The Inclusion-Exclusion Principle for IF-States

Abstract

Applying two definitions of the union of IF-events, P. Grzegorzewski gave two generalizations of the inclusion-exclusion principle for IF-events.<br />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.<br />Finally, we give some applications of this principle by extending some results regarding the classical probabilities to the case of the IF-states.