Determining project characteristics and critical path by a new approach based on modified NWRT method and risk assessment under an interval type-2 fuzzy environment

Document Type : Article


1 Department of Industrial Engineering, Faculty of Engineering, Shahed University, Tehran, Iran

2 Department of Industrial Engineering, Faculty of Industrial and Mechanical Engineering, Qazvin Branch, Islamic Azad University, Qazvin, Iran

3 Full professor, LCFC, Arts et Métier Paris Tech, Centre de Metz, Metz, France


In this paper with respect to the importance of risks in real-world projects and ability of interval type-2 fuzzy sets (IT2FSs) to tackle the uncertainty, a new approach is introduced to consider risks and the correlation among risk factors by subjective judgments of experts on the probability and impact under IT2FSs. Furthermore, a new impact function for considering the correlation among the risk factors are extended under an IT2F environment. Moreover, a new subtraction operator is introduced for the critical path analysis. The node-weighted rooted tree (NWRT) method is modified based on the proposed new operator to avoid producing negative number for characteristics of each activity. Also, in order to cope with the uncertainty of the projects, NWRT method is developed under the IT2FSs. Eventually, to illustrate the validity and capability of the proposed method, two examples from the literature are solved and compared.


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