Extreme lower probabilities

• Published in: Fuzzy sets and systems Vol. 159; no. 16; pp. 2163 - 2175
• Main Authors: Quaeghebeur, Erik, de Cooman, Gert
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier B.V 16-08-2008; Elsevier
• Subjects: Applied sciences; Circuit properties; Combinatorial problems; Computer science; control theory; systems; Control theory. Systems; Digital circuits; Electric, optical and optoelectronic circuits; Electronic circuits; Electronics; Exact sciences and technology; Extreme points; Imprecise probabilities; Information, signal and communications theory; Lower probabilities; Mathematical methods; Miscellaneous; Non-additive measures; System theory; Telecommunications and information theory; Theoretical computing; 14N10; Lower probabilities; Non-additive measures; 52B11; Extreme points; 60A99; Combinatorial problems; Imprecise probabilities; Engineering; Fuzzy system; 14N10;52B11;60A99; Permutation; Combinatorial problem; Information processing; Lower probabilities; Extreme points; Imprecise probabilities; Non-additive measures; Combinatorial problems; Probability distribution; Fuzzy set
• ISSN: 0165-0114; 1872-6801
• DOI: 10.1016/j.fss.2007.11.020

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:
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.