Lower Previsions

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Lower Previsions

Author : Matthias C. M. Troffaes
Publisher : John Wiley & Sons
ISBN 13 : 1118761138
Total Pages : 594 pages
Book Rating : 4.1/5 (187 download)

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Book Synopsis Lower Previsions by : Matthias C. M. Troffaes

Download or read book Lower Previsions written by Matthias C. M. Troffaes and published by John Wiley & Sons. This book was released on 2014-04-09 with total page 594 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book has two main purposes. On the one hand, it provides a concise and systematic development of the theory of lower previsions, based on the concept of acceptability, in spirit of the work of Williams and Walley. On the other hand, it also extends this theory to deal with unbounded quantities, which abound in practical applications. Following Williams, we start out with sets of acceptable gambles. From those, we derive rationality criteria---avoiding sure loss and coherence---and inference methods---natural extension---for (unconditional) lower previsions. We then proceed to study various aspects of the resulting theory, including the concept of expectation (linear previsions), limits, vacuous models, classical propositional logic, lower oscillations, and monotone convergence. We discuss n-monotonicity for lower previsions, and relate lower previsions with Choquet integration, belief functions, random sets, possibility measures, various integrals, symmetry, and representation theorems based on the Bishop-De Leeuw theorem. Next, we extend the framework of sets of acceptable gambles to consider also unbounded quantities. As before, we again derive rationality criteria and inference methods for lower previsions, this time also allowing for conditioning. We apply this theory to construct extensions of lower previsions from bounded random quantities to a larger set of random quantities, based on ideas borrowed from the theory of Dunford integration. A first step is to extend a lower prevision to random quantities that are bounded on the complement of a null set (essentially bounded random quantities). This extension is achieved by a natural extension procedure that can be motivated by a rationality axiom stating that adding null random quantities does not affect acceptability. In a further step, we approximate unbounded random quantities by a sequences of bounded ones, and, in essence, we identify those for which the induced lower prevision limit does not depend on the details of the approximation. We call those random quantities 'previsible'. We study previsibility by cut sequences, and arrive at a simple sufficient condition. For the 2-monotone case, we establish a Choquet integral representation for the extension. For the general case, we prove that the extension can always be written as an envelope of Dunford integrals. We end with some examples of the theory.

Introduction to Imprecise Probabilities

Author : Thomas Augustin
Publisher : John Wiley & Sons
ISBN 13 : 0470973811
Total Pages : 452 pages
Book Rating : 4.4/5 (79 download)

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Book Synopsis Introduction to Imprecise Probabilities by : Thomas Augustin

Download or read book Introduction to Imprecise Probabilities written by Thomas Augustin and published by John Wiley & Sons. This book was released on 2014-06-03 with total page 452 pages. Available in PDF, EPUB and Kindle. Book excerpt: In recent years, the theory has become widely accepted and has been further developed, but a detailed introduction is needed in order to make the material available and accessible to a wide audience. This will be the first book providing such an introduction, covering core theory and recent developments which can be applied to many application areas. All authors of individual chapters are leading researchers on the specific topics, assuring high quality and up-to-date contents. An Introduction to Imprecise Probabilities provides a comprehensive introduction to imprecise probabilities, including theory and applications reflecting the current state if the art. Each chapter is written by experts on the respective topics, including: Sets of desirable gambles; Coherent lower (conditional) previsions; Special cases and links to literature; Decision making; Graphical models; Classification; Reliability and risk assessment; Statistical inference; Structural judgments; Aspects of implementation (including elicitation and computation); Models in finance; Game-theoretic probability; Stochastic processes (including Markov chains); Engineering applications. Essential reading for researchers in academia, research institutes and other organizations, as well as practitioners engaged in areas such as risk analysis and engineering.

Synergies of Soft Computing and Statistics for Intelligent Data Analysis

Author : Rudolf Kruse
Publisher : Springer Science & Business Media
ISBN 13 : 364233041X
Total Pages : 555 pages
Book Rating : 4.6/5 (423 download)

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Book Synopsis Synergies of Soft Computing and Statistics for Intelligent Data Analysis by : Rudolf Kruse

