An Introduction to Random SetsThe study of random sets is a large and rapidly growing area with connections to many areas of mathematics and applications in widely varying disciplines, from economics and decision theory to biostatistics and image analysis. The drawback to such diversity is that the research reports are scattered throughout the literature, with the result that i |
Contents
| 1 | |
Some Random Sets in Statistics | 15 |
Finite Random Sets | 35 |
Random Sets and Related Uncertainty Measures | 71 |
Random Closed Sets | 109 |
The Choquet Integra | 131 |
Choquet Weak Convergence | 157 |
Some Aspects of Statistical Inference with Coarse Data | 183 |
Appendix Basic Concepts and Results of Probability Theory | 215 |
| 247 | |
| 255 | |
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Common terms and phrases
additive analysis associated Banach space Borel bounded called capacity functional Chapter Choquet clearly coarsening compact concept condition consider containing continuous convergence core(T countable defined definition denote density distribution function entropy equivalent estimation example exists expected fact finite finite set function F given going Hausdorff hence implies increasing infinite order integral interest Lemma maximum mean metric space monotone namely nonempty Note numbers observations obtain open sets possible probability law probability measures probability space problem Proof properties random closed sets random elements random set random variable random vector Remark respect result sample satisfies selection sense sequence set function Show situation Specifically statistical subsets Suppose theorem theory topology values weak convergence
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Page 250 - Interpretation of Membership Functions of Fuzzy Sets in Terms of Plausibility and Belief,