In the traditional treatment, risk situations are modeled by random variables. This paper focuses on risk situations described by fuzzy numbers. The goal of the paper is to define and characterize possibilistic risk aversion and study some of its indicators. Key–Words: Possibilistic risk aversion, possibilistic indicators

Possibility measures are interpreted as upper probabilities that are in particular supremum preserving. We define a possibilistic process as a special family of possibilistic variables, and show how its possibility distribution functions can be constructed. We introduce and study the notions of inner and outer regularity for possibility measures. Using these notions, we prove an analogon for po...

Propagating possibilistic and probabilistic variables through a mapping yields a fuzzy random variable. We propose a method to attach probability intervals to events pertaining to the output variable. We show that this method is consistent with classical approaches to fuzzy random variables and that the obtained probability interval is the mean value of the fuzzy probability defined by viewing ...

In this paper, I provide the basis for a measureand integral-theoretic formulation of possibility theory. It is shown that, using a general definition of possibility measures, and a generalization of Sugeno’s fuzzy integral – the seminormed fuzzy integral, or possibility integral –, a unified and consistent account can be given of many of the possibilistic results extant in the literature. The ...

Possibilistic logic bases and possibilistic graphs are two different frameworks of interest for representing knowledge. The former stratifies the pieces of knowledge (expressed by logical formulas) accor?i�g to their level of certainty, while the latter exhibits relationships between variables. The two types of representations are semantically equivalent when they lead to the same possibility d...

Possibility theory was initiated by Zadeh in 1978 as an alternative to probability theory. Probability theory is not efficient in the study of those uncertainty situations in which phenomena occur with a small frequency. In such cases it is preferable to apply techniques offered by possibility theory.In foundation of possibility theory one started on a paralel line with probability theory. Rand...

Like Bayesian networks, possibilistic ones compactly encode joint uncertainty representations over a set of variables. Learning possibilistic networks from data in general and from imperfect or scarce data in particular, has not received enough attention. Indeed, only few works deal with learning the structure and the parameters of a possibilistic network from a dataset. This paper provides a p...

The problem of merging multiple-source uncertain information is a crucial issue in many applications. This paper proposes an analysis of possibilistic merging operators where uncertain information is encoded by means of product-based (or quantitative) possibilistic networks. We first show that the product-based merging of possibilistic networks having the same DAG structures can be easily achie...

In this paper, based on possibilistic reliability theory, the hybrid variables structural reliability model, which includes fuzzy variables and interval variables, is researched. The hybrid variables structural reliability model is established based on possibilistic reliability theory. The analytical algorithms of minimum fuzzy reliability index and maximum failure possibility degree in hybrid ...

In any learning process, the learners arrive with a great deal of variables, such as their different learning styles, their affective states and their previous knowledge, among many others. In most cases, their previous knowledge is incomplete or it comes with a certain degree of uncertainty. Possibilistic Logic was developed as an approach to automated reasoning from uncertain or prioritized i...