Abstract
This research deals with problems of the criticality of paths in networks with generalized precedence relations (GPRs) and imprecise activity and time lag durations, represented by means of interval or fuzzy numbers. So far, these problems have been considered when networks have classical finish-start precedence relations by several authors. However, in practice it is often necessary to specify other than the finish-start precedence relations. Proposed theorems ascertain whether a given path is necessarily critical, possibly critical or necessarily non-critical in interval-valued networks with GPRs. The results are extended to networks with fuzzy activity and time lag durations and novel linear programming models are proposed to calculate the degree of necessity and possibility that a given path is critical.
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