1 Applications of Interval Computations: An Introduction.- 1 What are Interval Computations?.- 2 International Workshop on Applications of Interval Computations: How This Book Originated.- 3 General Optimization Problems.- 4 General Systems of Equations and Inequalities.- 5 Linear Interval Problems.- 6 Interval Computations Can Also Handle Possible Additional Information About the Input Data.- 7 Software and Hardware Support for Interval Computations.- References.- 2 A Review of Techniques in the Verified Solution of Constrained Global Optimization Problems.- 1 Introduction, Basic Ideas and Literature.- 2 On Constrained Optimization Problems.- 3 On Use of Interval Newton Methods.- 4 Applications.- 5 Summary and Present Work.- References.- 3 The Shape of the Symmetric Solution Set.- 1 Introduction.- 2 Notation.- 3 Results.- 4 Examples.- References.- 4 Linear Interval Equations: Computing Enclosures with Bounded Relative Overestimation is NP-Hard.- 1 Introduction.- 2 The Result.- 3 The Symmetric Case.- 4 Concluding Remark.- References.- 5 Quality Improvement via Optimization of Tolerance Intervals During the Design Stage.- 1 Introduction.- 2 Some Basic Models, and their Origins.- 3 Model of Performance Characteristic is Known Beforehand.- 4 Model Parameters Estimated in Controlled Conditions.- 5 Controlled Conditions are Unavailable.- 6 Temperature Controller.- 7 Conclusions.- References.- 6 Applications of Interval Computations to Regional Economic Input-Output Models.- 1 Economic Input-Output Models.- 2 Technical Coefficients are Only Known with Uncertainty.- 3 Statistical Methods are Not Directly Applicable, Hence, Interval Computations May Be Useful.- 4 Computational Algorithms.- 5 An Example.- References.- 7 Interval Arithmetic in Quantum Mechanics.- 1 Quantum Mechanics.- 2 Computer-Assisted Set-up.- 3 The Thomas-Fermi Equation.- 4 The Aperiodicity Inequality.- References.- 8 Interval Computations on the Spreadsheet.- 1 Limitations of Spreadsheet Computing.- 2 Extended IA on a Spreadsheet.- 3 Global IA on a Spreadsheet.- 4 Interval Constraint Spreadsheets.- 5 Discussion.- References.- 9 Solving Optimization Problems with Help of the UniCalc Solver.- 1 Introduction.- 2 The UniCalc Solver.- 3 The Algorithm of Sub definite Calculations.- 4 Solving Integer Programming Problems.- 5 Real-Valued Optimization.- 6 Future Developments.- References.- 10 Automatically Verified Arithmetic on Probability Distributions and Intervals.- 1 Introduction.- 2 Correctly Representing PDFs and Intervals with Histograms.- 3 Arithmetic Operations.- References.- 11 Nested Intervals and Sets: Concepts, Relations to Fuzzy Sets, and Applications.- 1 Introduction.- 2 Nested Intervals and Nested Sets.- 3 Other Problems Where Nested Sets and Nested Intervals Can Be Used: Identification, Optimization, Control, and Decision Making.- 4 Applications of Nested Sets and Nested Intervals.- Appendix A Proofs.- References.- 12 Fuzzy Interval Inference Utilizing the Checklist Paradigm and BK-Relational Products.- 1 Introduction.- 2 Many-Valued Logics for Interval Fuzzy Inference Based on the Checklist Paradigm.- 3 Groups of Logic Transformations of Interval Connectives.- 4 Special Types of Compositions of Relations.- 5 An Application: The Basic Knowledge Handling Mechanisms of CLIN AID by Means of Relational Inference.- 6 Toward Successful Utilization of Interval Methods in Soft Computing.- References.- 13 Computing Uncertainty in Interval Based Sets.- 1 Introduction.- 2 Evidence Sets as a Description of Uncertainty.- 3 Different Measures of Uncertainty, and How to Describethem Numerically.- 4 L-Fuzzy Sets, Interval Based L-Fuzzy Sets, and L-Evidence Sets.- 5 3-D Uncertainty Unit Cube.- References.- 14 Software and Hardware Techniques for Accurate, Self-Validating Arithmetic.- 1 Introduction.- 2 Software Tools.- 3 Hardware Designs.- 4 A Variable-Precision, Interval Arithmetic Coprocessor.- 5 Conclusions and Areas for Future Research.- References.- 15 Stimulating Hardware and Software Support for Interval Arithmetic.- 1 Introduction.- 2 The Participants.- 3 Stable Equilibrium.- 4 The Interval Paradigm Shift.- 5 System Supplier Demand.- 6 End-user Demand.- 7 Action Plan.- References.
