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A Generalized Pignistic Transformation
This chapter introduces a generalized pignistic transformation (GPT) developed in the DSmT framework as a tool for decision-making at the pignistic level. The GPT allows to construct quite easily a subjective probability measure from any generalized basic belief assignment provided by any corpus of evidence. We focus our presentation on the 3D case and we provide the full result obtained by the proposed GPT and its validation drawn from the probability theory.
AN INTRODUCTION TO DSMT IN INFORMATION FUSION
The management and combination of uncertain, imprecise, fuzzy and even paradoxical or highly confliicting sources of information has always been, and still remains today, of primal importance for the development of reliable modern information systems involving artificial reasoning. In this introduction, we present a survey of our recent theory of plausible and paradoxical reasoning, known as Dezert-Smarandache Theory (DSmT), developed for dealing with imprecise, uncertain and conflicting sources of information. We focus our presentation on the foundations of DSmT and on its most important rules of combination, rather than on browsing specific applications ofDSmT available in literature. Several simple examples are given throughout this presentation to show the effciency and the generality of this new theory.
Belief Functions in Business Decisions
The book focuses on applications of belief functions to business decisions. Section I introduces the intuitive, conceptual and historical development of belief functions. Three different interpretations (the marginally correct approximation, the qualitative model, and the quantitative model) of belief functions are investigated, and rough set theory and structured query language (SQL) are used to express belief function semantics. Section II presents applications of belief functions in information systems and auditing. Included are discussions on how a belief-function framework provides a more efficient and effective audit methodology and also the appropriateness of belief functions to represent uncertainties in audit evidence. The third section deals with applications of belief functions to mergers and acquisitions; financial analysis of engineering enterprises; forecast demand for mobile satellite services; modeling financial portfolios; and economics.
Decision Making in Uncertain Situations
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 confl...
Classic Works of the Dempster-Shafer Theory of Belief Functions
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.
Representing Uncertain Knowledge
The representation of uncertainty is a central issue in Artificial Intelligence (AI) and is being addressed in many different ways. Each approach has its proponents, and each has had its detractors. However, there is now an in creasing move towards the belief that an eclectic approach is required to represent and reason under the many facets of uncertainty. We believe that the time is ripe for a wide ranging, yet accessible, survey of the main for malisms. In this book, we offer a broad perspective on uncertainty and approach es to managing uncertainty. Rather than provide a daunting mass of techni cal detail, we have focused on the foundations and intuitions behind the various schools. The ...
Qualitative and Quantitative Practical Reasoning
This book constitutes the refereed proceedings of the First International Joint Conference on Qualitative and Quantitative Practical Reasoning, ECSQARU-FAPR'97, held in Bad Honnef, Germany, in June 1997. The volume presents 33 revised full papers carefully selected for inclusion in the book by the program committee as well as 12 invited contributions. Among the various aspects of human practical reasoning addressed in the papers are nonmonotonic logics, default reasoning, modal logics, belief function theory, Bayesian networks, fuzzy logic, possibility theory, inference algorithms, dynamic reasoning with partial models, and user modeling approaches.
Computational Logic: Logic Programming and Beyond
Alan Robinson This set of essays pays tribute to Bob Kowalski on his 60th birthday, an anniversary which gives his friends and colleagues an excuse to celebrate his career as an original thinker, a charismatic communicator, and a forceful intellectual leader. The logic programming community hereby and herein conveys its respect and thanks to him for his pivotal role in creating and fostering the conceptual paradigm which is its raison d’Œtre. The diversity of interests covered here reflects the variety of Bob’s concerns. Read on. It is an intellectual feast. Before you begin, permit me to send him a brief personal, but public, message: Bob, how right you were, and how wrong I was. I sho...
Symbolic and Quantitative Approaches to Uncertainty
A variety of formalisms have been developed to address such aspects of handling imperfect knowledge as uncertainty, vagueness, imprecision, incompleteness, and partial inconsistency. Some of the most familiar approaches in this research field are nonmonotonic logics, modal logics, probability theory (Bayesian and non-Bayesian), belief function theory, and fuzzy sets and possibility theory. ESPRIT Basic Research Action 3085, entitled Defeasible Reasoning and Uncertainty Management Systems (DRUMS), aims to contribute to the elucidation of similarities and differences between these formalisms. It consists of 11 active European research groups. The European Conference on Symbolic and Quantitative Approaches to Uncertainty (ESQAU) provides a forum for these groups to meet and discuss their scientific results. This volume contains 42 contributions accepted for the ESQAU meeting held in October 1991 in Marseille, together with 12 articles presenting the activities of the DRUMS groups and two invited presentations.
Information Algebras
Information usually comes in pieces, from different sources. It refers to different, but related questions. Therefore information needs to be aggregated and focused onto the relevant questions. Considering combination and focusing of information as the relevant operations leads to a generic algebraic structure for information. This book introduces and studies information from this algebraic point of view. Algebras of information provide the necessary abstract framework for generic inference procedures. They allow the application of these procedures to a large variety of different formalisms for representing information. At the same time they permit a generic study of conditional independence, a property considered as fundamental for knowledge presentation. Information algebras provide a natural framework to define and study uncertain information. Uncertain information is represented by random variables that naturally form information algebras. This theory also relates to probabilistic assumption-based reasoning in information systems and is the basis for the belief functions in the Dempster-Shafer theory of evidence.
