Sklar’s theorem is an important tool that connects bidimensional distribution functions with their marginals by means of a copula. When there is imprecision about the marginals, we can model the available information by means of pboxes, that are pairs of ordered distribution functions. Similarly, we can consider a set of copulas instead of a single one. We study the extension of Sklar’s theorem...

This paper continues an investigation into the merits of an alternative approach to the statistical evaluation of quality-control rules. In this report, computer simulation is used to evaluate and compare quality-control rules designed to detect increases in within-run or between-run imprecision. When out-of-control conditions are evaluated in terms of their impact on total analytical imprecisi...

Many aspects of social welfare are intrinsically multidimensional. Composite indices attempting to reduce this complexity to a unique measure abound in many areas of economics and public policy. Comparisons based on such measures depend, sometimes critically, on how the different dimensions of performance are weighted. Thus, a policy maker maker may wish to take into account imprecision over co...

Numerical possibility theory, belief function have been suggested as useful tools to represent imprecise, vague or incomplete information. They are particularly appropriate in uncertainty analysis where information is typically tainted with imprecision or incompleteness. Based on their experience or their knowledge about a random phenomenon, experts can sometimes provide a class of distribution...

One of the objectives of the authors’ studies on the monitoring of agricultural practices is to deal with imperfect spatial and quantitative information, and to always associate a quality evaluation with acquired or computed data from each location in the territory being studied. In order to produce quantitative information for each location and to consider the imprecision of data, this paper i...

I this note we consider five different relevant problems in AI and machine learning. We argue that possible solutions to such problems might be achieved by replacing the probability distributions in the systems with sets of them. Such a robust approach is based on the so-called impreciseprobabilistic framework. The proposed solutions provide a persuasive justification of the imprecise framework...

This paper presents a non exhaustive list of different methods of uncertainty propagation when the knowledge of some parameters of physical models is represented by probability measures, and others by possibility measures or belief functions.

We define fuzzy constraint networks and prove a theorem about their relationship to fuzzy logic. Then we introduce Khayyam, a fuzzy constraint-based programming language in which any sentence in the first-order fuzzy predicate calculus is a well-formed constraint statement. Finally, using Khayyam to address an equipment selection application, we illustrate the expressive power of fuzzy constrai...

Alternative definitions of Process Capability Indices (PCIs), based on different approaches, have been proposed in literature. Most of the research works related to Process Capability Indices assume no gauge measurement errors. However, in industrial applications, despite the use of highly advanced measuring instruments, account needs to be taken of gauge imprecision. The aim of this paper is f...

The success and the failure of a data warehouse (DW) project are mainly related to the design phase according to most researchers in this domain. When analyzing the decision-making system requirements, many recurring problems appear and requirements modeling difficulties are detected. Also, we encounter the problem associated with the requirements expression by non-IT professionals and non-expe...