Abstract: In this study entropy, cross-entropy and discrimination information measures of stochastic intuitionistic fuzzy sets which result from hesitancy and randomness are proposed. It is an extension of De Luca and Termini’s formula for SIFSs. It is also intended to extend the measures proposed by Vlachos and Sergiadis. We will prove that in special cases these measures lead to the same results as the measures proposed by others. We also suggest the application of these measures in image processing in future researches.