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Symmetry in Special and General Relativity

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ISBN: 9783039280940 / 9783039280957 Year: Pages: 100 DOI: 10.3390/books978-3-03928-095-7 Language: eng
Publisher: MDPI - Multidisciplinary Digital Publishing Institute
Subject: Physics (General) --- Science (General)
Added to DOAB on : 2020-01-30 16:39:46
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The development of special and general relativity has relied significantly on ideas of symmetry. Similarly, modern efforts to test these theories have often sought either violations or extensions of the symmetries seen, and symmetry is regularly used a tool in seeking new applications. In this Special Issue of symmetry, we explore some contemporary research related to symmetry in special and general relativity.

Current Trends in Symmetric Polynomials with their Applications

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ISBN: 9783039216208 / 9783039216215 Year: Pages: 238 DOI: 10.3390/books978-3-03921-621-5 Language: eng
Publisher: MDPI - Multidisciplinary Digital Publishing Institute
Subject: Science (General) --- Mathematics
Added to DOAB on : 2019-12-09 16:10:12
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This Special Issue presents research papers on various topics within many different branches of mathematics, applied mathematics, and mathematical physics. Each paper presents mathematical theories, methods, and their application based on current and recently developed symmetric polynomials. Also, each one aims to provide the full understanding of current research problems, theories, and applications on the chosen topics and includes the most recent advances made in the area of symmetric functions and polynomials.

Keywords

Fubini polynomials --- w-torsion Fubini polynomials --- fermionic p-adic integrals --- symmetric identities --- Chebyshev polynomials --- sums of finite products --- hypergeometric function --- Fubini polynomials --- Euler numbers --- symmetric identities --- elementary method --- computational formula --- two variable q-Berstein polynomial --- two variable q-Berstein operator --- q-Euler number --- q-Euler polynomial --- Fubini polynomials --- Euler numbers --- congruence --- elementary method --- q-Bernoulli numbers --- q-Bernoulli polynomials --- two variable q-Bernstein polynomials --- two variable q-Bernstein operators --- p-adic integral on ?p --- the degenerate gamma function --- the modified degenerate gamma function --- the degenerate Laplace transform --- the modified degenerate Laplace transform --- Fibonacci --- Lucas --- linear form in logarithms --- continued fraction --- reduction method --- sums of finite products of Chebyshev polynomials of the third and fourth kinds --- Hermite --- generalized Laguerre --- Legendre --- Gegenbauer --- Jacobi --- third-order character --- classical Gauss sums --- rational polynomials --- analytic method --- recursive formula --- fermionic p-adic q-integral on ?p --- q-Euler polynomials --- q-Changhee polynomials --- symmetry group --- Apostol-type Frobenius–Euler polynomials --- three-variable Hermite polynomials --- symmetric identities --- explicit relations --- operational connection --- q-Volkenborn integral on ?p --- Bernoulli numbers and polynomials --- generalized Bernoulli polynomials and numbers of arbitrary complex order --- generalized Bernoulli polynomials and numbers attached to a Dirichlet character ? --- Changhee polynomials --- Changhee polynomials of type two --- fermionic p-adic integral on ?p --- Chebyshev polynomials of the first, second, third, and fourth kinds --- sums of finite products --- representation --- catalan numbers --- elementary and combinatorial methods --- recursive sequence --- convolution sums --- well-posedness --- stability --- acoustic wave equation --- perfectly matched layer --- Fibonacci polynomials --- Lucas polynomials --- trivariate Fibonacci polynomials --- trivariate Lucas polynomials --- generating functions --- central incomplete Bell polynomials --- central complete Bell polynomials --- central complete Bell numbers --- Legendre polynomials --- Laguerre polynomials --- generalized Laguerre polynomials --- Gegenbauer polynomials --- hypergeometric functions 1F1 and 2F1 --- Euler polynomials --- Bernoulli polynomials --- elementary method --- identity --- congruence --- new sequence --- Catalan numbers --- elementary and combinatorial methods --- congruence --- conjecture --- fluctuation theorem --- thermodynamics of information --- stochastic thermodynamics --- mutual information --- non-equilibrium free energy --- entropy production

Symmetry in Graph Theory

Author:
ISBN: 9783038976585 Year: Pages: 340 DOI: 10.3390/books978-3-03897-659-2 Language: eng
Publisher: MDPI - Multidisciplinary Digital Publishing Institute
Subject: Mathematics --- Science (General)
Added to DOAB on : 2019-03-21 15:50:41
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This book contains the successful invited submissions to a Special Issue of Symmetry on the subject of ""Graph Theory"". Although symmetry has always played an important role in Graph Theory, in recent years, this role has increased significantly in several branches of this field, including but not limited to Gromov hyperbolic graphs, the metric dimension of graphs, domination theory, and topological indices. This Special Issue includes contributions addressing new results on these topics, both from a theoretical and an applied point of view.

