De Gruyter Studies in Mathematics / Decision Making under Interval Uncertainty
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The series is devoted to the publication of monographs and high-level textbooks in mathematics, mathematical methods and their applications. Apart from covering important areas of current interest, a major aim is to make topics of an interdisciplinary nature accessible to the non-specialist.
The works in this series are addressed to advanced students and researchers in mathematics and theoretical physics. In addition, it can serve as a guide for lectures and seminars on a graduate level.
The series de Gruyter Studies in Mathematics was founded ca. 30 years ago by the late Professor Heinz Bauer and Professor Peter Gabriel with the aim to establish a series of monographs and textbooks of high standard, written by scholars with an international reputation presenting current fields of research in pure and applied mathematics.
While the editorial board of the Studies has changed with the years, the aspirations of the Studies are unchanged. In times of rapid growth of mathematical knowledge carefully written monographs and textbooks written by experts are needed more than ever, not least to pave the way for the next generation of mathematicians. In this sense the editorial board and the publisher of the Studies are devoted to continue the Studies as a service to the mathematical community.
Please submit any book proposals to Niels Jacob.
- 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.
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
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
- Autor: Vladik Kreinovich
- 2025, X, 280 Seiten, Maße: 21 x 24 cm, Gebunden, Englisch
- Verlag: De Gruyter
- ISBN-10: 3110301717
- ISBN-13: 9783110301717
- Erscheinungsdatum: 29.01.2025
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