The Geometry of Uncertainty

Idioma: inglés

Editorial: Springer, Springer Dez 2021, 2021

3030631559 / 9783030631550

Serie: Libro 9 de 15 - Artificial Intelligence: Foundations, Theory, and Algorithms

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This item is printed on demand - Print on Demand Titel. Neuware -The principal aim of this book is to introduce to the widest possible audience an original view of belief calculus and uncertainty theory. In this geometric approach to uncertainty, uncertainty measures can be seen as points of a suitably complex geometric space, and manipulated in that space, for example, combined or conditioned.In the chapters in Part I, Theories of Uncertainty, the author offers an extensive recapitulation of the state of the art in the mathematics of uncertainty. This part of the book contains the most comprehensive summary to date of the whole of belief theory, with Chap. 4 outlining for the first time, and in a logical order, all the steps of the reasoning chain associated with modelling uncertainty using belief functions, in an attempt to provide a self-contained manual for the working scientist. In addition, the book proposes in Chap. 5 what is possibly the most detailed compendium available of all theories of uncertainty. Part II, The Geometry of Uncertainty, is the core of this book, as it introduces the author's own geometric approach to uncertainty theory, starting with the geometry of belief functions: Chap. 7 studies the geometry of the space of belief functions, or belief space, both in terms of a simplex and in terms of its recursive bundle structure; Chap. 8 extends the analysis to Dempster's rule of combination, introducing the notion of a conditional subspace and outlining a simple geometric construction for Dempster's sum; Chap. 9 delves into the combinatorial properties of plausibility and commonality functions, as equivalent representations of the evidence carried by a belief function; then Chap. 10 starts extending the applicability of the geometric approach to other uncertainty measures, focusing in particular on possibility measures (consonant belief functions) and the related notion of a consistent belief function. The chapters in Part III, Geometric Interplays, are concerned with the interplay of uncertainty measures of different kinds, and the geometry of their relationship, with a particular focus on the approximation problem. Part IV, Geometric Reasoning, examines the application of the geometric approach to the various elements of the reasoning chain illustrated in Chap. 4, in particular conditioning and decision making. Part V concludes the book by outlining a future, complete statistical theory of random sets, future extensions of the geometric approach, and identifying high-impact applications to climate change, machine learning and artificial intelligence.The book is suitable for researchers in artificial intelligence, statistics, and applied science engaged with theories of uncertainty. The book is supported with the most comprehensive bibliography on belief and uncertainty theory.Springer-Verlag KG, Sachsenplatz 4-6, 1201 Wien 876 pp. Englisch.

N° de ref. del artículo 9783030631550

Título
The Geometry of Uncertainty
Autor
Fabio Cuzzolin
Editorial
Springer, Springer Dez 2021
Año de publicación
2021
Estado
Neu
Encuadernación
Taschenbuch
Idioma
inglés
ISBN 10
3030631559
ISBN 13
9783030631550
Peso del artículo
1299 gramos
Dimensiones
235x155x47 mm
Serie
Libro 9 de 15: Artificial Intelligence: Foundations, Theory, and Algorithms

buchversandmimpf2000

Emtmannsberg, BAYE, Alemania

Vendedor de 5 estrellas

Vendedor de AbeBooks desde 23 de enero de 2017

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