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This book presents the theory and methods of flexible and generalized uncertainty optimization. Particularly, it describes the theory of generalized uncertainty in the context of optimization modeling. The book starts with an overview of flexible and generalized uncertainty optimization. It covers uncertainties that are both associated with lack of information and that more general than stochastic theory, where well-defined distributions are assumed. Starting from families of distributions that are enclosed by upper and lower functions, the book presents construction methods for obtaining flexible and generalized uncertainty input data that can be used in a flexible and generalized uncertainty optimization model. It then describes the development of such a model in detail. All in all, the book provides the readers with the necessary background to understand flexible and generalized uncertainty optimization and develop their own optimization model.
List of contents
1 An Introduction to Generalized Uncertainty Optimization.- 2 Generalized Uncertainty Theory: A Language for Information Deficiency.- 3 The Construction of Flexible and Generalized Uncertainty Optimization Input Data.- 4 An Overview of Flexible and Generalized Uncertainty Optimization.- 5 Flexible Optimization.- 6 Generalized Uncertainty Optimization.- References.
About the author
Weldon Alexander Lodwick is a Full Professor of Mathematics at the University of Colorado Denver. He holds a Ph.D. degree in mathematics (1980) from the Oregon State University. He is the co-editor of the book Fuzzy Optimization: Recent Developments and Applications, Studies in Fuzziness and Soft Computing Vol. 254, Springer-Verlag Berlin Heidelberg, 2010, and the author of the book Interval and Fuzzy Analysis: A Unified Approach in Advances in Imaging and Electronic Physics, Vol. 148, pp. 76–192, Elsevier, 2007. His current research interests include interval analysis, distance geometry, as well as flexible and generalized uncertainty optimization. Over the last thirty years he has taught applied mathematical modeling to undergraduate and graduate students, which covers topics such as radiation therapy of tumor, fuzzy and possibilistic optimization modeling, global optimization, optimal control, molecular distance geometry problems, and neural networks applied to control problems.
Phantipa Thipwiwatpotjana is an Assistant Professor of Mathematics at the Chulalongkorn University, Bangkok, Thailand. She received her Ph. D. in Applied Mathematics from the University of Colorado Denver in 2010 for the dissertation titled “Linear programming problems for generalized uncertainty”. She received scholarships from the Development and Promotion of Science and Technology Talents Project and Thai Government to study Mathematics for both undergraduate and graduate levels. Her primary research interests are in optimization under uncertainty, uncertainty relationship, and their applications.
Summary
This book presents the theory and methods of flexible and generalized uncertainty optimization. Particularly, it describes the theory of generalized uncertainty in the context of optimization modeling. The book starts with an overview of flexible and generalized uncertainty optimization. It covers uncertainties that are both associated with lack of information and that more general than stochastic theory, where well-defined distributions are assumed. Starting from families of distributions that are enclosed by upper and lower functions, the book presents construction methods for obtaining flexible and generalized uncertainty input data that can be used in a flexible and generalized uncertainty optimization model. It then describes the development of such a model in detail. All in all, the book provides the readers with the necessary background to understand flexible and generalized uncertainty optimization and develop their own optimization model.
