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Applications of Continuous Mathematics to Computer Science
Hung T. Nguyen,Vladik Kreinovich +1 more
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TLDR
This book discusses Algorithm Complexity, Randomness, Chaos, and Fractals, and the Basics of Fuzzy Logic, which is an Application to Computational Statistics.Abstract:
Preface. 1. Algorithm Complexity: Two Simple Examples. 2. Solving General Linear Functional Equations: An Application to Algorithm Complexity. 3. Program Testing: A Problem. 4. Optimal Program Testing. 5. Optimal Choice of a Penalty Function: Simplest Case of Algorithm Design. 6. Solving General Linear Differential Equations with Constant Coefficients: An Application to Constrained Optimization. 7. Simulated Annealing: 'Smooth' (Local) Discrete Optimization. 8. Genetic Algorithms: 'Non-Smooth' Discrete Optimization. 9. RISC Computer Architecture and Internet Growth: Two Applications of Extrapolation. 10. Systems of Differential Equations and Their Use in Computer-Related Extrapolation Problems. 11. Network Congestion: An Example of Non-Linear Extrapolation. 12. Neural Networks: A General Form of Non-Linear Extrapolation. 13. Expert Systems and the Basics of Fuzzy Logic. 14. Intelligent and Fuzzy Control. 15. Randomness, Chaos, and Fractals. A: Simulated Annealing Revisited. B: Software Cost Estimation. C: Electronic Engineering: How to Describe PN-Junctions. D: Log-Normal Distribution Justified: An Application to Computational Statistics. E: Optimal Robust Statistical Methods. F: How to Avoid Paralysis of Neural Networks. G: Estimating Computer Prices. H: Allocating Bandwidth on Computer Networks. I: Algorithm Complexity Revisited. J: How Can a Robot Avoid Obstacles: Case Study of Real-Time Optimization. K: Discounting in Robot Control: A Case Study of Dynamic Optimization. Index.read more
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ReportDOI
Constructing Probability Boxes and Dempster-Shafer Structures
TL;DR: A variety of the most useful and commonly applied methods for obtaining Dempster-Shafer structures, and their mathematical kin probability boxes, from empirical information or theoretical knowledge are summarized.
Journal ArticleDOI
A systematic approach.
E. G. Walshaw,C. J. Mannion +1 more
TL;DR: An old saying in the text is not quoted to imply that the majority of problems which occur in dyeing is due to inadequate preparation, but that in many cases problems which are not detected in preparation do lead to problems.
Book ChapterDOI
Decision Making Under Interval Uncertainty (and Beyond)
TL;DR: This chapter shows how the utility-based decision theory can be extended to realistic (interval) cases, where the user is often unable to select one of these alternatives when the alternatives are close.
Journal IssueDOI
Decision making beyond arrow's “impossibility theorem,” with the analysis of effects of collusion and mutual attraction
TL;DR: In this paper, it is shown that if we follow the main ideas of modern decision making and game theory and also collect information about the preferences between lotteries (i.e., collect the utility values of different alternatives), then reasonable decision-making rules are possible, e.g., Nash's rule in which we select an alternative for which the product of utilities is the largest possible.
Journal ArticleDOI
Interval Arithmetic, Affine Arithmetic, Taylor Series Methods: Why, What Next?
TL;DR: Questions about linear functions and polynomials and how this dependence is approximated are answered are answered in this paper.