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Algebraic Structures of Neutrosophic Triplets, Neutrosophic Duplets, or Neutrosophic Multisets
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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.
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Keywords
- (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
- 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
- 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
- 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 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
- 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)
- 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
- 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
Links
DOI: 10.3390/books978-3-03897-385-0Editions