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

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 (o...

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Bibliographic Details
Main Author:	Ali, Mumtaz (auth)
Other Authors:	Smarandache, Florentin (auth), Zhang, Xiaohong (auth)
Format:	Book Chapter
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 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
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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.
Physical Description:	1 electronic resource (478 p.)
ISBN:	books978-3-03897-385-0 9783038973843
Access:	Open Access

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

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