Purpose: When performing uncertainty propagation, most LCA practitioners choose to represent uncertainties by single probability distributions and to propagate them using stochastic methods. However the selection of single probability distributions appears often arbitrary when faced with scarce information or expert judgement (epistemic uncertainty). Possibility theory has been developed over t...

Abstract: Uncertain information about a system variable described by a random set or an equivalent Dempster-Shafer structure on a finite space of singletons determines an infinite convex set of probability distributions, given by the convex hull of a finite set of extreme distributions. Extreme distributions allow one to evaluate (through the Choquet integral) exact upper/lower bounds of the ex...

Cluster analysis is a tool for data analysis. It is a method for finding clusters of a data set with most similarity in the same group and most dissimilarity between different groups. In general, there are two ways, mixture distributions and classification maximum likelihood method, to use probability models for cluster analysis. However, the corresponding probability distributions to most clus...

Design optimization is an important engineering design activity. Performing design optimization in the presence of uncertainty has been an active area of research. The approaches used require modeling the random variables using precise probability distributions or representing uncertain quantities as fuzzy sets. This work, however, considers problems in which the random variables are described ...

Dubois and Prade defined an interval-valued expectation of fuzzy numbers, viewing them as consonant random sets. Carlsson and Fullér defined an interval-valued mean value of fuzzy numbers, viewing them as possibility distributions. In this paper we shall introduce the notation of weighted interval-valued possibilistic mean value of fuzzy numbers and investigate its relationship to the interval-...

In real problems, there are basically two kind of uncertainty: uncertainty due to the lack of knowledge with respect to well defined objects, but for which there are different hypothetical situations, and uncertainty due to the intrinsic vagueness of the objects. Traditionally, the first type of uncertainty has been studied with the help of Probability Theory while the second one has used Fuzzy...

The concepts of Soft Computing introduced by Lotfi A. Zadeh in 1991 has integrated different methodologies and approaches, as: fuzzy set theory, fuzzy logic, approximate reasoning, linguistic expression of knowledge, probabilistic reasoning, and others for solving problems of complex systems in the way similar to human perception, recognition and solving problem methods. Linguistic fuzzy modell...

In risk analysis, the treatment of the epistemic uncertainty associated to the probability of occurrence of an event is fundamental. Traditionally, probabilistic distributions have been used to characterize the epistemic uncertainty due to imprecise knowledge of the parameters in risk models. On the other hand, it has been argued that in certain instances such uncertainty may be best accounted ...

Statistical distribution of language structures reflect important regularities controlling informational and psycho-physiological processes, which accompany the generation of verbal language or printed texts. In this paper, fuzzy quantitative models of language statistics are constructed. The suggested models are based on the assumption about a super-position of two kinds of uncertainties: prob...