A review of main methods of the probability theory on IF-events is presented in the case that the used connectives are Lukasiewicz\begin{align}\label{b_1} \nonumber f\oplus g&=(f+g)\wedge 1\,,\\ \nonumber f\odot g&=(f+g-1)\vee 0\,,\end{align}($f$, $g$ are functions, $f,g:\Omega\rightarrow\left\langle 0,1\right\rangle$). Representation theorem for probabilities on IF-events is given. For sequences of independent observables the central limit theorem is presented as well as basic results about conditional expectation. Finally the Lukasiewicz probability theory to the MV-algebra probability theory is embedded.
@article{81,
title = {On the Lukasiewicz probability theory on IF-sets},
journal = {Tatra Mountains Mathematical Publications},
volume = {45},
year = {2010},
doi = {10.2478/tatra.v46i0.81},
language = {EN},
url = {http://dml.mathdoc.fr/item/81}
}
Riečan, Beloslav; Petrovičová, Jozefína. On the Lukasiewicz probability theory on IF-sets. Tatra Mountains Mathematical Publications, Tome 45 (2010) . doi : 10.2478/tatra.v46i0.81. http://gdmltest.u-ga.fr/item/81/