"An Example for Dealing with the Impreciseness of Future Cash Flows
During the Selection of Economic Alternatives"
Inter'l Journal of Industrial Engineering:
Applications and Practice,
Vol. 6, No. 1, March, pp. 38-47, (1999).
Salvador Nieto Sanchez, T. Warren Liao,
Thomas G. Ray, and Evangelos Triantaphyllou
An accurate estimation of future cash flows is a crux for
decision makers during the selection of economic alternatives.
Often, such estimations are imprecise because decision makers do
not posses enough knowledge about the future events that may
affect the cash flows. Usually, such estimations are secured
either by pure human intuition, statistical methodologies (e.g.,
regression analysis), or combinations of these. Regardless of
the data source, the risk of an alternative is measured by the
dispersion (i.e., variance) of the cash flow estimations
(Fabrycky et al. 1998). The measure of this risk is possible
because cash flows estimations are often assumed to be normally
distributed and rely on the Central Limit Theorem (Taha 1997).
This paper presents an approach of how to deal with the
imprecision of future cash flows that do not rely on the above
theorem. The approach deals with the selection of economic
alternatives when cash flows are modeled as triangular fuzzy
numbers and the internal rate of return is used as the criterion
decision. Although the example presented in this paper considered
a symmetric imprecision (or vagueness) about the most promising
value of the cash flows, a more realistic situation can be easily
modeled by using asymmetry on the cash flows.
This paper illustrates an application that does not rely on the
central limit theorem to deal with the imprecision of estimated
Fuzzy decision-making, ranking of fuzzy numbers, internal rate of
return, weighted method, Chang's method, Kaufmann and Gupta's