RANDOM SETS AND FUZZY INTERVAL-ANALYSIS

A general expression of functions with random set-valued arguments is stated, which encompasses Zadeh's extension principle as well as functions of random variables, and interval analysis. A monotonicity property is derived for algebraic operations performed between random set-valued variables. This property extends the monotonicity of functions with set-valued arguments, in the sense of inclusion. The application of this result to the approximate calculation of functions of random variables is suggested and illustrated by an example.