The Inclusion-Exclusion Principle for IF-States

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 extending some results regarding the classical probabilities to the case of the IF-states.

کلیدواژه ها:

IF-set ، IF-event ، IFS-probability ، IF-state ، Inclusion-exclusion principle ، Boole inequality ، Bonferroni inequality ، L ukasiewicz connectives