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Interactions between Group Theory, Symmetry and Cryptology

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ISBN: 9783039288021 / 9783039288038 Year: Pages: 164 DOI: 10.3390/books978-3-03928-803-8 Language: eng
Publisher: MDPI - Multidisciplinary Digital Publishing Institute
Subject: Science (General) --- Mathematics
Added to DOAB on : 2020-06-09 16:38:57
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Cryptography lies at the heart of most technologies deployed today for secure communications. At the same time, mathematics lies at the heart of cryptography, as cryptographic constructions are based on algebraic scenarios ruled by group or number theoretical laws. Understanding the involved algebraic structures is, thus, essential to design robust cryptographic schemes. This Special Issue is concerned with the interplay between group theory, symmetry and cryptography. The book highlights four exciting areas of research in which these fields intertwine: post-quantum cryptography, coding theory, computational group theory and symmetric cryptography. The articles presented demonstrate the relevance of rigorously analyzing the computational hardness of the mathematical problems used as a base for cryptographic constructions. For instance, decoding problems related to algebraic codes and rewriting problems in non-abelian groups are explored with cryptographic applications in mind. New results on the algebraic properties or symmetric cryptographic tools are also presented, moving ahead in the understanding of their security properties. In addition, post-quantum constructions for digital signatures and key exchange are explored in this Special Issue, exemplifying how (and how not) group theory may be used for developing robust cryptographic tools to withstand quantum attacks.

Topological Groups. Advances, Surveys, and Open Questions

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ISBN: 9783038976448 Year: Pages: 160 DOI: 10.3390/books978-3-03897-645-5 Language: English
Publisher: MDPI - Multidisciplinary Digital Publishing Institute
Subject: Science (General) --- Mathematics
Added to DOAB on : 2019-03-08 11:42:05
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Following the tremendous reception of our first volume on topological groups called ""Topological Groups: Yesterday, Today, and Tomorrow"", we now present our second volume. Like the first volume, this collection contains articles by some of the best scholars in the world on topological groups. A feature of the first volume was surveys, and we continue that tradition in this volume with three new surveys. These surveys are of interest not only to the expert but also to those who are less experienced. Particularly exciting to active researchers, especially young researchers, is the inclusion of over three dozen open questions. This volume consists of 11 papers containing many new and interesting results and examples across the spectrum of topological group theory and related topics. Well-known researchers who contributed to this volume include Taras Banakh, Michael Megrelishvili, Sidney A. Morris, Saharon Shelah, George A. Willis, O'lga V. Sipacheva, and Stephen Wagner.

Symmetry in Classical and Fuzzy Algebraic Hypercompositional Structures

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ISBN: 9783039287086 / 9783039287093 Year: Pages: 208 DOI: 10.3390/books978-3-03928-709-3 Language: eng
Publisher: MDPI - Multidisciplinary Digital Publishing Institute
Subject: Science (General) --- Mathematics
Added to DOAB on : 2020-06-09 16:38:57
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This book is a collection of 12 innovative research papers in the field of hypercompositional algebra, 7 of them being more theoretically oriented, with the other 5 presenting strong applicative aspects in engineering, control theory, artificial intelligence, and graph theory. Hypercompositional algebra is now a well-established branch of abstract algebra dealing with structures endowed with multi-valued operations, also called hyperoperations, having a set as the result of the interrelation between two elements of the support set. The theoretical papers in this book are principally related to three main topics: (semi)hypergroups, hyperfields, and BCK-algebra. Heidari and Cristea present a natural generalization of breakable semigroups, defining the breakable semihypergroups where every non-empty subset is a subsemihypergroup. Using the fundamental relation ? on a hypergroup, some new properties of the

New types of Neutrosophic Set/Logic/Probability, Neutrosophic Over-/Under-/Off-Set, Neutrosophic Refined Set, and their Extension to Plithogenic Set/Logic/Probability, with Applications

