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New Trends in Differential and Difference Equations and Applications

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ISBN: 9783039215386 / 9783039215393 Year: Pages: 198 DOI: 10.3390/books978-3-03921-539-3 Language: eng
Publisher: MDPI - Multidisciplinary Digital Publishing Institute
Subject: Science (General) --- Mathematics
Added to DOAB on : 2019-12-09 11:49:15
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This Special Issue aims to be a compilation of new results in the areas of differential and difference Equations, covering boundary value problems, systems of differential and difference equations, as well as analytical and numerical methods. The objective is to provide an overview of techniques used in these different areas and to emphasize their applicability to real-life phenomena, by the inclusion of examples. These examples not only clarify the theoretical results presented, but also provide insight on how to apply, for future works, the techniques used.

Keywords

Legendre wavelets --- collocation method --- three-step Taylor method --- asymptotic stability --- time-dependent partial differential equations --- non-instantaneous impulses --- Caputo fractional derivative --- differential equations --- state dependent delays --- lipschitz stability --- limit-periodic solutions --- difference equations --- exponential dichotomy --- strong nonlinearities --- effective existence criteria --- population dynamics --- discrete Lyapunov equation --- difference equations --- Hilbert space --- dichotomy --- exponential stability --- ?-Laplacian operator --- mean curvature operator --- heteroclinic solutions --- problems in the real line --- lower and upper solutions --- Nagumo condition on the real line --- fixed point theory --- coupled nonlinear systems --- functional boundary conditions --- Schauder’s fixed point theory --- Arzèla Ascoli theorem --- lower and upper solutions --- first order periodic systems --- SIRS epidemic model --- mathematical modelling --- Navier–Stokes equations --- global solutions --- regular solutions --- a priori estimates --- weak solutions --- kinetic energy --- dissipation --- Bäcklund transformation --- Clairin’s method --- generalized Liouville equation --- Miura transformation --- Korteweg-de Vries equation --- second-order differential/difference/q-difference equation of hypergeometric type --- non-uniform lattices --- divided-difference equations --- polynomial solution --- integro-differentials --- Sumudu decomposition method --- dynamical system

Fractional Differential Equations: Theory, Methods and Applications

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ISBN: 9783039217328 / 9783039217335 Year: Pages: 172 DOI: 10.3390/books978-3-03921-733-5 Language: eng
Publisher: MDPI - Multidisciplinary Digital Publishing Institute
Subject: Science (General) --- Mathematics
Added to DOAB on : 2019-12-09 11:49:16
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Fractional calculus provides the possibility of introducing integrals and derivatives of an arbitrary order in the mathematical modelling of physical processes, and it has become a relevant subject with applications to various fields, such as anomalous diffusion, propagation in different media, and propogation in relation to materials with different properties. However, many aspects from theoretical and practical points of view have still to be developed in relation to models based on fractional operators. This Special Issue is related to new developments on different aspects of fractional differential equations, both from a theoretical point of view and in terms of applications in different fields such as physics, chemistry, or control theory, for instance. The topics of the Issue include fractional calculus, the mathematical analysis of the properties of the solutions to fractional equations, the extension of classical approaches, or applications of fractional equations to several fields.

Nonlinear Dynamics and Entropy of Complex Systems with Hidden and Self-excited Attractors

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ISBN: 9783038978985 / 9783038978992 Year: Pages: 290 DOI: 10.3390/books978-3-03897-899-2 Language: eng
Publisher: MDPI - Multidisciplinary Digital Publishing Institute
Subject: Technology (General) --- General and Civil Engineering
Added to DOAB on : 2019-06-26 10:09:00
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In recent years, entropy has been used as a measure of the degree of chaos in dynamical systems. Thus, it is important to study entropy in nonlinear systems. Moreover, there has been increasing interest in the last few years regarding the novel classification of nonlinear dynamical systems including two kinds of attractors: self-excited attractors and hidden attractors. The localization of self-excited attractors by applying a standard computational procedure is straightforward. In systems with hidden attractors, however, a specific computational procedure must be developed, since equilibrium points do not help in the localization of hidden attractors. Some examples of this kind of system are chaotic dynamical systems with no equilibrium points; with only stable equilibria, curves of equilibria, and surfaces of equilibria; and with non-hyperbolic equilibria. There is evidence that hidden attractors play a vital role in various fields ranging from phase-locked loops, oscillators, describing convective fluid motion, drilling systems, information theory, cryptography, and multilevel DC/DC converters. This Special Issue is a collection of the latest scientific trends on the advanced topics of dynamics, entropy, fractional order calculus, and applications in complex systems with self-excited attractors and hidden attractors.

