Analysis of Possibility Theory for Reasoning under Uncertainty

Algebraic Uncertainty Theory: A Unifying Perspective on Reasoning under Uncertainty

The question of how to represent and process uncertainty is of fundamental importance to the scientific process, but also in everyday life. Currently there exist a lot of different calculi for managing uncertainty, each having its own advantages and disadvantages. Especially, almost all are defining the domain and structure of uncertainty values a priori, e.g., one real number, two real numbers...

Theorem Proving Under Uncertainty - A Possibility Theory-based Approach

Fuzzy relations, Possibility theory, Measures of uncertainty, Mathematical modeling.

A central aim of educational research in the area of mathematical modeling and applications is to recognize the attainment level of students at defined states of the modeling process. In this paper, we introduce principles of fuzzy sets theory and possibility theory to describe the process of mathematical modeling in the classroom. The main stages of the modeling process are represented as fuzz...

Nonmonotonic Reasoning via Possibility Theory

I I I I We introduce the operation of possibility qualification and show how I this modal-like operator can be used to represent "typical" or default knowledge in a theory of nonmonotonic reasoning. We investigate the representational power of this ·approach I by· looking at a number of prototypical problems from the nonmonotoni� reasoning literature. particular we look at the so called Yale sh...

Possibility theory and statistical reasoning

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...