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BL
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| Record Number
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889825
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| Title & Author
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Recent Advances in Applications of Computational and Fuzzy Mathematics /\ Snehashish Chakraverty, Sanjeewa Perera, editors.
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| Publication Statement
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Singapore :: Springer,, 2018.
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| Page. NO
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1 online resource
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| ISBN
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9789811311536
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: 9811311536
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9789811311529
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9811311528
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| Bibliographies/Indexes
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Includes bibliographical references and index.
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| Contents
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Intro; Preface; About the Book; Contents; Editors and Contributors; 1 2-D Shallow Water Wave Equations withFuzzy Parameters; 1.1 Introduction; 1.2 Preliminaries ofShallow Water Wave Equations; 1.3 Preliminaries ofFuzzy Sets; 1.4 Homotopy Perturbation Method; 1.4.1 Convergence ofHPM Solution; 1.5 Solution of2D Coupled Shallow Water Wave Equations; 1.6 Shallow Water Wave Equations withFuzzy Basin Depth; 1.7 Solution ofShallow Water Wave Equations withFuzzy Basin Depth; 1.7.1 Convergence ofHPM Solution forShallow Water Equations withFuzzy Initial Condition
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1.8 Numerical Results andDiscussion1.9 Conclusion; References; 2 ANN Based Solution ofStatic Structural Problem withFuzzy Parameters; 2.1 Introduction; 2.2 Architecture ofArtificial Neural Network; 2.2.1 Feed-Forward Neural Network; 2.2.2 Feedback Neural Network; 2.3 Learning Rules; 2.3.1 Error Back-Propagation Learning Algorithm orDelta Learning Rule; 2.4 Activation Functions; 2.4.1 Sigmoid Function; 2.4.2 Tangent Hyperbolic Function; 2.5 Linear System ofEquations; 2.5.1 Fully Interval Linear System ofEquations
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2.6 ANN Based Procedure forSolving Fully Interval Linear System ofEquations2.6.1 Algorithm; 2.6.2 Convergence Theorem; 2.7 Numerical Examples; 2.8 Conclusion; References; 3 Fuzzy Matrix Contractor Based Approach forLocalization ofRobots; 3.1 Introduction; 3.2 Preliminaries; 3.2.1 Fuzzy Sets; 3.2.2 Fuzzy Lattice; 3.3 Contractors; 3.3.1 Constraint Satisfaction Problem (CSP); 3.3.2 Fuzzy Contractors; 3.4 Localization ofGroup ofRobots; 3.4.1 Absolute Localization; 3.4.2 Relative Localization; 3.5 Conclusion; References
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4 Modeling Radon Diffusion Equation byUsing Fuzzy Polynomials inGalerkin's Method4.1 Introduction; 4.2 Preliminaries; 4.2.1 Fuzzy Number; 4.2.2 Triangular Fuzzy Number(TFN); 4.2.3 Arithmetic Operations ofFuzzy Numbers; 4.3 Parametric Approach; 4.4 Boundary Characteristic Orthogonal Polynomials (Crisp); 4.5 Galerkin's Method; 4.6 Galerkin's Method Based onBCOPs toSolve Fuzzy Boundary Value Problems; 4.6.1 Fuzzy Boundary Characteristic Orthogonal Polynomials (FBCOPs); 4.7 Radon Diffusion Mechanism; 4.8 Radon Diffusion Mechanism withUncertainty
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4.8.1 Fuzzy Boundary Characteristic Orthogonal Polynomials4.8.2 Galerkin's Method Based onFuzzy Boundary Characteristic Orthogonal Polynomials; 4.9 Results andDiscussions; 4.10 Conclusion; References; 5 Solving Fuzzy Static Structural Problems Using Symmetric Group Method; 5.1 Introduction; 5.2 Preliminaries; 5.2.1 Finding Differential Equations forFamilies ofCurves [14]; 5.2.2 Symmetries andODEs; 5.3 Static Deflection ofaEuler-Bernoulli Beam withDistributed Load; 5.3.1 Solution bySymmetry Method; 5.3.2 Preliminaries ofFuzzy andInterval [15, 16]
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| Abstract
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This book addresses the basics of interval/fuzzy set theory, artificial neural networks (ANN) and computational methods. It presents step-by-step modeling for application problems along with simulation and numerical solutions. In general, every science and engineering problem is inherently biased by uncertainty, and there is often a need to model, solve and interpret problems in the world of uncertainty. At the same time, exact information about models and parameters of practical applications is usually not known and precise values do not exist. This book discusses uncertainty in both data and models. It consists of seven chapters covering various aspects of fuzzy uncertainty in application problems, such as shallow water wave equations, static structural problems, robotics, radon diffusion in soil, risk of invasive alien species and air quality quantification. These problems are handled by means of advanced computational and fuzzy theory along with machine intelligence when the uncertainties involved are fuzzy. The proposed computational methods offer new fuzzy computing methods that help other areas of knowledge construction where inexact information is present.
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| Subject
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Fuzzy logic.
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Logic, Symbolic and mathematical.
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Mathematics.
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Fuzzy logic.
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Logic, Symbolic and mathematical.
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| Subject
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MATHEMATICS-- General.
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| Subject
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Mathematics.
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| Dewey Classification
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511.3/13
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| LC Classification
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QA9.64
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| Added Entry
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Chakraverty, Snehashish
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Perera, Sanjeewa
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