Representation of IF-probability on MV-algebras

A probability theory on IF-events has been constructed by Grzegorzewski and Mrówka in [2] and axiomatically characterized by B. Riečan in [6]. More general situation was studied by B. Riečan in [5]. He introduced the IF-probability, which is decomposed onto two probabilities on Lukasiewicz tribe. The aim of this paper is to define the IF-probability and IF-observable on MV-algebras. We show that some known results of [7] can be applied also for these IF-events.