Download or read book Synergies of Soft Computing and Statistics for Intelligent Data Analysis written by Rudolf Kruse and published by Springer Science & Business Media. This book was released on 2012-09-07 with total page 555 pages. Available in PDF, EPUB and Kindle. Book excerpt: In recent years there has been a growing interest to extend classical methods for data analysis. The aim is to allow a more flexible modeling of phenomena such as uncertainty, imprecision or ignorance. Such extensions of classical probability theory and statistics are useful in many real-life situations, since uncertainties in data are not only present in the form of randomness --- various types of incomplete or subjective information have to be handled. About twelve years ago the idea of strengthening the dialogue between the various research communities in the field of data analysis was born and resulted in the International Conference Series on Soft Methods in Probability and Statistics (SMPS). This book gathers contributions presented at the SMPS'2012 held in Konstanz, Germany. Its aim is to present recent results illustrating new trends in intelligent data analysis. It gives a comprehensive overview of current research into the fusion of soft computing methods with probability and statistics. Synergies of both fields might improve intelligent data analysis methods in terms of robustness to noise and applicability to larger datasets, while being able to efficiently obtain understandable solutions of real-world problems.

Advances in Computational Intelligence, Part III

Author : Salvatore Greco
Publisher : Springer
ISBN 13 : 3642317189
Total Pages : 626 pages
Book Rating : 4.6/5 (423 download)

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Book Synopsis Advances in Computational Intelligence, Part III by : Salvatore Greco

Download or read book Advances in Computational Intelligence, Part III written by Salvatore Greco and published by Springer. This book was released on 2012-07-20 with total page 626 pages. Available in PDF, EPUB and Kindle. Book excerpt: These four volumes (CCIS 297, 298, 299, 300) constitute the proceedings of the 14th International Conference on Information Processing and Management of Uncertainty in Knowledge-Based Systems, IPMU 2012, held in Catania, Italy, in July 2012. The 258 revised full papers presented together with six invited talks were carefully reviewed and selected from numerous submissions. The papers are organized in topical sections on fuzzy machine learning and on-line modeling; computing with words and decision making; soft computing in computer vision; rough sets and complex data analysis: theory and applications; intelligent databases and information system; information fusion systems; philosophical and methodological aspects of soft computing; basic issues in rough sets; 40th anniversary of the measures of fuziness; SPS11 uncertainty in profiling systems and applications; handling uncertainty with copulas; formal methods to deal with uncertainty of many-valued events; linguistic summarization and description of data; fuzzy implications: theory and applications; sensing and data mining for teaching and learning; theory and applications of intuitionistic fuzzy sets; approximate aspects of data mining and database analytics; fuzzy numbers and their applications; information processing and management of uncertainty in knowledge-based systems; aggregation functions; imprecise probabilities; probabilistic graphical models with imprecision: theory and applications; belief function theory: basics and/or applications; fuzzy uncertainty in economics and business; new trends in De Finetti's approach; fuzzy measures and integrals; multicriteria decision making; uncertainty in privacy and security; uncertainty in the spirit of Pietro Benvenuti; coopetition; game theory; probabilistic approach.

Foundations of Reasoning under Uncertainty

Author : Bernadette Bouchon-Meunier
Publisher : Springer
ISBN 13 : 3642107281
Total Pages : 272 pages
Book Rating : 4.6/5 (421 download)

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Book Synopsis Foundations of Reasoning under Uncertainty by : Bernadette Bouchon-Meunier

Download or read book Foundations of Reasoning under Uncertainty written by Bernadette Bouchon-Meunier and published by Springer. This book was released on 2010-01-11 with total page 272 pages. Available in PDF, EPUB and Kindle. Book excerpt: Uncertainty exists almost everywhere, except in the most idealized situations; it is not only an inevitable and ubiquitous phenomenon, but also a fundamental sci- ti?c principle. Furthermore, uncertainty is an attribute of information and, usually, decision-relevant information is uncertain and/or imprecise, therefore the abilities to handle uncertain information and to reason from incomplete knowledge are c- cial features of intelligent behaviour in complex and dynamic environments. By carefully exploiting our tolerance for imprecision and approximation we can often achieve tractability, robustness, and better descriptions of reality than traditional - ductive methods would allow us to obtain. In conclusion, as we move further into the ageofmachineintelligence,theproblemofreasoningunderuncertainty,in other words, drawing conclusions from partial knowledge, has become a major research theme. Not surprisingly,the rigoroustreatment of uncertaintyrequiressophisticated - chinery, and the present volume is conceived as a contribution to a better und- standing of the foundations of information processing and decision-making in an environment of uncertainty, imprecision and partiality of truth. This volume draws on papers presented at the 2008 Conference on Information Processing and Management of Uncertainty (IPMU), held in Malaga, ́ Spain, or- nized by the University of Mal ́ aga. The conference brought together some of the world’s leading experts in the study of uncertainty.

