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 (, , ) where is the states (or parameters) space, the set of available decisions and is a family of real valued functions defined on and expressing numerically the consequences of choosing when the state is . The set is regarded as a subset of the space of all real valued functions on endowed with the topology of pointwise convergence.As for as admissibility is concerned all the pertinent information about decisions are contained in the corresponding functionsW .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.
Lavoro svolto nell'ambito del Gruppo Nazionale per l'Analisi Funzionale e le sue Applicazioni del C.N.R. 相似文献
It is known that in Decision Theory under Uncertainty the notion of admissibility and almost-admissibility plays an important role since it does not depend properly on the chosen optimality criterion. The main goal of the known notions of ε-admissibility is to conveniently enlarge the class of the admissible decision rules, which for some problems can be empty. Once observed that the notion of ε-equivalence between two decision rules is based on the fact that the decision are “close” each other, it is then natural to study the notion of ε-equivalence in a topological context. Here the functional space of the loss functions associated to the class of the decision rules is equipped with the product topology which the functional space is naturally endoved of. It this framework it is possible to study the notion of almost-admissibility independently of the characteristics of the states space. The known definitions of ε-admissibility are then reduced to particular cases of this more general approach.
Lavoro eseguito nell’ambito del Gruppo Nazionale per l’Analisi Funzionale e le sue Applicazioni del C.N.R. 相似文献
This study discusses how the role of entrepreneurship in addressing the so-called “grand challenges” (e.g., poverty, inequality, pollution, climate change) is evolving and could further evolve, based on the ongoing conversation in the scholarly community. To develop the discussion, we conducted the following steps: (1) a computer-aided semantic analysis; (2) an analysis of the evolution of literature streams; and (3) a network analysis of advocated theories and approaches. All three analyses were based on a selection of 358 publications retrieved via a keyword search and 27 further publications retrieved via an analysis of five recent and relevant special issues published by important scientific journals. Our results show that the call to address grand challenges, particularly after the publication of the United Nations’ Sustainable Development Goals (SDGs), is radically transforming entrepreneurship research, with new issues emerging and replacing traditional issues as core to the discipline, marking a rapid and complex dynamics of research stream divergence and convergence. Similarly, the network of theories and approaches advocated by recent agenda-setting articles depicts an emerging theoretical landscape that is highly innovative. This new theoretical landscape revolves around systems thinking and Ostrom’s theory of the commons as the two key poles, with the embeddedness, stakeholder, institutional, effectuation, processual, and design-oriented approaches being the cross-fertilizing forces linking these two poles. In the final section, we present the nine articles included in the special issue titled “Grand Challenges and Entrepreneurship: Emerging Issues and Research Streams” and briefly synthesize these in the light of the ongoing evolution of the literature.
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