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ISBN: 9783039219384 9783039219391 Year: Pages: 714 DOI: 10.3390/books978-3-03921-939-1 Language: English
Publisher: MDPI - Multidisciplinary Digital Publishing Institute
Subject: Technology (General) --- General and Civil Engineering
Added to DOAB on : 2019-12-09 16:39:37
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This book contains 37 papers by 73 renowned experts from 13 countries around the world, on following topics: neutrosophic set; neutrosophic rings; neutrosophic quadruple rings; idempotents; neutrosophic extended triplet group; hypergroup; semihypergroup; neutrosophic extended triplet group; neutrosophic extended triplet semihypergroup and hypergroup; neutrosophic offset; uninorm; neutrosophic offuninorm and offnorm; neutrosophic offconorm; implicator; prospector; n-person cooperative game; ordinary single-valued neutrosophic (co)topology; ordinary single-valued neutrosophic subspace; ?-level; ordinary single-valued neutrosophic neighborhood system; ordinary single-valued neutrosophic base and subbase; fuzzy numbers; neutrosophic numbers; neutrosophic symmetric scenarios; performance indicators; financial assets; neutrosophic extended triplet group; neutrosophic quadruple numbers; refined neutrosophic numbers; refined neutrosophic quadruple numbers; multigranulation neutrosophic rough set; nondual; two universes; multiattribute group decision making; nonstandard analysis; extended nonstandard analysis; monad; binad; left monad closed to the right; right monad closed to the left; pierced binad; unpierced binad; nonstandard neutrosophic mobinad set; neutrosophic topology; nonstandard neutrosophic topology; visual tracking; neutrosophic weight; objectness; weighted multiple instance learning; neutrosophic triangular norms; residuated lattices; representable neutrosophic t-norms; De Morgan neutrosophic triples; neutrosophic residual implications; infinitely ?-distributive; probabilistic neutrosophic hesitant fuzzy set; decision-making; Choquet integral; e-marketing; Internet of Things; neutrosophic set; multicriteria decision making techniques; uncertainty modeling; neutrosophic goal programming approach; shale gas water management system.