Uncertainty in Engineering

Author : Louis J. M. Aslett
Publisher : Springer Nature
ISBN 13 : 3030836401
Total Pages : 148 pages
Book Rating : 4.0/5 (38 download)

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Book Synopsis Uncertainty in Engineering by : Louis J. M. Aslett

Download or read book Uncertainty in Engineering written by Louis J. M. Aslett and published by Springer Nature. This book was released on 2022 with total page 148 pages. Available in PDF, EPUB and Kindle. Book excerpt: This open access book provides an introduction to uncertainty quantification in engineering. Starting with preliminaries on Bayesian statistics and Monte Carlo methods, followed by material on imprecise probabilities, it then focuses on reliability theory and simulation methods for complex systems. The final two chapters discuss various aspects of aerospace engineering, considering stochastic model updating from an imprecise Bayesian perspective, and uncertainty quantification for aerospace flight modelling. Written by experts in the subject, and based on lectures given at the Second Training School of the European Research and Training Network UTOPIAE (Uncertainty Treatment and Optimization in Aerospace Engineering), which took place at Durham University (United Kingdom) from 2 to 6 July 2018, the book offers an essential resource for students as well as scientists and practitioners.

Symbolic and Quantiative Approaches to Resoning with Uncertainty

Author : Linda C. van der Gaag
Publisher : Springer
ISBN 13 : 3642390919
Total Pages : 546 pages
Book Rating : 4.6/5 (423 download)

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Book Synopsis Symbolic and Quantiative Approaches to Resoning with Uncertainty by : Linda C. van der Gaag

Download or read book Symbolic and Quantiative Approaches to Resoning with Uncertainty written by Linda C. van der Gaag and published by Springer. This book was released on 2013-07-04 with total page 546 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the refereed proceedings of the 12th European Conference on Symbolic and Quantitative Approaches to Reasoning with Uncertainty, ECSQARU 2013, held in Utrecht, The Netherlands, in July 2013. The 44 revised full papers presented were carefully reviewed and selected from 89 submissions. Papers come from researchers interested in advancing the technology and from practitioners using uncertainty techniques in real-world applications. The scope of the ECSQARU conferences encompasses fundamental issues, representation, inference, learning, and decision making in qualitative and numeric uncertainty paradigms.

Combining Soft Computing and Statistical Methods in Data Analysis

Author : Christian Borgelt
Publisher : Springer Science & Business Media
ISBN 13 : 3642147461
Total Pages : 640 pages
Book Rating : 4.6/5 (421 download)

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Book Synopsis Combining Soft Computing and Statistical Methods in Data Analysis by : Christian Borgelt

Download or read book Combining Soft Computing and Statistical Methods in Data Analysis written by Christian Borgelt and published by Springer Science & Business Media. This book was released on 2010-10-12 with total page 640 pages. Available in PDF, EPUB and Kindle. Book excerpt: Over the last forty years there has been a growing interest to extend probability theory and statistics and to allow for more flexible modelling of imprecision, uncertainty, vagueness and ignorance. The fact that in many real-life situations data uncertainty is not only present in the form of randomness (stochastic uncertainty) but also in the form of imprecision/fuzziness is but one point underlining the need for a widening of statistical tools. Most such extensions originate in a "softening" of classical methods, allowing, in particular, to work with imprecise or vague data, considering imprecise or generalized probabilities and fuzzy events, etc. About ten years ago the idea of establishing a recurrent forum for discussing new trends in the before-mentioned context was born and resulted in the first International Conference on Soft Methods in Probability and Statistics (SMPS) that was held in Warsaw in 2002. In the following years the conference took place in Oviedo (2004), in Bristol (2006) and in Toulouse (2008). In the current edition the conference returns to Oviedo. This edited volume is a collection of papers presented at the SMPS 2010 conference held in Mieres and Oviedo. It gives a comprehensive overview of current research into the fusion of soft methods with probability and statistics.

