Interval and fuzzy Average Internal Rate of Return for investment appraisal

In investment appraisal, uncertainty can be managed through intervals or fuzzy numbers because the arithmetical properties and the extension principle are well established and can be successfully applied in a rigorous way. We apply interval and fuzzy numbers to the Average Internal Rate of Return (AIRR), recently introduced for overcoming the problems of the traditional Internal Rate of Return (IRR). In the setting of interval and fuzzy arithmetic, we establish relations between the interim capitals invested, the profits and the cash flows, which are the ingredients of the AIRR, and shed lights on the different ways uncertainty propagates depending on which variable is known and which one is derived. The relations between fuzzy AIRR and fuzzy Net Present Value are also investigated.