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

• Main Authors: Ali, Mumtaz, Smarandache, Florentin, Zhang, Xiaohong
• Format: eBook
• Language: English
• Published: MDPI - Multidisciplinary Digital Publishing Institute 2019
• Subjects: (commutative) ideal; 2-tuple linguistic neutrosophic sets (2TLNSs); 2ingle-valued neutrosophic set; 2TLNNs TODIM method; action learning; aggregation operator; aggregation operators; algorithm; analytic hierarchy process (AHP); analytic network process; and second neutro-isomorphism theorem; applications of neutrosophic cubic graphs; BCI-algebra; BE-algebra; big data; bipolar fuzzy set; Bol-Moufang; Bonferroni mean; Book Industry Communication; Choquet integral; CI-algebra; classical group of neutrosophic triplets; cloud model; clustering; clustering algorithm; commutative generalized neutrosophic ideal; complement; complex neutrosophic graph; complex neutrosophic set; computability; computation; construction project; cosine measure; criterion functions; data mining; de-neutrosophication methods; decision making; decision-making algorithms; decision-making trial and evaluation laboratory (DEMATEL); defuzzification; dependent degree; dermoscopy; Dice measure; DSmT; dual aggregation operators; dual domains; emerging technology commercialization; expert set; exponential operational laws of interval neutrosophic numbers; extended ELECTRE III; extended TOPSIS method; fault diagnosis; Fenyves identities; filter; first neutro-isomorphism theorem; fixed point theory (FPT); forecasting; fundamental neutro-homomorphism theorem; fuzzy graph; fuzzy measure; fuzzy time series; G-metric; generalized aggregation operators; generalized De Morgan algebra; generalized group; generalized neutrosophic ideal; generalized neutrosophic set; generalized partitioned Bonferroni mean operator; grasp type; grasping configurations; group; Hamming distance; hesitant fuzzy set; homomorphism theorem; image segmentation; inclusion relation; integrated weight; interdependency of criteria; intersection; interval neutrosophic numbers (INNs); interval neutrosophic set (INS); interval neutrosophic sets; interval neutrosophic weighted exponential aggregation (INWEA) operator; interval number; interval valued neutrosophic support soft sets; interval-valued neutrosophic set; Jaccard measure; LA-semihypergroups; linear and non-linear neutrosophic number; linguistic neutrosophic sets; LNGPBM operator; LNGWPBM operator; logic; loop; Maclaurin symmetric mean; MADM; Mathematics & science; matrix representation; maximizing deviation; MCGDM problems; medical diagnosis; membership; MGNRS; MM operator; Muirhead mean; multi-attribute decision making; multi-attribute decision-making (MADM); multi-attribute group decision-making (MAGDM); multi-criteria decision-making; multi-criteria decision-making (MCDM) techniques; multi-criteria group decision making; multi-criteria group decision-making (MCGDM); multi-valued neutrosophic set; multicriteria decision-making; multigranulation neutrosophic rough set (MNRS); multiple attribute decision making (MADM); multiple attribute decision making problem; multiple attribute decision-making; multiple attribute group decision-making (MAGDM); NC power dual MM operator (NCPDMM) operator; NCPMM operator; neutosophic extended triplet subgroups; neutro-automorphism; neutro-epimorphism; neutro-homomorphism; neutro-monomorphism; neutrosophic association rule; neutrosophic big data; neutrosophic bipolar fuzzy set; neutrosophic bipolar fuzzy weighted averaging operator; neutrosophic c-means clustering; neutrosophic classification; neutrosophic clustering; neutrosophic computation; neutrosophic cubic graphs; neutrosophic cubic set; Neutrosophic cubic sets; neutrosophic duplets; neutrosophic G-metric; neutrosophic logic; neutrosophic multiset (NM); neutrosophic rough set; neutrosophic set; neutrosophic set theory; neutrosophic sets; neutrosophic sets (NSs); neutrosophic soft set; neutrosophic triplet; neutrosophic triplet cosets; neutrosophic triplet group; neutrosophic triplet group (NTG); neutrosophic triplet groups; neutrosophic triplet normal subgroups; neutrosophic triplet quotient groups; neutrosophic triplet set; neutrosophic triplet set (NTS); neutrosophy; normal distribution; NT-subgroup; oracle computation; oracle Turing machines; PA operator; partial metric spaces (PMS); photovoltaic plan; possibility degree; potential evaluation; power aggregation operator; power aggregation operators; power operator; prioritized operator; probabilistic rough sets over two universes; probabilistic single-valued (interval) neutrosophic hesitant fuzzy set; pseudo primitive elements; pseudo-BCI algebra; Q-linguistic neutrosophic variable set; Q-neutrosophic; Q1-390; QA1-939; quantum computation; quasi neutrosophic loops; quasi neutrosophic triplet group; quasi neutrosophic triplet loop; quasigroup; recursive enumerability; region growing; robotic dexterous hands; S-semigroup of neutrosophic triplets; school administrator; semi-neutrosophic triplets; semigroup; shopping mall; similarity measure; similarity measures; simplified neutrosophic linguistic numbers; simplified neutrosophic sets (SNSs); simplified neutrosophic weighted averaging operator; single valued neutrosophic multiset (SVNM); single valued neutrosophic set (SVNS); single valued trapezoidal neutrosophic number; single-valued neutrosophic multisets; skin cancer; soft set; soft sets; support soft sets; sustainable supplier selection problems (SSSPs); SVM; SWOT analysis; symmetry; Technique for Order Preference by Similarity to an Ideal Solution (TOPSIS); TFNNs VIKOR method; three-way decisions; TODIM model; TOPSIS; totally dependent-neutrosophic set; totally dependent-neutrosophic soft set; triangular fuzzy neutrosophic sets (TFNSs); two universes; two-factor fuzzy logical relationship; typhoon disaster evaluation; vector similarity measure; VIKOR model; weak commutative neutrosophic triplet group
• ISBN: 9783038973843; 303897384X
• DOI: 10.3390/books978-3-03897-385-0

Neutrosophy (1995) is a new branch of philosophy that studies triads of the form ( , , ), where is an entity {i.e. element, concept, idea, theory, logical proposition, etc.}, is the opposite of , while is the neutral (or indeterminate) between them, i.e., neither nor .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.