A Counterexample to the Forward Recursion in Fuzzy Critical Path
  Analysis Under Discrete Fuzzy Sets
  Fuzzy logic is an alternate approach for quantifying uncertainty relating to
activity duration. The fuzzy version of the backward recursion has been shown
to produce results that incorrectly amplify the level of uncertainty. However,
the fuzzy version of the forward recursion has been widely proposed as an
approach for determining the fuzzy set of critical path lengths. In this paper,
the direct application of the extension principle leads to a proposition that
must be satisfied in fuzzy critical path analysis. Using a counterexample it is
demonstrated that the fuzzy forward recursion when discrete fuzzy sets are used
to represent activity durations produces results that are not consistent with
the theory presented. The problem is shown to be the application of the fuzzy
maximum. Several methods presented in the literature are described and shown to
provide results that are consistent with the extension principle.
