We show that analogously to classical probability theory the conditional expectation E ( ? ~ X ) of a fuzzy random variable Y w.r.t. a fuzzy random variable X is w.r.t. a suitable metric the best approximation o f ? by measurable functions ofX. Furthermore, several linear regression functions, i.e. best approximation of ? by linear functions o f z and examples for random LR-fuzzy numbers and Ga...

This paper presents an approach to the allocation of surplus and profit loads to different product lines or policies within a single insurance company. The method presented calculates the allocation for each line based on the expected value conditional on the full surplus being exhausted. The use of conditional expectations produces a familiar variance-based allocation for a number of specific ...

Given uncertainty in the input model and parameters of a simulation study, the goal of the simulation study often becomes the estimation of a conditional expectation. The conditional expectation is expected performance conditional on the selected model and parameters. The distribution of this conditional expectation describes precisely, and concisely, the impact of input uncertainty on performa...