東華大學圖書館 |

The geometry of uncertainty = the geometry of imprecise probabilities /

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	The geometry of uncertainty/ by Fabio Cuzzolin.
其他題名:	the geometry of imprecise probabilities /
作者:	Cuzzolin, Fabio.
出版者:	Cham :Springer International Publishing : : 2021.,
面頁冊數:	xxv, 850 p. :ill., digital ;24 cm.
內容註:	Introduction -- Part I: Theories of Uncertainty -- Belief Functions -- Understanding Belief Functions -- Reasoning with Belief Functions -- A Toolbox for the Working Scientist -- The Bigger Picture -- Part II: The Geometry of Uncertainty -- The Geometry of Belief Functions -- Geometry of Dempster's Rule -- Three Equivalent Models -- The Geometry of Possibility -- Part III: Geometry Interplays -- Probability Transforms: The Affine Family -- Probability Transforms: The Epistemic Family -- Consonant Approximation -- Consistent Approximation -- Part IV: Geometric Reasoning -- Geometric Conditioning -- Decision Making with Epistemic Transforms -- Part V The Future of Uncertainty -- An Agenda for the Future -- References.
Contained By:	Springer Nature eBook
標題:	Uncertainty (Information theory) -
電子資源:	https://doi.org/10.1007/978-3-030-63153-6
ISBN:	9783030631536

The geometry of uncertainty = the geometry of imprecise probabilities /
Cuzzolin, Fabio.

The geometry of uncertaintythe geometry of imprecise probabilities /[electronic resource] :by Fabio Cuzzolin. - Cham :Springer International Publishing :2021. - xxv, 850 p. :ill., digital ;24 cm. - Artificial intelligence: foundations, theory, and algorithms,2365-3051. - Artificial intelligence: foundations, theory, and algorithms..

Introduction -- Part I: Theories of Uncertainty -- Belief Functions -- Understanding Belief Functions -- Reasoning with Belief Functions -- A Toolbox for the Working Scientist -- The Bigger Picture -- Part II: The Geometry of Uncertainty -- The Geometry of Belief Functions -- Geometry of Dempster's Rule -- Three Equivalent Models -- The Geometry of Possibility -- Part III: Geometry Interplays -- Probability Transforms: The Affine Family -- Probability Transforms: The Epistemic Family -- Consonant Approximation -- Consistent Approximation -- Part IV: Geometric Reasoning -- Geometric Conditioning -- Decision Making with Epistemic Transforms -- Part V The Future of Uncertainty -- An Agenda for the Future -- References.

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.

ISBN: 9783030631536

Standard No.: 10.1007/978-3-030-63153-6doiSubjects--Topical Terms:

587701
Uncertainty (Information theory)

LC Class. No.: Q375

Dewey Class. No.: 003.54

The geometry of uncertainty = the geometry of imprecise probabilities /
LDR:04571nmm a2200337 a 4500 001 2236763
003 DE-He213
005 20201217140830.0
006 m d
007 cr nn 008maaau
008 211111s2021 sz s 0 eng d
020 $a 9783030631536 $q (electronic bk.)
020 $a 9783030631529 $q (paper)
024 7 $a 10.1007/978-3-030-63153-6 $2 doi
035 $a 978-3-030-63153-6
040 $a GP $c GP
041 0 $a eng
050 4 $a Q375
072 7 $a UYQ $2 bicssc
072 7 $a COM004000 $2 bisacsh
072 7 $a UYQ $2 thema
082 0 4 $a 003.54 $2 23
090 $a Q375 $b .C993 2021
100 1 $a Cuzzolin, Fabio. $3 2106834
245 1 4 $a The geometry of uncertainty $h [electronic resource] : $b the geometry of imprecise probabilities / $c by Fabio Cuzzolin.
260 $a Cham : $b Springer International Publishing : $b Imprint: Springer, $c 2021.
300 $a xxv, 850 p. : $b ill., digital ; $c 24 cm.
490 1 $a Artificial intelligence: foundations, theory, and algorithms, $x 2365-3051
505 0 $a Introduction -- Part I: Theories of Uncertainty -- Belief Functions -- Understanding Belief Functions -- Reasoning with Belief Functions -- A Toolbox for the Working Scientist -- The Bigger Picture -- Part II: The Geometry of Uncertainty -- The Geometry of Belief Functions -- Geometry of Dempster's Rule -- Three Equivalent Models -- The Geometry of Possibility -- Part III: Geometry Interplays -- Probability Transforms: The Affine Family -- Probability Transforms: The Epistemic Family -- Consonant Approximation -- Consistent Approximation -- Part IV: Geometric Reasoning -- Geometric Conditioning -- Decision Making with Epistemic Transforms -- Part V The Future of Uncertainty -- An Agenda for the Future -- References.
520 $a 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.
650 0 $a Uncertainty (Information theory) $3 587701
650 1 4 $a Artificial Intelligence. $3 769149
650 2 4 $a Statistical Theory and Methods. $3 891074
650 2 4 $a Probability Theory and Stochastic Processes. $3 891080
710 2 $a SpringerLink (Online service) $3 836513
773 0 $t Springer Nature eBook
830 0 $a Artificial intelligence: foundations, theory, and algorithms. $3 2160111
856 4 0 $u https://doi.org/10.1007/978-3-030-63153-6
950 $a Computer Science (SpringerNature-11645)