Algebraic Structures of Neutrosophic Triplets, Neutrosophic Duplets, or Neutrosophic Multisets

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

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.