In the first part of this thesis, we first of all present fuzzy logic which models linguistic vagueness that is unusable in classic propositionnal logic. We then take a look at possibility theory which allows to measure the possibility and the certainty of any event regardless its real probability.
In the second part, we focus on the concept of random sequence. We first enumerate different steps that leaded to the present definition and then present Chaitin's constant Omega. Although this number is uncomputable, its decimals form a random sequence that could allow us to solve a lot of mathematical problems.