Keywords

new chaotic system --- multiple attractors --- electronic circuit realization --- S-Box algorithm --- chaotic systems --- circuit design --- parameter estimation --- optimization methods --- Gaussian mixture model --- chaotic system --- empirical mode decomposition --- permutation entropy --- image encryption --- hidden attractors --- fixed point --- stability --- nonlinear transport equation --- stochastic (strong) entropy solution --- uniqueness --- existence --- multiscale multivariate entropy --- multistability --- self-reproducing system --- chaos --- hidden attractor --- self-excited attractor --- fractional order --- spectral entropy --- coexistence --- multistability --- chaotic flow --- hidden attractor --- multistable --- entropy --- core entropy --- Thurston’s algorithm --- Hubbard tree --- external rays --- chaos --- Lyapunov exponents --- multiple-valued --- static memory --- strange attractors --- fractional discrete chaos --- entropy --- projective synchronization --- full state hybrid projective synchronization --- generalized synchronization --- inverse full state hybrid projective synchronization --- inverse generalized synchronization --- multichannel supply chain --- service game --- chaos --- entropy --- BOPS --- Hopf bifurcation --- self-excited attractors --- multistability --- sample entropy --- PRNG --- Non-equilibrium four-dimensional chaotic system --- entropy measure --- adaptive approximator-based control --- neural network --- uncertain dynamics --- synchronization --- fractional-order --- complex-variable chaotic system --- unknown complex parameters --- chaotic map --- fixed point --- chaos --- approximate entropy --- implementation --- hidden attractor --- hyperchaotic system --- multistability --- entropy analysis --- hidden attractor --- complex systems --- fractional-order --- entropy --- chaotic maps --- chaos --- spatial dynamics --- Bogdanov Map --- chaos --- laser --- resonator

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: eng
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 with Operator Theory and Equations

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ISBN: 9783039216666 / 9783039216673 Year: Pages: 208 DOI: 10.3390/books978-3-03921-667-3 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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A plethora of problems from diverse disciplines such as Mathematics, Mathematical: Biology, Chemistry, Economics, Physics, Scientific Computing and also Engineering can be formulated as an equation defined in abstract spaces using Mathematical Modelling. The solutions of these equations can be found in closed form only in special case. That is why researchers and practitioners utilize iterative procedures from which a sequence is being generated approximating the solution under some conditions on the initial data. This type of research is considered most interesting and challenging. This is our motivation for the introduction of this special issue on Iterative Procedures.

Iterative Methods for Solving Nonlinear Equations and Systems

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ISBN: 9783039219407 / 9783039219414 Year: Pages: 494 DOI: 10.3390/books978-3-03921-941-4 Language: eng
Publisher: MDPI - Multidisciplinary Digital Publishing Institute
Subject: Science (General) --- Mathematics
Added to DOAB on : 2020-01-07 09:08:26
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Solving nonlinear equations in Banach spaces (real or complex nonlinear equations, nonlinear systems, and nonlinear matrix equations, among others), is a non-trivial task that involves many areas of science and technology. Usually the solution is not directly affordable and require an approach using iterative algorithms. This Special Issue focuses mainly on the design, analysis of convergence, and stability of new schemes for solving nonlinear problems and their application to practical problems. Included papers study the following topics: Methods for finding simple or multiple roots either with or without derivatives, iterative methods for approximating different generalized inverses, real or complex dynamics associated to the rational functions resulting from the application of an iterative method on a polynomial. Additionally, the analysis of the convergence has been carried out by means of different sufficient conditions assuring the local, semilocal, or global convergence. This Special issue has allowed us to present the latest research results in the area of iterative processes for solving nonlinear equations as well as systems and matrix equations. In addition to the theoretical papers, several manuscripts on signal processing, nonlinear integral equations, or partial differential equations, reveal the connection between iterative methods and other branches of science and engineering.

Keywords

point projection --- intersection --- parametric curve --- n-dimensional Euclidean space --- Newton’s second order method --- fixed point theorem --- nonlinear equations --- multiple zeros --- optimal iterative methods --- higher order of convergence --- nonlinear operator equation --- Fréchet derivative --- ?-continuity condition --- Newton-like method --- Frédholm integral equation --- nonlinear equations --- Padé approximation --- iterative method --- order of convergence --- numerical experiment --- fourth order iterative methods --- local convergence --- banach space --- radius of convergence --- nonlinear equation --- iterative process --- non-differentiable operator --- Lipschitz condition --- high order --- sixteenth order convergence method --- local convergence --- dynamics --- Banach space --- Newton’s method --- semi-local convergence --- Kantorovich hypothesis --- iterative methods --- Steffensen’s method --- R-order --- with memory --- computational efficiency --- non-linear equation --- basins of attraction --- optimal order --- higher order method --- computational order of convergence --- nonlinear equations --- multiple roots --- Chebyshev–Halley-type --- optimal iterative methods --- efficiency index --- Banach space --- semilocal convergence --- ?-continuity condition --- Jarratt method --- error bound --- Fredholm integral equation --- Newton’s method --- global convergence --- variational inequality problem --- split variational inclusion problem --- multi-valued quasi-nonexpasive mappings --- Hilbert space --- sixteenth-order optimal convergence --- multiple-root finder --- asymptotic error constant --- weight function --- purely imaginary extraneous fixed point --- attractor basin --- drazin inverse --- generalized inverse --- iterative methods --- higher order --- efficiency index --- integral equation --- efficiency index --- nonlinear models --- iterative methods --- higher order --- nonlinear equations --- optimal iterative methods --- multiple roots --- efficiency index --- iterative methods --- nonlinear equations --- Newton-type methods --- smooth and nonsmooth operators --- heston model --- Hull–White --- option pricing --- PDE --- finite difference (FD) --- iteration scheme --- Moore–Penrose --- rectangular matrices --- rate of convergence --- efficiency index --- nonlinear equations --- conjugate gradient method --- projection method --- convex constraints --- signal and image processing --- nonlinear monotone equations --- conjugate gradient method --- projection method --- signal processing --- nonlinear systems --- multipoint iterative methods --- divided difference operator --- order of convergence --- Newton’s method --- computational efficiency index --- system of nonlinear equations --- Newton method --- Newton-HSS method --- nonlinear HSS-like method --- Picard-HSS method --- convexity --- least square problem --- accretive operators --- signal processing --- point projection --- intersection --- planar algebraic curve --- Newton’s iterative method --- the improved curvature circle algorithm --- systems of nonlinear equations --- King’s family --- order of convergence --- multipoint iterative methods --- nonlinear equations --- Potra–Pták method --- optimal methods --- weight function --- basin of attraction --- engineering applications --- Kung–Traub conjecture --- multipoint iterations --- nonlinear equation --- optimal order --- basins of attraction

