Choquet integral with stochastic entries

Yann Petot (1) , Pierre Vallois (1) , Alexandre Voisin (2)

1 IECL - Institut Élie Cartan de Lorraine
2 CRAN - Centre de Recherche en Automatique de Nancy

We analyze the probabilistic features of the Choquet integral with respect to a capacity where the inputs are random variables. Only a few papers deal with this issue. We give two different formulas for the density function of the output when the input variables are independent and identically distributed random variables. We also calculate the first moment of the Choquet integral, and we compare our results with the ones obtained in the literature which mainly concerns the cases where the common distribution of the input variables is either uniform or exponential.

Mots clés: exponential distribution; capacity; uniform distribution; Choquet integral; moments; density function

Domaines: Probabilités [math.PR]

Yann Petot, Pierre Vallois, Alexandre Voisin. Choquet integral with stochastic entries. Fuzzy Sets and Systems, 2021, 412, pp.80-94. ⟨10.1016/j.fss.2020.05.012⟩. ⟨hal-01926695⟩