Search

Based on a real-world industrial case-study, the DIDOM project investigates new forms of industrial production strategies, having a dual trade-project structure, and involving distributed decisions, with a view to specify realistic decision-support tools adapted to such contexts. After introducing some features of multi-project management and our methodology, the paper presents the main results achieved in two main areas: on the one hand, the crucial role, in the decision process, of a workplan involving temporal landmarks, its construction and its repair, and, on the other hand, the cooperation procedures appearing in a distributed decision framework.

Tracking malfunctions in reasonable time on an engine dyno test bench is becoming too complex for human beings. An online diagnosis system is being studied for this purpose. Knowledge about possible effects of a malfunction on an attribute and (imprecise) observations are modelled by possibility distributions. Any kind of attributes (binary, numerical, . . .) is allowed. The paper assumes the single-fault hypothesis. Two main indices are respectively used for respectively detecting i) the malfunctions whose presence is more or less inconsistent with the available observations and ii) the malfunctions (most of) all the expected effects of which have been more or less certainly observed (using abduction).

The state of a fuzzy system can be described by fuzzy numbers. For a theory of fuzzy systems to be realistic, weak definitions of reachability, observability, stability must be established. Such concepts stem from basic notions of equality of numbers, and convergence of sequences of numbers. This paper discusses several points of view for natural extensions of these notions to fuzzy numbers. Relaxed versions of equality and convergence are provided. They account for the fact that membership functions of fuzzy numbers can never be precisely estimated.

AND ORGANIZATION OF THE PAPER This short paper deals successively with two important fields of applications of fuzzy set and possibility theory:-data bases with fuzzy information and fuzzy queries-approximate/plausible reasoning in expert systems.

The work reported here focuses on different uncertainty problems encountered in the design of a common interface to various sources of information pertaining to characteristic parameters of classes of objects. The paper more particularly considers i) the problem of producing plausible parameter estimates from incomplete collections of data and expert knowledge for extrapolating missing values ; ii) the evaluation of fuzzy queries pertaining to vaguely specified classes of objects ; iii) the combination of pieces of information issued from the different sources. Fuzzy sets and possibility theory is the framework which is used here for dealing with imprecision and uncertainty.

A fuzzy number is defined as a convex normalized fuzzy set of the real line with an upper semi-continuous membership function. The addition of fuzzy numbers denoted ⊕, and defined via a sup- t-norm convolution is now well-understood from both theoretical and computational points of view, at least for the t-norm ’min’. Moreover, there exists an “inverse”, -A, of a fuzzy number A, i.e. -A restricts the possible values of the variable -u iff A restricts the possible values of u. However, the identify A ⊕ [— A] = 0 does not hold but when A is a genuine real number. Thus, the solution X of the equation of fuzzy numbers : X ⊕ A = B, when it exists, is NOT given by X = B ⊕ [-А].

In a seminal paper, fifteen years ago, Dempster introduced the concepts of upper and lower probabilities by considering a probability space together with a multivalued mapping. In this paper, we study the analogous situation when a possibility space is given and the same multivalued mapping Then, we get upper and lower possibilities. While an upper possibility is still a possibility, a lower possibility is no longer a possibility usually. These concepts are applied to an approximate reasoning problem which turns out to be a “possibilist ic” version of a classical problem dealt with in decision theory .

Relative orders of magnitude of quantities (e.g. a is slightly larger than b, c is negligible in comparison with d, e is close to f) are a kind of partial knowledge which is often available in engineering problems. In this paper we study how to represent this type of information and how to reason with it. Order-of-magnitude relations are modelled by fuzzy relations. This kind of semantics enables us to acknowledge that i) the extent to which two numerical values satisfy such relations is often a matter of degree and is also context-dependent; ii) these relations are often weakly or strongly transitive rather than just transitive in the usual sense. Conclusions can be obtained by composing fuzzy relations representing relative-order-of-magnitude information together, or by propagating these relations through algebraic constraints. A proper choice of the form of the fuzzy relations reduces the composition operations in practice to arithmetic operations on fuzzy numbers which are easy to compute. Rules which enables a formal manipulation of the relations between variables, in agreement with the fuzzy semantics, are derived. This improves approaches to qualitative reasoning problems previously developed in Artificial Intelligence, in a way which better sticks to the semantics of the available information.

An approach based on possibility theory, has been recently proposed by the authors for the representation of precisely, partially or fuzzily known attribute values in relational data bases. A query language, where fuzzy specifications of requested properties or fuzzy comparators are allowed, and which is based on an extended relational algebra, has been developed and implemented. The main characteristics of this approach are first recalled in the paper.