A mathematical theory of evidence pdf download

With numerous examples of applications, this book provides a comprehensive treatment of the RFV approach to uncertainty that is suitable for any graduate student or researcher with interests in the measurement field. The main problem addressed by this work is how to model and combine bodies of knowledge or evidence while maintaining the representation of the unkowledge and of the conflict among the bodies.

The book includes a foreword reflecting the development of the theory in the last forty years. This book brings together a collection of classic research papers on the Dempster-Shafer theory of belief functions.

A Mathematical Theory of Hints. Lecture Notes in Economics and Mathematical Systems, vol. For senior and graduate level courses in the sociology of social change and sociology of development as well as courses in economic and public administration. In a seminal paper published in , Dempster has described a rule for combining independent sources of information. This book, a short course and a variety of technical papers are tangible evidence of a successful stay in the UK.

I am also pleased that Professor Bedrikovetsky acted on my suggestion to publish this book with Kluwer as part of the Examines the representation of uncertainty in intelligent systems. Areas covered include fuzzy set theory, probability theory and mathematical theory of evidence. In: Yager, R. Advances in the Dempster-Shafer Theory of Evidence , pp. Kohlas, J. The theory draws on the work of A. Dempster but diverges from Depster's viewpoint by identifying his "lower probabilities" as epistemic probabilities and taking his rule for combining "upper and lower probabilities" as fundamental.

The book opens with a critique of the well-known Bayesian theory of epistemic probability. It then proceeds to develop an alternative to the additive set functions and the rule of conditioning of the Bayesian theory: set functions that need only be what Choquet called "monotone of order of infinity.

This rule, together with the idea of "weights of evidence," leads to both an extensive new theory and a better understanding of the Bayesian theory.

The book concludes with a brief treatment of statistical inference and a discussion of the limitations of epistemic probability. Appendices contain mathematical proofs, which are relatively elementary and seldom depend on mathematics more advanced that the binomial theorem. The reader benefits from a new approach to uncertainty modeling which extends classical probability theory.

The kind of reasoning we are using is composed of two aspects. The first one is inspired from classical reasoning in formal logic, where deductions are made from a knowledge base of observed facts and formulas representing the domain spe cific knowledge. In this book, the facts are the statistical observations and the general knowledge is represented by an instance of a special kind of sta tistical models called functional models. A supplementary downloadable program allows the readers to interact with the proposed approach by generating and combining RFVs through custom measurement functions.

With numerous examples of applications, this book provides a comprehensive treatment of the RFV approach to uncertainty that is suitable for any graduate student or researcher with interests in the measurement field. The main problem addressed by this work is how to model and combine bodies of knowledge or evidence while maintaining the representation of the unkowledge and of the conflict among the bodies. This is a problem with far-reaching applications in many knowledge segments, in particular for the fields of artificial intelligence, product design, decision making, knowledge engineering and uncertain probability.

It must be kept in mind that knowledge based systems depend on algorithms able to relate the inputs of a system to a correct answer coming out of the knowledge-base, and both the inputs and the knowledge-base are subject to information imperfections caused by the unknowledge and the conflict. There are several formalism to deal with knowledge representation and combination, among them the Mathematical Theory of Evidence or Dempster-Shafer Theory.

This work extends the Mathematical Theory of Evidence through the adoption of a new rule for the combination of evidence and a companion set of concepts.

This extension solves the counter-intuitive problems illustrated in the original theory, extends its power of expression and allows the representation of uncertainty in the results.

The representation of uncertainty implies the possibility of its use in decision-making and also makes explicit the relationship between the numeric results achieved and the results from classical probability theory. This is a collection of classic research papers on the Dempster-Shafer theory of belief functions. The book is the authoritative reference in the field of evidential reasoning and an important archival reference in a wide range of areas including uncertainty reasoning in artificial intelligence and decision making in economics, engineering, and management.

The book includes a foreword reflecting the development of the theory in the last forty years. Reasoning under uncertainty is always based on a specified language or for malism, including its particular syntax and semantics, but also on its associated inference mechanism. In the present volume of the handbook the last aspect, the algorithmic aspects of uncertainty calculi are presented.

Theory has suffi ciently advanced to unfold some generally applicable fundamental structures and methods. On the other hand, particular features of specific formalisms and ap proaches to uncertainty of course still influence strongly the computational meth ods to be used. Both general as well as specific methods are included in this volume. Broadly speaking, symbolic or logical approaches to uncertainty and nu merical approaches are often distinguished.

Although this distinction is somewhat misleading, it is used as a means to structure the present volume. This is even to some degree reflected in the two first chapters, which treat fundamental, general methods of computation in systems designed to represent uncertainty. It has been noted early by Shenoy and Shafer, that computations in different domains have an underlying common structure.

Essentially pieces of knowledge or information are to be combined together and then focused on some particular question or domain. This can be captured in an algebraic structure called valuation algebra which is described in the first chapter. Here the basic operations of combination and focus ing marginalization of knowledge and information is modeled abstractly subject to simple axioms.

Examines the representation of uncertainty in intelligent systems. Areas covered include fuzzy set theory, probability theory and mathematical theory of evidence. Statistical Evidence and Belief Functions. In his recent monograph? The mathematical theory of evidence has been introduced by Glenn Shafer in as a new approach to the representation of uncertainty.

This theory can be represented under several distinct but more … Expand. Highly Influenced. View 11 excerpts, cites background and methods. Towards another logical interpretation of Theory of Evidence and a new combination rule. Publisher Summary This chapter focuses on the logical interpretation of the Theory of Evidence and a new combination rule. Theory of Evidence is a mathematical theory, which allows reasoning with … Expand. View 11 excerpts, cites background. Evidence, knowledge, and belief functions.

Dempster's rule of combination. Varieties of Bayesianism. Publisher Summary A Bayesian theory is any theory of non-deductive reasoning that uses the mathematical theory of probability to formulate its rules. Several disagreements are noticed within this … Expand. Quantifying knowledge with a new calculus for belief functions - a generalization of probability theory.