Fuzzy analytical solution for activity duration estimation under uncertainty

Document Type


Publication Date



Visual and Built Environments

Publication Title

ASCE-ASME Journal of Risk and Uncertainty in Engineering Systems, Part A: Civil Engineering


The dynamic nature of construction projects triggers uncertainty in activity durations. Several approaches such as interval analysis, probabilistic models, and fuzzy set theory have been proposed in the literature to address this uncertainty and provide more realistic duration estimates. However, difficulties in defining the boundaries of duration intervals in the presence of uncertainty and unavailability of historical data make the fuzzy set theory an effective alternative. Despite the potency of fuzzy set theory in providing a systematic tool to address the uncertainty caused by incomplete or ill-defined data, its application in activity duration estimation is very limited. This limitation mainly stems from the complexity of fuzzy calculations and lack of a precise analytical solution for the fuzzy weighted average. To address this gap, this paper presents a fuzzy analytical solution with a concise structure and efficient computation process to estimate the activity durations under uncertainty. The developed model generates a set of risk-related duration modifiers by considering the dependency and combinatory effect of different risk factors. Experts' confidence level has been modeled using interval-valued fuzzy numbers and an analytical solution based on the Karnik-Mendel (KM) algorithm has been employed to calculate the fuzzy weighted average. The advantages of this approach compared to existing models are (1) considering the dependency and combinatory effect of risk factors on activity durations, (2) accounting for uncertainty in experts' evaluations by employing the interval-valued fuzzy numbers, and (3) avoiding the creation of incorrect membership functions by using an analytical solution rather than a discrete algorithm to calculate the fuzzy weighted average. To elaborate the model, a simulated bridge project and four risk factors affecting activity durations have been presented. Applying the proposed methodology, a set of duration modifiers to calculate the optimistic, most likely, and pessimistic duration values for each activity under uncertainty are calculated. Compared to similar approaches, the resultant modified durations are more reliable since the combinatory effect of risk factors and the uncertainty of decision makers are taken into consideration.

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