ISSN:
1129-6569
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
,
Economics
Description / Table of Contents:
Abstract In this paper a new characterization of admissibility is given for general decision problems. It is based on an adequate use of the notion of partial admissibility. A general decision problem is usually synthetized by a triplet (Θ, δ, $$\mathcal{W}$$ ) where Г is the states (or parameters) space, Δ the set of available decisions and $$\mathcal{W} = \{ W_\delta ,\delta \in \Delta \} $$ is a family of real valued functions defined on Θ and expressing numerically the consequences of choosing δ when the state is θ. The set $$\mathcal{W}$$ is regarded as a subset of the space $$\mathcal{F}$$ of all real valued functions on Θ endowed with the topology of pointwise convergence. As for as admissibility is concerned all the pertinent information about decisions δ are contained in the corresponding functionsW δ. This allows to introduce a notion of partial admissibility through the neigh-bourhoods of this topology. Admissibile decisions are then shown to be limits of monotone non increasing sequences of partially admissible decisions. Moreover this topological characterization allows to prove the completeness of classes of admissible decisions under “acceptable” systems of conditions which contain as special cases, known results in literature.
Notes:
Abstract In questo lavoro viene fornita una nuova caratterizzazione dell'ammissibilità attraverso un adeguato uso della nozione di ammissibilità parziale. Questa caratterizzazione consente di affrontare le questioni riguardanti la completezza della classe delle decisioni ammissibiliti sotto condizioni «maneggevoli». Fornisce inoltre un approccio unificante al problema della completezza che consente di derivare, come casi particolari, alcuni risultati già noti nella letteratura sull'argomento.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF02092139
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