Integral Transforms and Operational Calculus

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ISBN: 9783039216185 / 9783039216192 Year: Pages: 510 DOI: 10.3390/books978-3-03921-619-2 Language: eng
Publisher: MDPI - Multidisciplinary Digital Publishing Institute
Subject: Technology (General) --- General and Civil Engineering
Added to DOAB on : 2019-12-09 11:49:16
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Researches and investigations involving the theory and applications of integral transforms and operational calculus are remarkably wide-spread in many diverse areas of the mathematical, physical, chemical, engineering and statistical sciences.

Keywords

highly oscillatory --- convolution quadrature rule --- volterra integral equation --- Bessel kernel --- convergence --- higher order Schwarzian derivatives --- Janowski star-like function --- Janowski convex function --- bound on derivatives --- tangent numbers --- tangent polynomials --- Carlitz-type q-tangent numbers --- Carlitz-type q-tangent polynomials --- (p,q)-analogue of tangent numbers and polynomials --- (p,q)-analogue of tangent zeta function --- symmetric identities --- zeros --- Lommel functions --- univalent functions --- starlike functions --- convex functions --- inclusion relationships --- analytic function --- Hankel determinant --- exponential function --- upper bound --- nonlinear boundary value problems --- fractional-order differential equations --- Riemann-Stieltjes functional integral --- Liouville-Caputo fractional derivative --- infinite-point boundary conditions --- advanced and deviated arguments --- existence of at least one solution --- Fredholm integral equation --- Schauder fixed point theorem --- Hölder condition --- generalized Kuramoto–Sivashinsky equation --- modified Kudryashov method --- exact solutions --- Maple graphs --- analytic function --- Hadamard product (convolution) --- partial sum --- Srivastava–Tomovski generalization of Mittag–Leffler function --- subordination --- differential equation --- differential inclusion --- Liouville–Caputo-type fractional derivative --- fractional integral --- existence --- fixed point --- Bernoulli spiral --- Grandi curves --- Chebyshev polynomials --- pseudo-Chebyshev polynomials --- orthogonality property --- symmetric --- encryption --- password --- hash --- cryptography --- PBKDF --- q–Bleimann–Butzer–Hahn operators --- (p,q)-integers --- (p,q)-Bernstein operators --- (p,q)-Bleimann–Butzer–Hahn operators --- modulus of continuity --- rate of approximation --- K-functional --- Hurwitz-Lerch zeta function --- generalized functions --- analytic number theory --- ?-generalized Hurwitz-Lerch zeta functions --- derivative properties --- series representation --- basic hypergeometric functions --- generating functions --- q-polynomials --- analytic functions --- Mittag–Leffler functions --- starlike functions --- convex functions --- Hardy space --- vibrating string equation --- initial conditions --- spectral decomposition --- regular solution --- the uniqueness of the solution --- the existence of a solution --- analytic --- ?-convex function --- starlike function --- strongly-starlike function --- subordination --- q -Sheffer–Appell polynomials --- generating relations --- determinant definition --- recurrence relation --- q -Hermite–Bernoulli polynomials --- q -Hermite–Euler polynomials --- q -Hermite–Genocchi polynomials --- Volterra integral equations --- highly oscillatory Bessel kernel --- Hermite interpolation --- direct Hermite collocation method --- piecewise Hermite collocation method --- differential operator --- q-hypergeometric functions --- meromorphic function --- Mittag–Leffler function --- Hadamard product --- differential subordination --- starlike functions --- Bell numbers --- radius estimate --- (p, q)-integers --- Dunkl analogue --- generating functions --- generalization of exponential function --- Szász operator --- modulus of continuity --- function spaces and their duals --- distributions --- tempered distributions --- Schwartz testing function space --- generalized functions --- distribution space --- wavelet transform of generalized functions --- Fourier transform --- analytic function --- subordination --- Dziok–Srivastava operator --- nonlinear boundary value problem --- nonlocal --- multi-point --- multi-strip --- existence --- Ulam stability --- functions of bounded boundary and bounded radius rotations --- subordination --- functions with positive real part --- uniformly starlike and convex functions --- analytic functions --- univalent functions --- starlike and q-starlike functions --- q-derivative (or q-difference) operator --- sufficient conditions --- distortion theorems --- Janowski functions --- analytic number theory --- ?-generalized Hurwitz–Lerch zeta functions --- derivative properties --- recurrence relations --- integral representations --- Mellin transform --- natural transform --- Adomian decomposition method --- Caputo fractional derivative --- generalized mittag-leffler function --- analytic functions --- Hadamard product --- starlike functions --- q-derivative (or q-difference) operator --- Hankel determinant --- q-starlike functions --- fuzzy volterra integro-differential equations --- fuzzy general linear method --- fuzzy differential equations --- generalized Hukuhara differentiability --- spectrum symmetry --- DCT --- MFCC --- audio features --- anuran calls --- analytic functions --- convex functions --- starlike functions --- strongly convex functions --- strongly starlike functions --- uniformly convex functions --- Struve functions --- truncated-exponential polynomials --- monomiality principle --- generating functions --- Apostol-type polynomials and Apostol-type numbers --- Bernoulli, Euler and Genocchi polynomials --- Bernoulli, Euler, and Genocchi numbers --- operational methods --- summation formulas --- symmetric identities --- Euler numbers and polynomials --- q-Euler numbers and polynomials --- Hurwitz-Euler eta function --- multiple Hurwitz-Euler eta function --- higher order q-Euler numbers and polynomials --- (p, q)-Euler numbers and polynomials of higher order --- symmetric identities --- symmetry of the zero

