Numerical possibility distributions can encode special convex families of probability measures. The connection between possibility theory and probability theory is potentially fruitful in the scope of statistical reasoning when uncertainty due to variability of observations should be distinguished from uncertainty due to incomplete information. This paper proposes an overview of numerical possi...

In this paper, we extend the domains of affirmation and negation operators, and more important, of triangular (semi)norms and (semi)conorms from the unit interval to bounded partially ordered sets. The fundamental properties of the original operators are proven to be conserved under this extension. This clearly shows that they are essentially based upon order-theoretic notions. Consequently, a ...

Our paper deals with the necessary properties in Fuzzy Measures. Therefore, it belongs to Fuzzy Mathematical Analysis. The Possibility Theory was created by Zadeh in a paper of 1978. As general purpose, to obtain a way to model flexible restrictions constructed from vague pieces of information. If we study the counterparts of expectations (from Probability Theory) in Possibility Theory, we obta...

This paper is a reply to Laviolette and Seaman’s critical discussion of fuzzy set theory. Rather than questioning the interest of the Bayesian approach to uncertainty, some reasons why Bayesian find the idea of a fuzzy set not palatable are laid bare. Some links between fuzzy sets and probability that Laviolette and Seaman seem not to be aware of are pointed out. These links suggest that, contr...

If an agent desires that φ and desires that ψ, this agent often also desires that φ and ψ hold at the same time (φ∧ψ). However, there are cases where φ ∧ ψ may be found less satisfactory for the agent than each of φ or ψ alone. This paper is a first attempt at modeling such nonmonotonic desires. The approach is developed in the setting of possibility theory, since it has been recently pointed o...

Preferences and uncertainty occur in many real-life problems. The theory of possibility is one non-probabilistic way of dealing with uncertainty, which allows for easy integration with fuzzy preferences. In this paper we consider an existing technique to perform such an integration and, while following the same basic idea, we propose various alternative semantics which allow us to observe both ...

A fuzzy morphological approach is here presented to retrieve structural properties of images considered as fuzzy sets. The basic concepts of the possibility theory and of the mathematical morphology are brieey illustrated, together with their suggested integration. Some applications to astronomical images are also shown.

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.

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...