Keywords

single-valued neutrosophic soft number and its operations --- SVN soft weighted arithmetic averaging operator --- SVN soft weighted geometric averaging operator --- decision-making --- optimization solution --- sampling plan --- producer’s risk’ --- consumer’s risk --- sample size --- decision making --- neutrosophic set --- Q-neutrosophic set --- Q-neutrosophic soft set --- soft set --- Neutrosophic compound orthogonal neural network --- Neutrosophic number --- Neutrosophic function --- Function approximation --- triangular neutrosophic cubic fuzzy number --- Einstein t-norm --- arithmetic averaging operator --- Multi-attribute decision making --- numerical application --- neutrosophic statistical interval method --- classical statistics --- fuzzy logic --- producer’s risk --- consumer’s risk --- neutrosophic cubic weighted geometric operator (NCWG) --- neutrosophic cubic ordered weighted geometric operator (NCOWG) --- neutrosophic cubic Einstein weighted geometric operator (NCEWG) --- neutrosophic cubic Einstein ordered weighted geometric operator (NCEOWG) --- multi-attribute decision making --- single-valued neutrosophic set --- aggregation --- TOPSIS --- single-valued neutrosophic linguistic set --- distance measure --- combined weighted average --- MAGDM --- low-carbon supplier selection --- weighted geometric operator --- weighted average operator --- neutrosophic cubic sets --- multi-attribute decision-making (MADM) --- neutrosophic cubic hybrid weighted arithmetic and geometric aggregation operator (NCHWAGA) --- neutrosophic sets --- cubic sets --- soft sets --- neutrosophic cubic soft sets --- neutrosophic cubic soft expert system --- multicriteria decision-making --- neutrosophic extended triplet group --- generalized neutrosophic extended triplet group --- quasi-completely regular semigroup --- clifford semigroup --- prostate cancer --- neutrosophic statistics --- dietary fat level --- neutrosophic regression --- neutrosophic correlation --- single valued neutrosophic sets --- logarithmic operational laws --- logarithmic aggregation operators --- MCGDM problems --- complex neutrosophic set --- complex neutrosophic soft expert set --- fuzzy parameterized single valued neutrosophic soft expert set --- single valued neutrosophic set --- soft expert set --- decision making --- membership function --- neutrosophic set --- neutrosophic soft rough --- relations --- rough set approximation --- soft set --- neutrosophic time series --- triangular neutrosophic number --- neutrosophic logical relationship --- neutrosophic logical relationship groups --- smart port --- simplified neutrosophic set --- single-valued neutrosophic set --- exponential similarity measure --- port evaluation --- nonstandard analysis --- extended nonstandard analysis --- open and closed monads to the left/right --- pierced and unpierced binads --- MoBiNad set --- infinitesimals --- infinities --- nonstandard reals --- standard reals --- nonstandard neutrosophic lattices of first type (as poset) and second type (as algebraic structure), nonstandard neutrosophic logic --- extended nonstandard neutrosophic logic --- nonstandard arithmetic operations --- nonstandard unit interval --- nonstandard neutrosophic infimum --- nonstandard neutrosophic supremum --- intuitionistic fuzzy parameters --- uncertainty modeling --- neutrosophic goal programming approach --- shale gas water management system --- e-marketing --- Internet of Things --- neutrsophic set --- multi-criteria decision making techniques --- probabilistic neutrosophic hesitant fuzzy set (PNHFS) --- decision-making --- Choquet integral --- neutrosophic extended triplet group --- neutrosophic quadruple numbers --- neutrosophic set --- BNHWA aggregation operator --- BNHOWA aggregation operator --- BNHHA aggregation operator --- score function --- accuracy function --- certainty function --- group decision making --- non-standard analysis --- extended non-standard analysis --- monad --- binad --- left monad closed to the right --- right monad closed to the left --- pierced binad --- unpierced binad --- non-standard neutrosophic mobinad set --- neutrosophic topology --- non-standard neutrosophic topology --- neutrosophic sets --- neutrosophic triangular norms --- residuated lattices --- representable neutrosophic t-norms --- De Morgan neutrosophic triples --- neutrosophic residual implications --- infinitely ?-distributive --- visual tracking --- neutrosophic weight --- objectness --- weighted multiple instance learning --- supply chain sustainability metrics --- plithogeny --- aggregation operations --- neutrosophic set --- quality function deployment --- multi-granulation neutrosophic rough set --- non-dual --- two universes --- multi-attribute group decision making --- neutrosophic extended triplet group --- neutrosophic quadruple numbers --- refined neutrosophic numbers --- refined neutrosophic quadruple numbers --- neutrosophic set --- fuzzy numbers --- neutrosophic numbers --- neutrosophic symmetric scenarios --- performance indicators --- financial assets --- simplified neutrosophic hesitant fuzzy set --- multi-attribute decision-making --- maximizing deviation --- TOPSIS --- single valued neutrosophic set --- covering --- symmetric relation --- graph representation --- matrix representation --- paper defect diagnosis --- ordinary single valued neutrosophic (co)topology --- ordinary single valued neutrosophic subspace --- ?-level --- ordinary single valued neutrosophic neighborhood system --- ordinary single valued neutrosophic base --- ordinary single valued neutrosophic subbase --- neutrosophic offset --- uninorm --- neutrosophic offuninorm --- neutrosophic offnorm --- neutrosophic offconorm --- implicator --- prospector --- n-person cooperative game --- hypergroup --- semihypergroup --- neutrosophic extended triplet group --- neutrosophic extended triplet semihypergroup (NET-semihypergroup) --- NET-hypergroup --- neutrosophic rings --- neutrosophic quadruple rings --- idempotents --- neutrosophic extended triplet group --- neutrosophic set

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

Authors: --- ---
ISBN: 9783038973843 Year: Volume: 1 Pages: 478 DOI: 10.3390/books978-3-03897-385-0 Language: English
Publisher: MDPI - Multidisciplinary Digital Publishing Institute
Subject: Science (General) --- Mathematics
Added to DOAB on : 2019-04-05 10:34:31
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Abstract

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.

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

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

Authors: --- ---
ISBN: 9783038974758 Year: Volume: 2 Pages: 450 DOI: 10.3390/books978-3-03897-476-5 Language: English
Publisher: MDPI - Multidisciplinary Digital Publishing Institute
Subject: Science (General) --- Mathematics
Added to DOAB on : 2019-04-05 10:34:31
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Abstract

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.

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

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