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

Control and Nonlinear Dynamics on Energy Conversion Systems

Authors: ---
ISBN: 9783039211104 / 9783039211111 Year: Pages: 438 DOI: 10.3390/books978-3-03921-111-1 Language: eng
Publisher: MDPI - Multidisciplinary Digital Publishing Institute
Subject: Technology (General) --- General and Civil Engineering
Added to DOAB on : 2019-08-28 11:21:27
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The ever-increasing need for higher efficiency, smaller size, and lower cost make the analysis, understanding, and design of energy conversion systems extremely important, interesting, and even imperative. One of the most neglected features in the study of such systems is the effect of the inherent nonlinearities on the stability of the system. Due to these nonlinearities, these devices may exhibit undesirable and complex dynamics, which are the focus of many researchers. Even though a lot of research has taken place in this area during the last 20 years, it is still an active research topic for mainstream power engineers. This research has demonstrated that these systems can become unstable with a direct result in increased losses, extra subharmonics, and even uncontrollability/unobservability. The detailed study of these systems can help in the design of smaller, lighter, and less expensive converters that are particularly important in emerging areas of research like electric vehicles, smart grids, renewable energy sources, and others. The aim of this Special Issue is to cover control and nonlinear aspects of instabilities in different energy conversion systems: theoretical, analysis modelling, and practical solutions for such emerging applications. In this Special Issue, we present novel research works in different areas of the control and nonlinear dynamics of energy conversion systems.

Keywords

data-driven --- prediction --- neural network --- air-handling unit (AHU) --- supply air temperature --- pulverizing system --- soft sensor --- inferential control --- moving horizon estimation --- multi-model predictive control --- micro-grid --- droop control --- virtual impedance --- harmonic suppression --- power quality --- combined heat and power unit --- two-stage bypass --- dynamic model --- coordinated control system --- predictive control --- decoupling control --- power conversion --- model–plant mismatches --- disturbance observer --- performance recovery --- offset-free --- electrical machine --- electromagnetic vibration --- multiphysics --- rotor dynamics --- air gap eccentricity --- calculation method --- magnetic saturation --- corrugated pipe --- whistling noise --- Helmholtz number --- excited modes --- switched reluctance generator --- capacitance current pulse train control --- voltage ripple --- capacitance current --- feedback coefficient --- distributed architecture --- maximum power point tracking --- sliding mode control --- overvoltage --- permanent magnet synchronous motor (PMSM) --- single artificial neuron goal representation heuristic dynamic programming (SAN-GrHDP) --- single artificial neuron (SAN) --- reinforcement learning (RL) --- goal representation heuristic dynamic programming (GrHDP) --- adaptive dynamic programming (ADP) --- sliding mode observer (SMO) --- permanent magnet synchronous motor (PMSM) --- extended back electromotive force (EEMF) --- position sensorless --- bridgeless converter --- discontinuous conduction mode (DCM) --- high step-up voltage gain --- power factor correction (PFC) --- space mechanism --- multi-clearance --- nonlinear dynamic model --- planetary gears --- vibration characteristics --- new step-up converter --- ultrahigh voltage conversion ratio --- small-signal model --- average-current mode control --- slope compensation --- monodromy matrix --- current mode control --- boost-flyback converter --- explosion-magnetic generator --- plasma accelerator --- current-pulse formation --- DC-DC buck converter --- contraction analysis --- global stability --- matrix norm --- DC micro grid --- efficiency optimization --- variable bus voltage MG --- variable switching frequency DC-DC converters --- centralized vs. decentralized control --- local vs. global optimization --- buck converter --- DC motor --- bifurcations in control parameter --- sliding control --- zero average dynamics --- fixed-point inducting control --- DC-DC converters --- quadratic boost --- maximum power point tracking (MPPT) --- nonlinear dynamics --- subharmonic oscillations --- photovoltaic (PV) --- steel catenary riser --- rigid body rotation --- wave --- the load of suspension point in the z direction --- Cable3D

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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eng (12)


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2019 (12)