Optimal boundaries for decisions
In this paper we state and prove some new results on the optimal boundaries. These boundaries (called Pareto boundaries too) are of increasing importance in the applications to Decision Theory. First of all the Pareto boundaries are the first and most important generalization of the concept of optim...
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| Format: | Article |
| Language: | English |
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Accademia Peloritana dei Pericolanti
2008-01-01
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| Series: | Atti della Accademia Peloritana dei Pericolanti : Classe di Scienze Fisiche, Matematiche e Naturali |
| Online Access: | http://dx.doi.org/10.1478/C1A0801002 |
| Summary: | In this paper we state and prove some new results on the optimal boundaries. These boundaries (called Pareto boundaries too) are of increasing importance in the applications to Decision Theory. First of all the Pareto boundaries are the first and most important generalization of the concept of optimum; on the other hand, if f is a real functional defined on a non empty set X and K is a part of X, the determination of the optimal boundaries of the part K with respect to some preorder of X for which f is strictly increasing permits to reduce the optimization problem (f, K, inf) (or (f, K, sup)) to the problem (f, minP(K), inf) (resp. (f, maxP(K), sup)), where by minP(K) we denoted the minimal boundary of K (that in general is greatly smoller than K). |
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| ISSN: | 0365-0359 1825-1242 |