On extreme points of p-boxes and belief functions
نویسندگان
چکیده
منابع مشابه
Extreme Points of Vector Functions
Several previous investigations have appeared in the literature which discuss the nature of the set T in »-dimensional space spanned by the vectors ifsdui, ■ ■ ■ , fsdp.n) where 5 ranges over all measurable sets. It was first shown by Liapounov that xi ui, • • ■ , un are atomless measures, then the set F is convex and closed. Extensions of this result were achieved by D. Blackwell [l] and Dvore...
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We give necessary and sufficient conditions for a maxitive function to be the upper probability of a bivariate p-box, in terms of its associated possibility distribution and its focal sets. This allows us to derive conditions in terms of the lower and upper distribution functions of the bivariate p-box. In particular, we prove that only bivariate p-boxes with a non-informative lower or upper di...
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Abstract: Uncertain information about a system variable described by a random set or an equivalent Dempster-Shafer structure on a finite space of singletons determines an infinite convex set of probability distributions, given by the convex hull of a finite set of extreme distributions. Extreme distributions allow one to evaluate (through the Choquet integral) exact upper/lower bounds of the ex...
متن کاملThe starlikeness, convexity, covering theorem and extreme points of p-harmonic mappings
The main aim of this paper is to introduce three classes $H^0_{p,q}$, $H^1_{p,q}$ and $TH^*_p$ of $p$-harmonic mappings and discuss the properties of mappings in these classes. First, we discuss the starlikeness and convexity of mappings in $H^0_{p,q}$ and $H^1_{p,q}$. Then establish the covering theorem for mappings in $H^1_{p,q}$. Finally, we determine the extreme points of the class $TH^*_{p}$.
متن کامل$L_{p}$ Consonant Approximations of Belief Functions
In this paper we solve the problem of approximating a belief measure with a necessity measure or “consonant belief function” in a geometric framework. Consonant belief functions form a simplicial complex in both the space of all belief functions and the space of all mass vectors: partial approximations are first sought in each component of the complex, while global solutions are selected among ...
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ژورنال
عنوان ژورنال: Annals of Mathematics and Artificial Intelligence
سال: 2017
ISSN: 1012-2443,1573-7470
DOI: 10.1007/s10472-017-9562-x