Computing Statistics under Interval and Fuzzy Uncertainty: Applications to Computer Science and Engineering

Front Matter....Pages -
Front Matter....Pages 1-1
Formulation of the Problem....Pages 3-8
Computing Statistics under Probabilistic and Interval Uncertainty: A Brief Description....Pages 9-10
Computing Statistics under Fuzzy Uncertainty: Formulation of the Problem....Pages 11-17
Computing under Fuzzy Uncertainty Can Be Reduced to Computing under Interval Uncertainty....Pages 19-24
Computing under Interval Uncertainty: Traditional Approach Based on Uniform Distributions....Pages 25-27
Computing under Interval Uncertainty: When Measurement Errors Are Small....Pages 29-33
Computing under Interval Uncertainty: General Algorithms....Pages 35-45
Computing under Interval Uncertainty: Computational Complexity....Pages 47-50
Towards Selecting Appropriate Statistical Characteristics: The Basics of Decision Theory and the Notion of Utility....Pages 51-54
How to Select Appropriate Statistical Characteristics....Pages 55-58
Front Matter....Pages 59-59
Computing under Fuzzy Uncertainty Can Be Reduced to Computing under Interval Uncertainty: Reminder....Pages 61-61
Computing Mean under Interval Uncertainty....Pages 63-63
Computing Median (and Quantiles) under Interval Uncertainty....Pages 65-66
Computing Variance under Interval Uncertainty: An Example of an NP-Hard Problem....Pages 67-78
Types of Interval Data Sets: Towards Feasible Algorithms....Pages 79-94
Computing Variance under Interval Uncertainty: Efficient Algorithms....Pages 95-117
Computing Variance under Hierarchical Privacy-Related Interval Uncertainty....Pages 119-127
Computing Outlier Thresholds under Interval Uncertainty....Pages 129-151
Computing Higher Moments under Interval Uncertainty....Pages 153-166
Computing Mean, Variance, Higher Moments, and Their Linear Combinations under Interval Uncertainty: A Brief Summary....Pages 167-168
Front Matter....Pages 59-59
Computing Covariance under Interval Uncertainty....Pages 169-171
Computing Correlation under Interval Uncertainty....Pages 173-176
Computing Expected Value under Interval Uncertainty....Pages 177-180
Computing Entropy under Interval Uncertainty. I....Pages 181-191
Computing Entropy under Interval Uncertainty. II....Pages 193-209
Computing the Range of Convex Symmetric Functions under Interval Uncertainty....Pages 211-219
Computing Statistics under Interval Uncertainty: Possibility of Parallelization....Pages 221-224
Computing Statistics under Interval Uncertainty: Case of Relative Accuracy....Pages 225-234
Front Matter....Pages 235-235
How Reliable Is the Input Data?....Pages 237-242
How Accurate Is the Input Data?....Pages 243-248
Front Matter....Pages 249-249
From Computing Statistics under Interval and Fuzzy Uncertainty to Practical Applications: Need to Propagate the Statistics through Data Processing....Pages 251-259
Applications to Bioinformatics....Pages 261-264
Applications to Computer Science: Optimal Scheduling for Global Computing....Pages 265-275
Applications to Information Management: How to Estimate Degree of Trust....Pages 277-281
Applications to Information Management: How to Measure Loss of Privacy....Pages 283-287
Application to Signal Processing: Using 1-D Radar Observations to Detect a Space Explosion Core among the Explosion Fragments....Pages 289-298
Applications to Computer Engineering: Timing Analysis of Computer Chips....Pages 299-304
Applications to Mechanical Engineering: Failure Analysis under Interval and Fuzzy Uncertainty....Pages 305-316
Applications to Geophysics: Inverse Problem....Pages 317-329
Front Matter....Pages 331-331
Need to Go Beyond Interval and Fuzzy Uncertainty....Pages 333-334
Front Matter....Pages 331-331
Beyond Interval Uncertainty: Taking Constraints into Account....Pages 335-347
Beyond Interval Uncertainty: Case of Discontinuous Processes (Phase Transitions)....Pages 349-355
Beyond Interval Uncertainty in Describing Statistical Characteristics: Case of Smooth Distributions and Info-Gap Decision Theory....Pages 357-366
Beyond Traditional Interval Uncertainty in Describing Statistical Characteristics: Case of Interval Bounds on the Probability Density Function....Pages 367-378
Beyond Interval Uncertainty in Describing Statistical Characteristics: Case of Normal Distributions....Pages 379-389
Beyond Traditional Fuzzy Uncertainty: Interval-Valued Fuzzy Techniques....Pages 391-393
Beyond Traditional Fuzzy Uncertainty: Type-2 Fuzzy Techniques....Pages 395-399
Back Matter....Pages -