Decision Making under Interval Uncertainty: (De Gruyter Studies in Mathematics)

This book is about how to make decisions - mathematically based. These are the topics in focus: How to elicit user's preferences. How to select the best alternatives. Which characteristics should we select when describing probabilities? The need for interval uncertainty. Decision making under interval uncertainty: straightforward approach, remaining problems, solution. What if we cannot even elicit interval-valued uncertainty: symmetry approach. Questions beyond optimization.

Table of Contents:
Chapter 1. Introduction: How to make decisions Chapter 2. How to elicit user's preferences: utilities approach 2.1. A natural scale for preferences: utilities 2.2. Relation between different utility scales 2.3. How to compute utility of a decision Chapter 3. How to select the best alternatives. 3.1. Need for optimization 3.2. Traditional calculus approach and its limitations 3.2. How to guarantee that a region has no optima: need for interval computations 3.3. Main ideas behind interval computations: straightforward interval computations, mean value form 3.4. How interval computations can be effectively used in optimization: straightforward approach 3.5. How interval computations can be effectively used in optimization: advanced techniques Chapter 4. Which characteristics should we select when describing probabilities? 4.1. Need to select characteristic most appropriate for decision making 4.2. Case of a smooth objective function: moments 4.3. Case of a step-wise objective functions (e.g., satisfying constraints): cumulative distribution functions (cdf) Chapter 5. Describing probability distributions: need for interval uncertainty 5.1. Need for interval uncertainty 5.2. Bounds on moments and how to propagate them through computations 5.3. Bounds on cdfs (p-boxes) and how to propagate them through computations Chapter 6. Decision making under interval uncertainty: straightforward approach 6.1. Main idea: select a decision that may be optimal 6.2. From the idea to an algorithm 6.3. Limitations of the straightforward approach Chapter 7. Decision making under interval uncertainty: advanced approach 7.1. Natural requirement: the selection should not change if we re-scale utilities 7.2. Resulting idea: Hurwicz optimism-pessimism criterion 7.3. Too much optimism may lead to bad decisions Chapter 8. What if we cannot even elicit interval-valued uncertainty: symmetry approach 8.1. Need to go beyond interval-valued utilities: general problem 8.2. Case study: how to select a location for a meteorological tower 8.3. Symmetries 8.4. How to use symmetries to find the best decision under uncertainty 8.5. Case study: how we selected a location for a meteorological tower Chapter 9. Beyond optimization 9.1. Examples of problems beyond optimization: control, decision making under adversity, etc. 9.2. Control problems and the modal interval approach 9.3. Beyond modal intervals