**A Fuzzy Approach for Risk Analysis with Application in Project Management**

Sina Khanmohammadi1 and Javad Jassbi2

*1Faculty of Science, Technology and Creative Arts, School of Engineering and Technology, University of Hertfordshire, Hertfordshire, 2Department of Industrial Management, Islamic Azad University, Science and Research Branch, Tehran, 1UK 2Iran* 

#### **1. Introduction**

40 Fuzzy Inference System – Theory and Applications

http://63.234.227.130/pls/oshaweb/owadisp.show\_document?p\_table=STANDA

Reason, J. (1997). Managing the risks of organizational accidents, Ashgate Publishing

Turban, E., Aronson, J.& Liang, T.-P. (2004). Decision Support Systems and Intelligent

Turban, E., Sharda, R.& Delen, D. (2010). Decision Support and Business Intelligence

Yager, R. R. (1988). On Ordered Weighted Averaging Aggregation Operators in

Zimmermann, H.-J. (2001). Fuzzy Set Theory and Its Applications, Kluwer Academic

Multicriteria Decison Making. IEEE Transactions on Systems, Man, and

Administration.

Ltd,Aldershot Hants

Systems, Prentice Hall.

Cybernetics 18(1): 183-190.

Systems.

Publishers.

OSHA (2010c). Standard 1926.501: Duty to have fall protection.

Occupational Safety and Health Administration.

ARDS&p\_id=9715. U.S. Department of Labor. Occupational Safety and Health

RDS&p\_id=10757 (accessed in November 2010). U.S. Department of Labor.

The Critical Path Method (CPM) and its development to probabilistic environment, the Program Evaluation and Review Technique (PERT), are the most common tools for predicting and managing different short time or long time projects. However, one of the main difficulties in using mathematical models in real world applications is the vagueness and uncertainty of data and parameters such as activity durations and risky conditions. The constructed network for project management (as a mathematical model) is an aid for control of project implementation with deterministic time durations. However, realization of this approach is difficult in the situation where most of activities will be executed for the first time. One solution offered for this difficulty is the assignment of probabilistic values for estimated durations of activities. In PERT, three estimations called pessimistic, most likely and optimistic values are assigned for each activity. Then the mean duration and its standard deviation are calculated by

$$D = \frac{a + 4m + b}{6} \tag{1}$$

and

$$
\sigma = \frac{b - a}{6} \tag{2}
$$

Where a, m and b are the optimistic, most likely and pessimistic values respectively. D is the expected (weighted mean) duration of activity and σ is the standard deviation of the three values (Kerzner, 2009). The project duration (sum of durations of critical path) is estimated by using the estimated durations of activities. Also, the probability of finishing the project before a predicted time (by using PERT) is calculated based on the standard deviations

A Fuzzy Approach for Risk Analysis with Application in Project Management 43

Fig. 1. Risky situations classified in 4 levels

Fig. 2. Different levels of situations (contours of Fig. 1.)

without considering other real world factors such as probability of impacts on project (such as inflation or stagnation) , impact threat and ability to retaliate. Hence a new approach based on fuzzy inference system and fuzzy decision making is introduced to have more realistic procedure for project management in real world applications. Fuzzy set is introduced by Zadeh in 1965 (Zadeh, 1965). Different applications of fuzzy sets are studied by researches in different fields (Jamshidi et al., 1993). T. J. Ross has published an interesting book on fuzzy sets theory and its applications in engineering (Ross, 2010). Several papers are also published on applications of fuzzy sets in project management (Chanas et al., 2002; Shipley et al, 1997). M. F. Shipley et al. have used the fuzzy logic approach for determining probabilistic fuzzy expected values in a project management application (Shipley et al, 1996). An extension of their method is introduced and used for determination of expected values for estimated delays of activities in (Khanmohammadi et al., 2001). The procedure introduced here deals with defining multi-purpose criticalities for activities where some other features such as probability of impact, impact threat and ability to retaliate are considered as criticality factors of activities in project management process. In this way the risky situations (vulnerabilities) of activities are calculated using a fuzzy inference system which will be used for calculating the risky situation for each activity as a main criticality factor.

Considerable quantitative models have been introduced in literature to calculate the level of risk; which is simply defined as the rate of threat or future deficit of any system imposed by controllable or uncontrollable variables (Chavas, 2004; Doherty, 2000). Several factors such as probability of occurrence, impact threat and ability to retaliate are introduced as affecting factors on the risk. Then it is tried to find the mathematical relation between affecting factors and the value (level) of the risk (Li & Liao, 2007; McNeil et al., 2005). The concept of risk is considerably wide. It can contain strategic, financial, operational or any other type of risk.

The concept of fuzzy risky conditions for activities is introduced in sections 2 and 3. In section 4 the concept of Multi-Critical PERT by considering risky levels for activities is introduced and a typical project network is considered as a case study for analyzing the effect of imposing the risky level of activities to criticality. The results are compared to classic PERT by means of Mont Carlo simulation using random variables. Another typical example, project management of rescue robot that provides preliminary processes for helping injured people before the arrival of rescue teams, is studied in section 5. Analysis of obtained results and conclusions are presented in section 6.
