Fuzzy interval net present value

The evaluation of investment projects is an ever-present problem in everyday firm life and in several economic research fields. In this paper we propose a model in which we conjugate the operative usability of the net present value with the capability of the fuzzy and the interval approaches to manage uncertainty. In particular, our fuzzy interval net present value can be interpreted, besides the usual present value of an investment project, also as the present value of a contract in which the buyer lets the counterpart the possibility to release goods/services for money amounts that can vary in prefixed intervals, at time instants that can also vary in prefixed intervals. Given this interpretation, it is "natural" to represent the good/service money amounts and the time instants by means of triangular fuzzy numbers, and the cost of the buyer as a strictly-increasing function of the level alpha belonging to [0; 1] associated to the generic cut of the fuzzy interval net present value. In her/his turn, the buyer can reduce the widths of both these kinds of intervals by paying a proper cost. Of course, the buyer is characterized by an utility function that, in our case, depends on the features of the net present value of the contract and negatively depends on the cost. So, the buyer has to determine the optimal value of ® which maximizes her/his utility. As far the interest rates regard, noticing that usually the economic operators are ignorant of the future, we assume that they are only able to specify a variability range for each of the considered time period interest rate. This is why we represent the interest rates by means of interval numbers. Besides proposing our model, we formulate and solve the nonlinear optimization programming problems which have to be coped with in order to determine the extremals of the generic cut of the fuzzy interval net present value, and deal with some questions related to the utility function of the buyer.

The evaluation of investment projects is an ever-present problem in firm life and in several economic research fields. In this paper we propose a model in which we conjugate the operative usability of the net present value with the capability of the fuzzy and the interval approaches to manage uncertainty. In particular, our fuzzy interval net present value can be interpreted, besides the usual present value of an investment project, as the present value of a contract in which the buyer lets the counterpart the possibility to release goods/services for money amounts that can vary in prefixed intervals, at time instants that can also vary in prefixed intervals. In her/his turn, the buyer can reduce the widths of both these kinds of intervals by paying a proper cost. Given this interpretation, it is “natural” to represent the good/service money amounts and the time instants by means of triangular fuzzy numbers, and the cost of the buyer as a strictly-increasing function of the level α ∈ [0, 1] associated to the generic cut of the fuzzy interval net present value. Of course, the buyer is characterized by an utility function that, in our case, depends on the features of the net present value of the contract and on the cost. So, the buyer has to determine the optimal value of α which maximizes her/his utility. As far the interest rates regard, noticing that usually the economic operators are ignorant of the future, we assume that they are only able to specify a variability range for each of the considered period interest rate. This is why we represent the interest rates by means of interval numbers. Besides proposing our model, we formulate and solve the nonlinear optimization programming problems which have to be coped with in order to determine the extremals of the generic cut of the fuzzy interval net present value, and we deal with some questions related to the utility function of the buyer.