Reprint

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

## Volume 1

Edited by

April 2019

478 pages

- ISBN978-3-03897-384-3 (Paperback)
- ISBN978-3-03897-385-0 (PDF)

This is a Reprint of the Special Issue Algebraic Structures of Neutrosophic Triplets, Neutrosophic Duplets, or Neutrosophic Multisets that was published in

This Reprint is part of the book set Algebraic Structures of Neutrosophic Triplets, Neutrosophic Duplets, or Neutrosophic Multisets.

Biology & Life Sciences

Chemistry & Materials Science

Computer Science & Mathematics

Physical Sciences

Summary

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.

Format

- Paperback

License and Copyright

© 2019 by the authors; CC BY-NC-ND license

Keywords

generalized aggregation operators; interval neutrosophic set (INS); multi-attribute decision making (MADM); Choquet integral; fuzzy measure; clustering algorithm; neutrosophic association rule; data mining; neutrosophic sets; big data; analytic hierarchy process (AHP); SWOT analysis; multi-criteria decision-making (MCDM) techniques; neutrosophic set theory; neutrosophic clustering; image segmentation; neutrosophic c-means 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; decision-making trial and evaluation laboratory (DEMATEL); interval-valued neutrosophic set; extended ELECTRE III; symmetry; single valued neutrosophic set (SVNS); neutrosophic multiset (NM); single valued neutrosophic multiset (SVNM); cosine measure; multiple attribute decision-making;

*LNGPBM*operator;*LNGWPBM*operator; Linguistic neutrosophic sets; generalized partitioned Bonferroni mean operator; multiple attribute group decision-making (MAGDM); pseudo-BCI algebra; hesitant fuzzy set; neutrosophic set; filter; action learning; school administrator; SVM; neutrosophic classification; neutrosophic set; soft set; totally dependent-neutrosophic set; totally dependent-neutrosophic soft set; generalized De Morgan algebra; complex neutrosophic set; complex neutrosophic graph; fuzzy graph; matrix representation; neutrosophic triplet groups; semigroup; semi-neutrosophic triplets; classical group of neutrosophic triplets; S-semigroup 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; multi-criteria decision-making; neutrosophy; DSmT; decision-making 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; single-valued neutrosophic multisets; medical diagnosis; probabilistic rough sets over two universes; three-way decisions; similarity measures; neutrosophic cubic set; decision-making; 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; 2ingle-valued neutrosophic set; Technique for Order Preference by Similarity to an Ideal Solution (TOPSIS); integrated weight; maximizing deviation; multi-attribute decision-making (MADM); neutrosophic triplet set (NTS); partial metric spaces (PMS); fixed point theory (FPT); neutrosophic triplet; quasi neutrosophic triplet loop; quasi neutrosophic triplet group; BE-algebra; CI-algebra; fuzzy time series; forecasting; two-factor fuzzy logical relationship; multi-valued neutrosophic set; Hamming distance; neutrosophic set; prioritized operator; Muirhead mean; multicriteria decision-making; aggregation operators; dual aggregation operators; neutrosophic triplet group (NTG); NT-subgroup; homomorphism theorem; weak commutative neutrosophic triplet group; neutrosophic rough set; MGNRS; dual domains; inclusion relation; decision-making; neutro-monomorphism; neutro-epimorphism; neutro-automorphism; fundamental neutro-homomorphism theorem; first neutro-isomorphism theorem; and second neutro-isomorphism theorem; linear and non-linear neutrosophic number; de-neutrosophication 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; multi-criteria group decision-making; power aggregation operator; extended TOPSIS method; probabilistic single-valued (interval) neutrosophic hesitant fuzzy set; multi-attribute decision making; aggregation operator; quasigroup; loop; BCI-algebra; Bol-Moufang; quasi neutrosophic loops; Fenyves identities; G-metric; neutrosophic G-metric; 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; multi-attribute decision making (MADM); multiple attribute group decision making (MAGDM); 2-tuple 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; Q-linguistic neutrosophic variable set; vector similarity measure; cosine measure; Dice measure; Jaccard measure; decision making; inclusion relation; neutrosophic rough set; multi-attribute group decision-making (MAGDM); multigranulation neutrosophic rough set (MNRS); two universes; single valued trapezoidal neutrosophic number; multi-criteria group decision making; possibility degree; power aggregation operators; LA-semihypergroups; neutrosophic triplet set; neutro-homomorphism; algorithm; decision making; expert set; generalized neutrosophic set; neutrosophic sets; Q-neutrosophic; soft sets; simplified neutrosophic sets (SNSs); interval number; dependent degree; multi-criteria group decision-making (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