Keywords: uncertainty, construction project, fuzzy sets theory, fuzzy logic, risk analysis, risk quantitative analysis, fuzzy alpha-cut.

Cost estimating and construction planning are one of the most fundamental aspects for construction projects. The crucial difficulty related to these two processes is related to the uncertainty inherent in dealing with the act of estimation itself. Although, the estimations errors are accepted and appear as cost and duration estimations, yet this acceptance cannot be included above a certain level [1]. This level is usually related to the cost of these errors and the contract strategies that address the penalty against errors in case of occurrence. Despite that, in many cases the degree of these estimation errors could reach an unacceptable level due the nature of work or the nature of the project. In these circumstances these estimation errors could be treated as possible or probable risks [2]. With the increase of the number of the projects, finishing with over run costs and beyond the planned schedule, a new approach is needed to address this issue and to calculate more realistic cost and time estimations regardless the degree of uncertainty involved [3]. With the new contract procedures, the complicated designs and the high technologies more accurate estimations and lower level of errors in these estimations are demanded.

This paper looks at a method for applying fuzzy set theory in cost and duration estimation in order to address the uncertainty encountered in projects activities. The proposed method treats the activity cost and the activity duration as a fuzzy set number where the estimation of each activity duration and cost are represented by a triangular or trapezoidal distribution. As most estimators have a certain degree of certainty in their estimations, an alpha-cut method is applied to simulate the degree of belief in the estimations. The application the alpha-cut technique will lead to the generation of three estimated values i.e. optimistic, most likely and pessimistic. The range between the optimistic and pessimistic values is related to the degree of uncertainty involved in the estimates. However, an analysis study is presented in this paper to illustrate the way the proposed method identifies the link between the triangular or trapezoidal distributions with the alpha-cut method in a way that simulates the estimator's view and the uncertainty inherent in these estimations.

The paper argues that the proposed method is marked by its simplicity as well as its feasibility in application and estimation. In addition, the application of fuzzy set theory is practical and can be easily computerised. Borne out of this research, software has been developed to present a quantitative risk analysis method. An analysis study is presented in this paper to explain the way the proposed Fuzzy Alpha-Cut technique works. The results of the proposed method are comparable and they show the applicability to civil engineering projects. An analytical view is also presented to illustrate the new classifications for possible and probable risks in the civil engineering industry.

1

Perry J.G., Hayes R.W., "Risk and its Management in Construction Projects", Proc. of the institution of Civil Engineers. Engineering Management Group, Thomas Telford: London, pp. 499-521, 1985.

2

El-Cheikh M., Lamb J., "Risk Analysis between Possible and Probable", Proc. of the Int. Conf. of Risk Analysis, eds V. Popov & C.A. Brebbia , WIT: UK , pp. 3-12, 2006.

3

Flanagan R., The Hong Kong Polytechnic University Web Site, Managing Risk for Uncertain Future- A project Management perspective, URL, 2002.

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