Extreme lower probabilities
- 作者：Erik Quaeghebeur ; Gert de Cooman
- 关键词：Lower probabilities ; Extreme points ; Imprecise probabilities ; Non-additive measures ; Combinatorial problems
- 刊名：Fuzzy Sets and Systems
- 出版年：2008
- 期刊代码：55_01650114
- 类别：cp
- 出版时间：16 August 2008
- 卷：159
- 期：16
- 页码：2163-2175
- 文件大小：239 K
摘要
We consider lower probabilities on finite possibility spaces as models for the uncertainty about the state. These generalizations of classical probabilities can have some interesting properties; for example: decoration:none; color:black" href="/science?_ob=MathURL&_method=retrieve&_udi=B6V05-4R8MDJK-1&_mathId=mml1&_user=1067359&_cdi=5637&_rdoc=8&_acct=C000050221&_version=1&_userid=10&md5=9a425fa191f8e782510ca0f4b2d20745" title="Click to view the MathML source" alt="Click to view the MathML source">k-monotonicity, avoiding sure loss, coherence, permutation invariance. The sets formed by all the lower probabilities satisfying zero or more of these properties are convex. We show how the extreme points and rays of these sets—the extreme lower probabilities—can be calculated and we give an illustration of our results.