This comprehensive text examines the relatively new mathematical area of generalized measure theory. This area expands classical measure theory by abandoning the requirement of additivity and replacing it with various weaker requirements. Each of these weaker requirements characterizes a class of nonadditive measures. This results in new concepts and methods that allow us to deal with many problems in a more realistic way. For example, it allows us to work with imprecise probabilities. The exposition of generalized measure theory unfolds systematically. It begins with preliminaries and new concepts, followed by a detailed treatment of important new results regarding various types of nonadditive measures and the associated integration theory. The latter involves severaltypes of integrals: Sugeno integrals, Choquet integrals, pan-integrals, and lower and upper integrals. All of the topics are motivated by numerous examples, culminating in a final chapter on applications of generalized measure theory. Most up-to-date textbook in the field, covering recent applications Numerousexamples motivate the theory and exercises at the end of the chapter provide practice to the student Useful to an interdisciplinary cadre of mathematicians, engineers, computer scientists and specialists working in decision making INDICE: Preface.- Introduction.- Preliminaries.- Basic Ideas of Generalized Measure Theory.- Special Area of Generalized Measure Theory.- Extensions.- Structural Characteristics.- Measurable Functions on Monotone Measure Space.- Integration.- Sugeno Integrals.- Pan-Intergrals.- Choquet Integral.- Upper and Lower Integrations.- Constructing Generalized Measures.- Fuzzification in Generalized Measure Theory.- Applications of Generalized Measure Theory.- Bibliography.- Appendix A. Glossary of Key Concepts.- Appendix B. Glossary of Symbols.- Name Index.- Subject Index.
- ISBN: 978-0-387-76851-9
- Editorial: Springer
- Encuadernacion: Cartoné
- Páginas: 415
- Fecha Publicación: 01/12/2008
- Nº Volúmenes: 1
- Idioma: Inglés