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020 _a9783030631536
024 7 _a10.1007/978-3-030-63153-6
_2doi
040 _aES-MaUEC
_bspa
_cES-MaUEC
_dES-MaUEC
050 4 _aQ375
_b2021 EB
100 1 _aCuzzolin, Fabio
_eautor
_4http://id.loc.gov/vocabulary/relators/aut
_9678572
245 1 4 _aThe Geometry of Uncertainty :
_bThe Geometry of Imprecise Probabilities
_cby Fabio Cuzzolin
250 _aFirst edition 2021
264 1 _aCham, Switzerland
_bSpringer International Publising
_c2021
300 _a1 recurso en línea (XXV, 850 páginas)
_b140 ilustraciones, 100 ilustraciones a color
336 _2rdacontent
_aTexto
_btxt
337 _2rdamedia
_aelectrónico
_bc
338 _2rdacarrier
_arecurso electrónico
_bcr
347 _atext file
_bPDF
_2rda
490 0 _aArtificial Intelligence: Foundations Theory and Algorithms
_x2365-3051
505 0 _aIntroduction -- 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 3 _aThe 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.
988 _aSpringer_Computer_2021
650 7 _2embne
_aIncertidumbre (Teoría de la información)
_9667868
710 2 _aSpringerLink
776 0 8 _iPrinted edition:
_z9783030631529
776 0 8 _iPrinted edition:
_z9783030631543
776 0 8 _iPrinted edition:
_z9783030631550
856 4 0 _uhttps://go.openathens.net/redirector/universidadeuropea.es?url=https://doi.org/10.1007/978-3-030-63153-6
_zAcceso a este recurso digital (usuarios Universidad Europea de Madrid)
942 _2lcc
_cLE
998 _b05/2021
_dz
_ek
_zSI