The Geometry of Uncertainty : The Geometry of Imprecise Probabilities

Lingua: inglese

Editore: Springer, 2021

3030631559 / 9783030631550

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

Da: AHA-BUCH GmbH, Einbeck, GermaniaAHA-BUCH GmbH

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Druck auf Anfrage Neuware - Printed after ordering - 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.

Codice articolo 9783030631550

Titolo
The Geometry of Uncertainty : The Geometry of Imprecise Probabilities
Autore
Fabio Cuzzolin
Editore
Springer
Anno di pubblicazione
2021
Condizione
Neu
Rilegatura
Taschenbuch
Lingua
inglese
ISBN 10
3030631559
ISBN 13
9783030631550
Peso dell'articolo
1299 grammi
Dimensioni
235x155x47 mm
Serie
Libro 9 di 15: Artificial Intelligence: Foundations, Theory, and Algorithms

AHA-BUCH GmbH

Einbeck, Germania

Venditore con 5 stelle

Venditore AbeBooks dal 14 agosto 2006

Tariffe di spedizione da Germania a U.S.A.

ArticoloDa 7 a 10 giorni lavorativiDa 5 a 7 giorni lavorativi
Primo articoloEUR 39,59EUR 46,09
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