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# Fuzzy interval net present value

## Author

Listed:
• Marco Corazza

() (Department of Applied Mathematics, University of Venice)

• Silvio Giove

() (Department of Applied Mathematics, University of Venice)

## Abstract

In this paper we conjugate the operative usability of the net present value with the capability of the fuzzy and the interval approaches to manage uncertainty. 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, at time instants that can also vary. The buyer can reduce the widths of these variations by paying a cost. So, 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 a in [0, 1] associated to the generic cut of the fuzzy interval net present value. As usual, the buyer is characterized by a utility function, depending on a and on the cost, that he/she has to maximize. As far the interest rates regard, we assume that the economic operators are only able to specify a variability range for each of the considered period interest rate. So, we represent the interest rates by means of interval numbers. Besides proposing our model, we formulate and solve the programming problems which have to be coped with to determine the extremals of the cut of the fuzzy interval net present value, and we deal with some questions related to the utility function of the buyer.

## Suggested Citation

• Marco Corazza & Silvio Giove, 2008. "Fuzzy interval net present value," Working Papers 170, Department of Applied Mathematics, Università Ca' Foscari Venezia.
• Handle: RePEc:vnm:wpaper:170
as

File URL: http://virgo.unive.it/wpideas/storage/2008wp170.pdf
File Function: First version, 2008

### Keywords

net present value; fuzzy set theory; interval number theory; alpha-cut; utility function;

### JEL classification:

• C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
• G19 - Financial Economics - - General Financial Markets - - - Other

### NEP fields

This paper has been announced in the following NEP Reports:

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