In this paper, one presents how to use a new interval arithmetic framework based on free algebra construction, called pseudo-intervals, which is associative and distributive and permits to build well-defined inclusion function for interval semi-group and for its associated vector space. One introduces the ψ-algorithm (Probabilist Set Inversion), which performs set inversion of functions and exhibits some numerical examples.
Free algebra; pseudo-interval and interval arithmetic; set inversion; probability
