Robust optimization with scenarios using random fuzzy sets

In this paper a robust optimization problem with uncertain objective function is considered. The uncertainty is modeled by specifying a scenario set, containing a finite number of objective function coefficients, called scenarios. Additional knowledge in scenario set can be represented by using a mass function defined on the power set of scenarios. This mass function defines a belief function, which in turn induces a family of probability distributions in scenario set. One can then use a generalized Hurwicz criterion, i.e. a convex combination of the upper and lower expectations, to solve the uncertain problem. Recently, possibility theory has been applied to extend the model of uncertainty based on belief functions. Namely, belief function can be induced by a random fuzzy set. In this paper we show how this generalized model can be applied to robust optimization.

Automated summary

This paper discusses a robust optimization problem with uncertain objective function, modeling uncertainty by specifying a scenario set and using a mass function. A generalized Hurwicz criterion is used to solve the uncertain problem. Recently, possibility theory has been applied to extend the model of uncertainty based on belief functions.