Reflections on the Foundations of Probability and Statistics

Author : Thomas Augustin
Publisher : Springer Nature
ISBN 13 : 3031154363
Total Pages : 350 pages
Book Rating : 4.0/5 (311 download)

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Book Synopsis Reflections on the Foundations of Probability and Statistics by : Thomas Augustin

Download or read book Reflections on the Foundations of Probability and Statistics written by Thomas Augustin and published by Springer Nature. This book was released on 2023-01-14 with total page 350 pages. Available in PDF, EPUB and Kindle. Book excerpt: This Festschrift celebrates Teddy Seidenfeld and his seminal contributions to philosophy, statistics, probability, game theory and related areas. The 13 contributions in this volume, written by leading researchers in these fields, are supplemented by an interview with Teddy Seidenfeld that offers an abbreviated intellectual autobiography, touching on topics of timeless interest concerning truth and uncertainty. Indeed, as the eminent philosopher Isaac Levi writes in this volume: "In a world dominated by Alternative Facts and Fake News, it is hard to believe that many of us have spent our life’s work, as has Teddy Seidenfeld, in discussing truth and uncertainty." The reader is invited to share this celebration of Teddy Seidenfeld’s work uncovering truths about uncertainty and the penetrating insights they offer to our common pursuit of truth in the face of uncertainty.

Computational Intelligence for Knowledge-Based System Design

Author : Eyke Hüllermeier
Publisher : Springer Science & Business Media
ISBN 13 : 3642140483
Total Pages : 786 pages
Book Rating : 4.6/5 (421 download)

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Book Synopsis Computational Intelligence for Knowledge-Based System Design by : Eyke Hüllermeier

Download or read book Computational Intelligence for Knowledge-Based System Design written by Eyke Hüllermeier and published by Springer Science & Business Media. This book was released on 2010-06-17 with total page 786 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book constitutes the refereed proceedings of the 13th International Conference on Information Processing and Management of Uncertainty in Knowledge-Based Systems, IPMU 2010, held in Dortmund, Germany from June 28 - July 2, 2010. The 77 revised full papers were carefully reviewed and selected from 320 submissions and reflect the richness of research in the field of Computational Intelligence and represent developments on topics as: machine learning, data mining, pattern recognition, uncertainty handling, aggregation and fusion of information as well as logic and knowledge processing.

Advances in Intelligent Computing - IPMU '94

Author : Bernadette Bouchon-Meunier
Publisher : Springer Science & Business Media
ISBN 13 : 9783540601166
Total Pages : 648 pages
Book Rating : 4.6/5 (11 download)

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Book Synopsis Advances in Intelligent Computing - IPMU '94 by : Bernadette Bouchon-Meunier

Download or read book Advances in Intelligent Computing - IPMU '94 written by Bernadette Bouchon-Meunier and published by Springer Science & Business Media. This book was released on 1995-06-26 with total page 648 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a topical selection of full refereed research papers presented during the 5th International Conference on Information Processing and Management of Uncertainty in Knowledge-Based Systems, IPMU '94, held in Paris, France in July 1994. The topical focus is on the role of uncertainty in the contruction of intelligent computing systems and it is shown how the concepts of AI, neural networks, and fuzzy logic can be utilized for that purpose. In total, there are presented 63 thoroughly revised papers organized in sections on fundamental issues; theory of evidence; networks, probabilistic, statistical, and informational methods; possibility theory, logics, chaos, reusability, and applications.

Soft Computing And Its Applications

Author : Rafik Aziz Aliev
Publisher : World Scientific Publishing Company
ISBN 13 : 9813105879
Total Pages : 463 pages
Book Rating : 4.8/5 (131 download)

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Book Synopsis Soft Computing And Its Applications by : Rafik Aziz Aliev

Download or read book Soft Computing And Its Applications written by Rafik Aziz Aliev and published by World Scientific Publishing Company. This book was released on 2001-09-06 with total page 463 pages. Available in PDF, EPUB and Kindle. Book excerpt: The concept of soft computing is still in its initial stages of crystallization. Presently available books on soft computing are merely collections of chapters or articles about different aspects of the field. This book is the first to provide a systematic account of the major concepts and methodologies of soft computing, presenting a unified framework that makes the subject more accessible to students and practitioners. Particularly worthy of note is the inclusion of a wealth of information about neuro-fuzzy, neuro-genetic, fuzzy-genetic and neuro-fuzzy-genetic systems, with many illuminating applications and examples.

