Cardinal-Probabilistic Interaction Indices and their Applications: A Survey

2003 ◽  
Vol 7 (2) ◽  
pp. 79-85 ◽  
Author(s):  
Katsushige Fujimoto ◽  
Keyword(s):  
Choquet Integral ◽  
Axiomatic Characterization ◽  
Probability Measures ◽  
Choice Probability ◽  
Hierarchical Decomposition ◽  
Möbius Transform

The class of cardinal probabilistic interaction indices obtained as expected marginal interactions includes the Shapley, Banzhaf, and chaining interaction indices and the Möbius and co-Möbius transform so. We will survey cardinal-probabilistic interaction indices and their applications, focusing on axiomatic characterization of the class of cardinal-probabilistic interaction indices. We show that these typical cardinal-probabilistic interaction indices can be represented as the Stieltjes integrals with respect to choice-probability measures on [0,1]. We introduce a method for hierarchical decomposition of systems represented by the Choquet integral using interaction indices.

scholarly journals Weighted Regret-Based Likelihood: A New Approach to Describing Uncertainty

2015 ◽  
Vol 54 ◽  
pp. 471-492
Author(s):  
Joseph Y. Halpern
Keyword(s):  
Axiomatic Characterization ◽  
Lower Probability ◽  
Probability Measures ◽  
New Approach ◽  
Upper Probability ◽  
Weighted Probability ◽  
Natural Way

Recently, Halpern and Leung suggested representing uncertainty by a set of weighted probability measures, and suggested a way of making decisions based on this representation of uncertainty: maximizing weighted regret. Their paper does not answer an apparently simpler question: what it means, according to this representation of uncertainty, for an event E to be more likely than an event E'. In this paper, a notion of comparative likelihood when uncertainty is represented by a set of weighted probability measures is defined. It generalizes the ordering defined by probability (and by lower probability) in a natural way; a generalization of upper probability can also be defined. A complete axiomatic characterization of this notion of regret-based likelihood is given.

An Axiomatic Characterization of a Class of Petri Nets

1991 ◽  
Vol 14 (4) ◽  
pp. 477-491
Author(s):  
Waldemar Korczynski
Keyword(s):  
Petri Nets ◽  
Petri Net ◽  
Axiomatic Characterization ◽  
Algebraic Characterization

In this paper an algebraic characterization of a class of Petri nets is given. The nets are characterized by a kind of algebras, which can be considered as a generalization of the concept of the case graph of a (marked) Petri net.

scholarly journals A characterization of the 2-additive Choquet integral through cardinal information

2011 ◽  
Vol 184 (1) ◽  
pp. 84-105 ◽  
Author(s):  
Brice Mayag ◽  
Michel Grabisch ◽  
Christophe Labreuche
Keyword(s):  
Choquet Integral

scholarly journals Axiomatization and Measurement of Quasi-Hyperbolic Discounting *

2014 ◽  
Vol 129 (3) ◽  
pp. 1449-1499 ◽  
Author(s):  
José Luis Montiel Olea ◽  
Tomasz Strzalecki
Keyword(s):  
Hyperbolic Discounting ◽  
Partial Identification ◽  
Axiomatic Characterization ◽  
Discount Factors ◽  
Elasticity Of Intertemporal Substitution ◽  
Trade Offs ◽  
Subject Pool ◽  
Identification Approach ◽  
The Subject

Abstract This article provides an axiomatic characterization of quasi-hyperbolic discounting and a more general class of semi-hyperbolic preferences. We impose consistency restrictions directly on the intertemporal trade-offs by relying on what we call “annuity compensations.” Our axiomatization leads naturally to an experimental design that disentangles discounting from the elasticity of intertemporal substitution. In a pilot experiment we use the partial identification approach to estimate bounds for the distributions of discount factors in the subject pool. Consistent with previous studies, we find evidence for both present and future bias.

scholarly journals Axiomatic characterization of the interval function of a graph

2009 ◽  
Vol 30 (5) ◽  
pp. 1172-1185 ◽  
Author(s):  
Henry Martyn Mulder ◽  
Ladislav Nebeský
Keyword(s):  
Axiomatic Characterization ◽  
Interval Function
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