Possibilistic previsions
نویسنده
چکیده
The paper deals with a possibilistic imprecise second-order probability model. It is argued that such models appear naturally in a number of situations. They lead to the introduction of a new type of previsions, called possibilistic previsions, which formally generalise coherent upper and lower previsions. The converse problem is also looked at: given a possibilistic prevision, under what conditions can it be generated by a second-order possibility distribution? This leads to the definition of normality, representability and natural extension of possibilistic previsions. Finally, some attention is paid to the special class of full possibilistic previsions, which can be formally related to Zadeh’s fuzzy probabilities. The results have immediate applicability in decision making and statistical reasoning.
منابع مشابه
Further thoughts on possibilistic previsions: A rejoinder
This is a rejoinder to the comments [19, 20, 22, 27] by a number of authors on my paper [10] about possibilistic previsions. I wish to thank the respondents Serafı́n Moral [19], Romano Scozzafava [20], Lev Utkin [22] and Lotfi Zadeh [27] for their insightful comments on my paper [10]. In this rejoinder, I shall try and address their questions and/or objections individually, and in some detail. L...
متن کاملMaximin and Maximal Solutions for Linear Programming Problems with Possibilistic Uncertainty
We consider linear programming problems with uncertain constraint coefficients described by intervals or, more generally, possibility distributions. The uncertainty is given a behavioral interpretation using coherent lower previsions from the theory of imprecise probabilities. We give a meaning to the linear programming problems by reformulating them as decision problems under such imprecise-pr...
متن کاملEnvelope Theorems and Dilation with Convex Conditional Previsions
This paper focuses on establishing envelope theorems for convex conditional lower previsions, a recently investigated class of imprecise previsions larger than coherent imprecise conditional previsions. It is in particular discussed how the various theorems can be employed in assessing convex previsions. We also consider the problem of dilation for these kinds of imprecise previsions, and point...
متن کاملConvex Imprecise Previsions: Basic Issues and Applications
In this paper we study two classes of imprecise previsions, which we termed convex and centered convex previsions, in the framework of Walley’s theory of imprecise previsions. We show that convex previsions are related with a concept of convex natural estension, which is useful in correcting a large class of inconsistent imprecise probability assessments. This class is characterised by a condit...
متن کاملUncertainty modelling and conditioning with convex imprecise previsions
Two classes of imprecise previsions, which we termed convex and centered convex previsions, are studied in this paper in a framework close to Walley’s and Williams’ theory of imprecise previsions. We show that convex previsions are related with a concept of convex natural estension, which is useful in correcting a large class of inconsistent imprecise probability assessments, characterised by a...
متن کامل