Applying two definitions of the union of IF-events, P. Grzegorzewski gave two generalizations of the inclusion-exclusion principle for IF-events.In this paper we prove an inclusion-exclusion principle for IF-states based on a method which can also be used to prove Grzegorzewski's inclusion-exclusion principle for probabilities on IF-events.Finally, we give some applications of this principle by...

applying two definitions of the union of if-events, p. grzegorzewski gave two generalizations of the inclusion-exclusion principle for if-events.in this paper we prove an inclusion-exclusion principle for if-states based on a method which can also be used to prove grzegorzewski's inclusion-exclusion principle for probabilities on if-events.finally, we give some applications of this principle by...

Applying two definitions of the union of IF-events, P. Grzegorzewski gave two generalizations of the inclusion-exclusion principle for IF-events. In this paper we prove an inclusion-exclusion principle for IF-states based on a method which can also be used to prove Grzegorzewski’s inclusion-exclusion principle for probabilities on IF-events. Finally, we give some applications of this principle ...

ABSTRACT. Inspired by the article of P. Grzegorzewski [The inclusion-exclusion principle for IF-events, Inform. Sci. 181 (2011), 536–546], who has worked two generalizations of the inclusion-exclusion principle for IF-events, a generalization of the inclusion-exclusion principle for mappings with values in semigroups is presented here. The main idea is in replacing the distributivity and idempo...

In this paper, we present improved techniques for computing and getting bounds on the cardinality of a union of sets using the inclusion-exclusion principle and Bonferroni inequalities. We organize the terms involved in the inclusionexclusion sum as a tree, showing that a set inclusion between a parent and its children yields a cancellation, where we may prune an entire subtree. Next, we provid...