The inclusion–exclusion principle for L-states and IF-events

The principle of inclusion and exclusion for classical sets belongs to the very well-known theorems of combinatorics and probability theory. With the appearance of fuzzy sets and their generalizations it is natural to ask if this principle holds for them as well. It turns out that this is true e.g. for IF-events, which include fuzzy sets as a special case, as it was shown in [8]. In contrast to the mentioned paper we work with L-states and with a wider set of probabilities. As a consequence of this approach we obtain another method for proving the inclusion–exclusion principle for IF-sets.