Differential Geometry

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ISBN: 9783039218004 / 9783039218011 Year: Pages: 166 DOI: 10.3390/books978-3-03921-801-1 Language: eng
Publisher: MDPI - Multidisciplinary Digital Publishing Institute
Subject: Science (General) --- Mathematics
Added to DOAB on : 2019-12-09 16:10:12
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The present book contains 14 papers published in the Special Issue “Differential Geometry” of the journal Mathematics. They represent a selection of the 30 submissions. This book covers a variety of both classical and modern topics in differential geometry. We mention properties of both rectifying and affine curves, the geometry of hypersurfaces, angles in Minkowski planes, Euclidean submanifolds, differential operators and harmonic forms on Riemannian manifolds, complex manifolds, contact manifolds (in particular, Sasakian and trans-Sasakian manifolds), curvature invariants, and statistical manifolds and their submanifolds (in particular, Hessian manifolds). We wish to mention that among the authors, there are both well-known geometers and young researchers. The authors are from countries with a tradition in differential geometry: Belgium, China, Greece, Japan, Korea, Poland, Romania, Spain, Turkey, and United States of America. Many of these papers were already cited by other researchers in their articles. This book is useful for specialists in differential geometry, operator theory, physics, and information geometry as well as graduate students in mathematics.

Keywords

Euclidean submanifold --- position vector field --- concurrent vector field --- concircular vector field --- rectifying submanifold --- T-submanifolds --- constant ratio submanifolds --- Ricci soliton --- Kähler–Einstein metrics --- compact complex surfaces --- pinching of the curvatures --- statistical manifolds --- Hessian manifolds --- Hessian sectional curvature --- scalar curvature --- Ricci curvature --- Minkowski plane --- Minkowskian length --- Minkowskian angle --- Minkowskian pseudo-angle --- L2-harmonic forms --- Hodge–Laplacian --- manifold with singularity --- L2-Stokes theorem --- capacity --- k-th generalized Tanaka–Webster connection --- non-flat complex space form --- real hypersurface --- lie derivative --- shape operator --- conical surface --- developable surface --- generalized 1-type Gauss map --- cylindrical hypersurface --- inextensible flow --- lightlike surface --- ruled surface --- Darboux frame --- C-Bochner tensor --- generalized normalized ?-Casorati curvature --- Sasakian manifold --- slant --- invariant --- anti-invariant --- trans-Sasakian 3-manifold --- Reeb flow symmetry --- Ricci operator --- Sasakian statistical manifold --- conjugate connection --- Casorati curvature --- framed rectifying curves --- singular points --- framed helices --- centrodes --- circular rectifying curves --- statistical structure --- affine hypersurface --- affine sphere --- conjugate symmetric statistical structure --- sectional ?-curvature --- complete connection --- symplectic curves --- circular helices --- symplectic curvatures --- Frenet frame

