGWPBM operator KW - skin cancer KW - oracle computation KW - fault diagnosis KW - interval valued neutrosophic support soft sets KW - neutrosophic triplet normal subgroups KW - soft set KW - multi-criteria decision-making KW - neutrosophic triplet KW - generalized group KW - neutrosophic multiset (NM) KW - two universes KW - algorithm KW - multi-attribute decision making (MADM) KW - PA operator KW - BCI-algebra KW - neutrosophic triplet group (NTG) KW - single valued trapezoidal neutrosophic number KW - quasi neutrosophic triplet loop KW - neutrosophy KW - complex neutrosophic graph KW - S-semigroup of neutrosophic triplets KW - and second neutro-isomorphism theorem KW - MADM KW - dermoscopy KW - linguistic neutrosophic sets KW - defuzzification KW - construction project KW - potential evaluation KW - neutrosophic big data KW - decision-making algorithms KW - neutosophic extended triplet subgroups KW - applications of neutrosophic cubic graphs KW - fuzzy time series KW - TFNNs VIKOR method KW - two-factor fuzzy logical relationship KW - oracle Turing machines KW - grasp type KW - interval neutrosophic sets KW - multi-criteria group decision-making KW - interval neutrosophic weighted exponential aggregation (INWEA) operator KW - power aggregation operators KW - neutrosophic triplet group KW - MGNRS KW - 2-tuple linguistic neutrosophic sets (2TLNSs) KW - computation KW - filter KW - multi-valued neutrosophic set KW - integrated weight KW - Bol-Moufang KW - prioritized operator KW - interval number KW - logic KW - pseudo-BCI algebra KW - interval neutrosophic set (INS) KW - neutrosophic rough set KW - soft sets KW - Q-neutrosophic KW - Linguistic neutrosophic sets KW - fuzzy measure KW - homomorphism theorem KW - commutative generalized neutrosophic ideal KW - neutrosophic association rule KW - shopping mall KW - dependent degree KW - Q-linguistic neutrosophic variable set KW - quasi neutrosophic loops KW - symmetry KW - neutrosophic sets KW - neutrosophic logic KW - neutrosophic cubic set KW - complement KW - robotic dexterous hands KW - neutro-monomorphism KW - group KW - analytic network process KW - Muirhead mean KW - maximizing deviation KW - classical group of neutrosophic triplets KW - neutrosophic triplet quotient groups KW - generalized neutrosophic set KW - multi-criteria group decision-making (MCGDM) KW - support soft sets KW - decision making KW - generalized De Morgan algebra KW - multiple attribute group decision making (MAGDM) KW - single-valued neutrosophic multisets KW - 2TLNNs TODIM method KW - membership KW - grasping configurations KW - single valued neutrosophic set (SVNS) KW - multiple attribute decision making problem KW - SWOT analysis KW - neutrosophic clustering KW - hesitant fuzzy set KW - interval neutrosophic numbers (INNs) KW - quasi neutrosophic triplet group KW - triangular fuzzy neutrosophic sets (TFNSs) KW - interdependency of criteria KW - aggregation operator KW - cosine measure KW - neutrosophic set KW - neutrosophic computation KW - decision-making trial and evaluation laboratory (DEMATEL) KW - partial metric spaces (PMS) KW - NCPMM operator KW - clustering UR - https://www.unicat.be/uniCat?func=search&query=sysid:133881019 AB - 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. ER -