Random Sets: Theory and Applications

✍ Scribed by John Goutsias (auth.), John Goutsias, Ronald P. S. Mahler, Hung T. Nguyen (eds.)

• Publisher: Springer-Verlag New York
• Year: 1997
• Tongue: English
• Leaves: 416
• Series: The IMA Volumes in Mathematics and its Applications 97
• Edition: 1
• Category: Library

✦ Synopsis

This IMA Volume in Mathematics and its Applications RANDOM SETS: THEORY AND APPLICATIONS is based on the proceedings of a very successful 1996 three-day Summer Program on "Application and Theory of Random Sets." We would like to thank the scientific organizers: John Goutsias (Johns Hopkins University), Ronald P.S. Mahler (Lockheed Martin), and Hung T. Nguyen (New Mexico State University) for their excellent work as organizers of the meeting and for editing the proceedings. We also take this opportunity to thank the Army Research Office (ARO), the Office ofNaval Research (0NR), and the Eagan, MinnesotaEngineering Center ofLockheed Martin Tactical Defense Systems, whose financial support made the summer program possible. Avner Friedman Robert Gulliver v PREFACE "Later generations will regard set theory as a disease from which one has recovered. " - Henri Poincare Random set theory was independently conceived by D.G. Kendall and G. Matheron in connection with stochastic geometry. It was however G.

✦ Table of Contents

Front Matter....Pages i-xiv
Front Matter....Pages 1-1
Morphological Analysis of Random Sets an Introduction....Pages 3-26
Statistical Problems for Random Sets....Pages 27-45
On Estimating Granulometric Discrete Size Distributions of Random Sets....Pages 47-71
Logical Granulometric Filtering in the Signal—Union—Clutter Model....Pages 73-95
On Optimal Filtering of Morphologically Smooth Discrete Random Sets and Related Open Problems....Pages 97-104
Front Matter....Pages 105-105
On the Maximum of Conditional Entropy for Upper/Lower Probabilities Generated by Random Sets....Pages 107-127
Random Sets in Information Fusion an Overview....Pages 129-164
Cramér—Rao Type Bounds for Random Set Problems....Pages 165-183
Random Sets in Data Fusion Multi-Object State-Estimation as a Foundation of Data Fusion Theory....Pages 185-207
Extension of Relational and Conditional Event Algebra to Random Sets with Applications to Data Fusion....Pages 209-242
Belief Functions and Random Sets....Pages 243-255
Front Matter....Pages 257-257
Uncertainty Measures, Realizations and Entropies * ....Pages 259-295
Random Sets in Decision—Making....Pages 297-320
Random Sets Unify, Explain, and Aid Known Uncertainty Methods in Expert Systems....Pages 321-345
Laws of Large Numbers for Random Sets....Pages 347-360
Geometric Structure of Lower Probabilities....Pages 361-383
Some Static and Dynamic Aspects of Robust Bayesian Theory....Pages 385-406
Back Matter....Pages 407-416

✦ Subjects

Probability Theory and Stochastic Processes; Mathematical Logic and Foundations