Information Processing and Management of Uncertainty in Knowledge-Based Systems

Author : Eyke Hüllermeier
Publisher : Springer
ISBN 13 : 3642140556
Total Pages : 786 pages
Book Rating : 4.6/5 (421 download)

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Book Synopsis Information Processing and Management of Uncertainty in Knowledge-Based Systems by : Eyke Hüllermeier

Download or read book Information Processing and Management of Uncertainty in Knowledge-Based Systems written by Eyke Hüllermeier and published by Springer. This book was released on 2010-06-29 with total page 786 pages. Available in PDF, EPUB and Kindle. Book excerpt: The International Conference on Information Processing and Management of - certainty in Knowledge-Based Systems, IPMU, is organized every two years with the aim of bringing together scientists working on methods for the management of uncertainty and aggregation of information in intelligent systems. Since 1986, this conference has been providing a forum for the exchange of ideas between th theoreticians and practitioners working in these areas and related ?elds. The 13 IPMU conference took place in Dortmund, Germany, June 28–July 2, 2010. This volume contains 79 papers selected through a rigorous reviewing process. The contributions re?ect the richness of research on topics within the scope of the conference and represent several important developments, speci?cally focused on theoretical foundations and methods for information processing and management of uncertainty in knowledge-based systems. We were delighted that Melanie Mitchell (Portland State University, USA), Nihkil R. Pal (Indian Statistical Institute), Bernhard Sch ̈ olkopf (Max Planck I- titute for Biological Cybernetics, Tubing ̈ en, Germany) and Wolfgang Wahlster (German Research Center for Arti?cial Intelligence, Saarbruc ̈ ken) accepted our invitations to present keynote lectures. Jim Bezdek received the Kamp ́ede F ́ eriet Award, granted every two years on the occasion of the IPMU conference, in view of his eminent research contributions to the handling of uncertainty in clustering, data analysis and pattern recognition.

Combining, Modelling and Analyzing Imprecision, Randomness and Dependence

Author : Jonathan Ansari
Publisher : Springer Nature
ISBN 13 : 3031659937
Total Pages : 579 pages
Book Rating : 4.0/5 (316 download)

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Book Synopsis Combining, Modelling and Analyzing Imprecision, Randomness and Dependence by : Jonathan Ansari

Download or read book Combining, Modelling and Analyzing Imprecision, Randomness and Dependence written by Jonathan Ansari and published by Springer Nature. This book was released on with total page 579 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Uncertainty and Intelligent Information Systems

Author : Bernadette Bouchon
Publisher : World Scientific
ISBN 13 : 9812792341
Total Pages : 537 pages
Book Rating : 4.8/5 (127 download)

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Book Synopsis Uncertainty and Intelligent Information Systems by : Bernadette Bouchon

Download or read book Uncertainty and Intelligent Information Systems written by Bernadette Bouchon and published by World Scientific. This book was released on 2008 with total page 537 pages. Available in PDF, EPUB and Kindle. Book excerpt: Intelligent systems are necessary to handle modern computer-based technologies managing information and knowledge. This book discusses the theories required to help provide solutions to difficult problems in the construction of intelligent systems. Particular attention is paid to situations in which the available information and data may be imprecise, uncertain, incomplete or of a linguistic nature. The main aspects of clustering, classification, summarization, decision making and systems modeling are also addressed. Topics covered in the book include fundamental issues in uncertainty, the rapidly emerging discipline of information aggregation, neural networks, Bayesian networks and other network methods, as well as logic-based systems.

Coping with Uncertainty

Author : Kurt Marti
Publisher : Springer Science & Business Media
ISBN 13 : 3642037356
Total Pages : 280 pages
Book Rating : 4.6/5 (42 download)

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Book Synopsis Coping with Uncertainty by : Kurt Marti

Download or read book Coping with Uncertainty written by Kurt Marti and published by Springer Science & Business Media. This book was released on 2009-12-24 with total page 280 pages. Available in PDF, EPUB and Kindle. Book excerpt: Support for addressing the on-going global changes needs solutions for new scientific problems which in turn require new concepts and tools. A key issue concerns a vast variety of irreducible uncertainties, including extreme events of high multidimensional consequences, e.g., the climate change. The dilemma is concerned with enormous costs versus massive uncertainties of extreme impacts. Traditional scientific approaches rely on real observations and experiments. Yet no sufficient observations exist for new problems, and "pure" experiments, and learning by doing may be expensive, dangerous, or impossible. In addition, the available historical observations are often contaminated by past actions, and policies. Thus, tools are presented for the explicit treatment of uncertainties using "synthetic" information composed of available "hard" data from historical observations, the results of possible experiments, and scientific facts, as well as "soft" data from experts' opinions, and scenarios.

The Geometry of Uncertainty

Author : Fabio Cuzzolin
Publisher : Springer Nature
ISBN 13 : 3030631532
Total Pages : 850 pages
Book Rating : 4.0/5 (36 download)

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Book Synopsis The Geometry of Uncertainty by : Fabio Cuzzolin

Download or read book The Geometry of Uncertainty written by Fabio Cuzzolin and published by Springer Nature. This book was released on 2020-12-17 with total page 850 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.