This note provides a brief overview of the main ideas and notions underlying fifty years of research in fuzzy set and possibility theory, two important settings introduced by L. A. Zadeh for representing sets with unsharp boundaries and uncertainty induced by granules of information expressed with words. The discussion is organized on the basis of three potential understanding of the grades of ...

Survey of the mathematical models proposed to represent quantified beliefs, and their comparison. The models considered are separated into non standard probability and non probability models, according to the fact they are based on probability theory or not. The first group concerns the upper and lower probability models, the second the possibility theory and the transferable belief model.

When there is uncertainty about the values of a variable, it is possible to have different pieces of information about it. This can be due to the fact that they represent the points of view of different agents and these agents have followed different criteria when codify the pieces of information by means of numbers. The aim of this paper is to provide tools for the comparison of these represen...

Providing cognitive assistance in smart homes is a field of research that receives a lot of attention lately. In order to give adequate assistance at the opportune moment, we need to recognize the observed behavior when the patient carries out some activities in a smart home. To address this challenging issue, we present a formal activity recognition framework based on possibility theory. We pr...

Why do languages have the semantic categories they do? Each language partitions human experience into a system of semantic categories, labeled by words or morphemes, which are used to communicate about experience. These categories often differ widely across languages. Thus, languages do not merely provide different labels for the same universally shared set of categories—instead, both the label...

This paper presents and discusses several methods for reasoning from inconsistent knowledge bases. A so-called argumentative-consequence relation, taking into account the existence of consistent arguments in favor of a conclusion and the absence of consistent arguments in favor of its contrary, is particularly investigated. Flat knowledge bases, i.e. without any priority between their elements,...

Negotiation plays a key role as a means for sharing information and resources with the aim of looking for a common agreement. This paper proposes a new approach based on possibility theory, which integrates both the merits of argumentation-based negotiation and of heuristic methods looking for making trade-offs. Possibilistic logic is used as a unified setting, which proves to be convenient not...

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...

Possibilistic causal models have been proposed as an approach for prediction and diagnosis based on uncertain causal relations. However, the only way to develop the causal models is to acquire the possibilistic knowledge from the experts. The paper proposes an approach to develop the models from a dataset including causes and effects. It first develops a probabilistic causal model, then transfo...

Graphical belief models are compact and powerful tools for representing and reasoning under uncertainty. Possibilistic networks are graphical belief models based on possibility theory. In this paper, we address reasoning under uncertain inputs in both quantitative and qualitative possibilistic networks. More precisely, we first provide possibilistic counterparts of Pearl’s methods of virtual ev...