**3. Fuzzy logic**

good at supplying the required information. Some researchers try to convert experts' knowledge into probabilistic distributions. However, this can lead to pointless and unreliable results since the results are obtained based on experts' subjective judgments and assumptions [4]. Fuzzy Logic has been used successfully

This research proposes a fuzzy Monte Carlo simulation (FMCS) model that pro-

Monte Carlo simulation (MCS), or probability simulation, is a technique used to

In project management, you could use expert knowledge to estimate the time it will take to complete a particular job, you can also estimate the maximum time it might take, in the worst possible case, and the minimum time, in the best possible case. The same could be done for project costs. The Monte Carlo simulation method is used for estimating the output Y of a function (M) with random input variables

vides the capability of considering fuzzy and probabilistic uncertainty simulta-

understand the impact of risk and uncertainty cost, time, and other forecasting models [4]. MCS estimates the expected value based on historical data, or expertise in the field, or experience. While this estimate is useful for creating a model, it contains some intrinsic uncertainties, because it is an estimate of

*The output Y of a function M with random inputs can be calculated using Monte Carlo simulation.*

*A probability density function (PDF) developed based on historical data.*

for representing such uncertainties in experts' judgments [5].

**2. Monte Carlo simulation**

unknown values [4].

**Figure 1.**

**Figure 2.**

**172**

(R1, R2, … , Rn) (**Figure 1**).

neously to help improve decisions regarding crew configurations.

*Concepts, Applications and Emerging Opportunities in Industrial Engineering*

Fuzzy logic is a technique that offers a clear conclusion from unclear and inaccurate data. The Fuzzy Set concept was first introduced by Zadeh in 1965 [7]. He was inspired by witnessing that human thinking could utilize ideas that do not have precise borders [8]. Fuzzy logic and fuzzy hybrid methods have been used to capture and model risk, thereby improving workforce and project management [8]. Fuzzy logic can effectively capture expert knowledge and engineering judgment and combine these subjective elements with project data to improve construction decision making, performance, and productivity [9]. The triangular fuzzy number (TFN) is a common shape of fuzzy logic (**Figure 3**). The α-cut method is a common technique to do arithmetic operations on a Triangular Membership Function [10]. The α-cut signifies the degree of risk that the project managers are ready to take (i.e., no risk to full risk). Because the value of α could significantly affect the solution, it should be wisely chosen by project managers [11].

**Figure 3.** *Triangular fuzzy set developed based on experts' judgment.*
