Uncertainty and Vagueness in Knowledge Based Systems: Numerical Methods

✍ Scribed by Rudolf Kruse, Erhard Schwecke, Jochen Heinsohn (auth.)

• Publisher: Springer-Verlag Berlin Heidelberg
• Year: 1991
• Tongue: English
• Leaves: 494
• Series: Artificial Intelligence
• Edition: 1
• Category: Library

✦ Synopsis

The primary aim of this monograph is to provide a formal framework for the representation and management of uncertainty and vagueness in the field of artificial intelligence. It puts particular emphasis on a thorough analysis of these phenomena and on the development of sound mathematical modeling approaches. Beyond this theoretical basis the scope of the book includes also implementational aspects and a valuation of existing models and systems. The fundamental ambition of this book is to show that vagueness and un­ certainty can be handled adequately by using measure-theoretic methods. The presentation of applicable knowledge representation formalisms and reasoning algorithms substantiates the claim that efficiency requirements do not necessar­ ily require renunciation of an uncompromising mathematical modeling. These results are used to evaluate systems based on probabilistic methods as well as on non-standard concepts such as certainty factors, fuzzy sets or belief functions. The book is intended to be self-contained and addresses researchers and practioneers in the field of knowledge based systems. It is in particular suit­ able as a textbook for graduate-level students in AI, operations research and applied probability. A solid mathematical background is necessary for reading this book. Essential parts of the material have been the subject of courses given by the first author for students of computer science and mathematics held since 1984 at the University in Braunschweig.

✦ Table of Contents

Front Matter....Pages i-xi
General Considerations of Uncertainty and Vagueness....Pages 1-8
Introduction....Pages 9-27
Vague Data....Pages 29-44
Probability Theory....Pages 45-83
Random Sets....Pages 85-117
Mass Distributions....Pages 119-178
On Graphical Representations....Pages 179-209
Modeling Aspects....Pages 211-223
Heuristic Models....Pages 225-259
Fuzzy Set Based Models....Pages 261-277
Reasoning with L -Sets....Pages 279-298
Probability Based Models....Pages 299-370
Models Based on the Dempster-Shafer Theory of Evidence....Pages 371-414
Reasoning with Mass Distributions....Pages 415-445
Related Research....Pages 447-453
Back Matter....Pages 455-494

✦ Subjects

Artificial Intelligence (incl. Robotics); Probability Theory and Stochastic Processes; Statistics, general; Systems Theory, Control; Calculus of Variations and Optimal Control; Optimization; Operations Research/Decision Theory