Engineering Mathematics in Ship Design

Authors: --- ---
ISBN: 9783039218042 / 9783039218059 Year: Pages: 168 DOI: 10.3390/books978-3-03921-805-9 Language: eng
Publisher: MDPI - Multidisciplinary Digital Publishing Institute
Subject: General and Civil Engineering --- Technology (General)
Added to DOAB on : 2020-01-30 16:39:46
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Engineering mathematics is a branch of applied mathematics where mathematical methods and techniques are implemented for solving problems related to the engineering and industry. It also represents a multidisciplinary approach where theoretical and practical aspects are deeply merged with the aim at obtaining optimized solutions. In line with that, the present Special Issue, 'Engineering Mathematics in Ship Design', is focused, in particular, with the use of this sort of engineering science in the design of ships and vessels. Articles are welcome when applied science or computation science in ship design represent the core of the discussion.

Possible Scenarios for Homochirality on Earth

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ISBN: 9783039217229 / 9783039217236 Year: Pages: 318 DOI: 10.3390/books978-3-03921-723-6 Language: eng
Publisher: MDPI - Multidisciplinary Digital Publishing Institute
Subject: Science (General)
Added to DOAB on : 2019-12-09 11:49:16
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In 1978, Fred Hoyle proposed that interstellar comets carrying several viruses landed on Earth as part of the panspermia hypotheses. With respect to life, the origin of homochirality on Earth has been the greatest mystery because life cannot exist without molecular asymmetry. Many scientists have proposed several possible hypotheses to answer this long-standing L-D question. Previously, Martin Gardner raised the question about mirror symmetry and broken mirror symmetry in terms of the homochirality question in his monographs (1964 and 1990). Possible scenarios for the L-D issue can be categorized into (i) Earth and exoterrestrial origins, (ii) by-chance and necessity mechanisms, and (iii) mirror-symmetrical and non-mirror-symmetrical forces as physical and chemical origins. These scenarios should involve further great amplification mechanisms, enabling a pure L- or D-world.

Keywords

chirogenesis --- enantiomorphism --- nepheline --- magmatic flow --- etch figures --- origin of life --- biological homochirality --- deracemization --- super-high-velocity impact --- plasma reactor --- absolute asymmetric synthesis --- amino acids --- origin of life --- amino acid handedness --- nucleus–molecular coupling --- chirality --- circularly polarized luminescence --- circular dichroism --- symmetry breaking --- parity violation --- weak neutral current --- tunneling --- Z0 boson --- homochirality --- precision measurement --- homochirality --- circularly polarized light --- asymmetric reaction --- polymer --- ?-strand --- hidden chirality --- two-fold helix --- multi-point approximation --- tilt-chirality --- high dimensional chirality --- spin polarized electrons --- homochirality --- magnetism --- prebiotic --- environmental chirality --- C1- and C2-symmetric catalysts --- chiral field (memory) --- racemic field --- Viedma ripening effect --- Wallach’s rule --- heat capacity --- metal-organic framework --- triethylenediamine (DABCO) molecules --- racemate --- Salam hypothesis --- homochirality --- parity violation --- neutrinos --- gravitation --- enantiomer self-disproportionation --- SDE --- achiral stationary phase --- homochiral and heterochiral aggregates --- chiral separation --- chirality --- genesis of life chirality --- asymmetric autocatalysis --- homochirality --- chirality --- asymmetric synthesis --- Soai reaction --- biological homochirality --- enantioselective reaction --- autocatalysis --- origin of life --- replicators --- bioorganic homochirality --- circularly polarized photon --- spin-polarized lepton --- parity violation in the weak interaction --- symmetry breaking --- assemblies --- supramolecular chirality --- homochirality --- self-assembly --- vortex --- lipid --- supramolecular assembly --- symmetry breaking --- homochirality

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

Author:
ISBN: 9783039219384 / 9783039219391 Year: Pages: 714 DOI: 10.3390/books978-3-03921-939-1 Language: eng
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: eng
Publisher: MDPI - Multidisciplinary Digital Publishing Institute
Subject: Science (General) --- Mathematics
Added to DOAB on : 2019-04-05 10:34:31
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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.

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: eng
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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MDPI - Multidisciplinary Digital Publishing Institute (10)


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CC by-nc-nd (10)


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eng (10)


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2020 (2)

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