A New Analysis of Critical Paths in Mega Projects with Interval Type-2 Fuzzy Activities by Considering Time, Cost, Risk, Quality, and Safety Factors

Document Type : Original Manuscript


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

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


Critical path method (CPM) is categorized as a popular tool for scheduling mega projects. In this paper, to enjoy the advantages of interval type-2 fuzzy sets (IT2FSs) and better address uncertainty for the activities’ attributes, a new analysis model is presented to determine the critical path under an IT2F-environment. Also, new efficient factors on specifying critical paths, such as time, cost, risk, safety, and quality (TCRSQ), are presented to achieve a more robust plan assisting in megaproject success. Moreover, an IT2F weighting approach is suggested for specifying the weights of TCRSQ factors. Furthermore, a new IT2F-approach employing the relative preference relation is expressed for identifying the importance of each expert. Consequently, a new model for critical path determination procedure by considering efficient factors is developed under the IT2FSs environment. Finally, to demonstrate the suggested model's capability and the calculation process, an application from the previous research is solved.

Graphical Abstract

A New Analysis of Critical Paths in Mega Projects with Interval Type-2 Fuzzy Activities by Considering Time, Cost, Risk, Quality, and Safety Factors


  • IT2FSs are used in critical path analysis of mega projects to better address the uncertainty.
  • A new method to determine each decision maker's weight is introduced by using RPR developed by IT2FSs.
  • A new extension of the analysis model under an IT2F-environment is presented for the critical path analysis.
  • A new development of the entropy method under the IT2F-environment is expressed to specify the weight of several important factors, like TCRSQ.


Amiri, M., & Golozari, F. (2011). Application of fuzzy multi-attribute decision making in determining the critical path by using time, cost, risk, and quality criteria. International Journal of Advanced Manufacturing Technology, 54(1), 393-401.
Amiri, M., Zandieh, M., Vahdani, B., Soltani, R. and Roshanaei, V., (2010). An integrated eigenvector–DEA–TOPSIS methodology for portfolio risk evaluation in the FOREX spot market. Expert systems with applications, 37(1),  509-516.
Castro, J. R., Castillo, O., Melin, P., & Rodríguez-Díaz, A. (2009). A hybrid learning algorithm for a class of interval type-2 fuzzy neural networks. Information Sciences, 179(13), 2175-2193.
Chanas, S., & Zieliński, P. (2001). Critical path analysis in the network with fuzzy activity times. Fuzzy sets and systems, 122(2), 195-204.
Chen, S. M., & Lee, L. W. (2010). Fuzzy multiple attributes group decision-making based on the ranking values and the arithmetic operations of interval type-2 fuzzy sets. Expert Systems with applications, 37(1), 824-833.
Chen, S. P. (2007). Analysis of critical paths in a project network with fuzzy activity times. European Journal of Operational Research, 183(1), 442-459.
Chen, S. P., & Hsueh, Y. J. (2008). A simple approach to fuzzy critical path analysis in project networks. Applied Mathematical Modelling, 32(7), 1289-1297.
Dorfeshan, Y., & Mousavi, S.M. (2020). A novel interval type-2 fuzzy decision model based on two new versions of relative preference relation-based MABAC and WASPAS methods (with an application in aircraft maintenance planning). Neural Computing and Applications, 32, 3367–3385.
Dorfeshan, Y., Mousavi, S.M., Vahdani, B., & Siadat, A. (2019). 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, 26(4), 2579-2600.
Dorfeshan, Y., Mousavi, S.M., Zavadskas, E.K., & Antucheviciene, J. (2021). A new enhanced ARAS method for critical path selection of engineering projects with interval type-2 fuzzy sets. International Journal of Information Technology & Decision Making, 20(1), 37–65.
Eshghi, A., Mousavi, S.M., & Mohagheghi, V., (2019). A new interval type-2 fuzzy approach for analyzing and monitoring the performance of megaprojects based on earned value analysis (with a case study), Neural Computing and Applications, 31, 5109–5133.
Foroozesh, N., Tavakkoli-Moghaddam, R., Mousavi, S. M., & Vahdani, B. (2019). A new comprehensive possibilistic group decision approach for resilient supplier selection with mean–variance–skewness–kurtosis and asymmetric information under interval-valued fuzzy uncertainty. Neural Computing and Applications, 31(11), 6959-6979.
Foroozesh, N., Tavakkoli-Moghaddam, R., & Mousavi, S. M. (2017). Resilient supplier selection in a supply chain by a new interval-valued fuzzy group decision model based on possibilistic statistical concepts. Journal of Industrial and Systems Engineering, 10(2), 113-133.
Foroozesh, N., Tavakkoli-Moghaddam, R., & Mousavi, S. M. (2018). A novel group decision model based on mean–variance–skewness concepts and interval-valued fuzzy sets for a selection problem of the sustainable warehouse location under uncertainty. Neural Computing and Applications, 30(11), 3277-3293.
Gitinavard, H., Mousavi, S.M. and Vahdani, B., (2017a). Soft computing-based new interval-valued hesitant fuzzy multi-criteria group assessment method with last aggregation to industrial decision problems. Soft Computing, 21(12),  3247-3265.
Gitinavard, H., Mousavi, S.M. and Vahdani, B., (2017b). Soft computing based on hierarchical evaluation approach and criteria interdependencies for energy decision-making problems: A case study. Energy, 118,  556-577.
Haghighi, M.H., Mousavi, S.M., & Mohagheghi, V., (2019). A new soft computing model based on linear assignment and linear programming technique for multidimensional analysis of preference with interval type-2 fuzzy sets, Applied Soft Computing, 77, 780–796.
Hillier F.S., G.J. Liebermann. (2001). Introduction to Operations Research, seventh edition, McGraw Hill, Singapore.
Jammeh, E. A., Fleury, M., Wagner, C., Hagras, H., & Ghanbari, M. (2009). Interval type-2 fuzzy logic congestion control for video streaming across IP networks. IEEE Transactions on Fuzzy Systems, 17(5), 1123-1142.
Kaur, P., & Kumar, A. (2014). Linear programming approach for solving fuzzy critical path problems with fuzzy parameters. Applied Soft Computing, 21, 309-319.
Kiracı, K., & Akan, E. (2020). Aircraft selection by applying AHP and TOPSIS in interval type-2 fuzzy sets. Journal of Air Transport Management, 89, 101-114.
Krajewski L.J., L.P. Ritzman (2005). Operations Management: Process and Value chains, seventh edition, Prentice-Hill, New Jersey, 2005.
Kurihara, K., & Nishiuchi, N. (2002). Efficient Monte Carlo simulation method of GERT-type network for project management. Computers & Industrial Engineering, 42(2), 521-531.
Liang, Q., & Mendel, J. M. (2000). Interval type-2 fuzzy logic systems: theory and design. IEEE Transactions on Fuzzy systems, 8(5), 535-550.
Liang, S. K., Yang, K. L., & Chu, P. (2004). Analysis of fuzzy multiobjective programming to CPM in project management. Journal of Statistics and Management Systems, 7(3), 597-609.
Liao, T. W. (2015). Two interval type 2 fuzzy TOPSIS material selection methods. Materials & Design, 88, 1088-1099.
Liu, P., & Gao, H. (2020). A novel green supplier selection method based on the interval type-2 fuzzy prioritized choquet bonferroni means. IEEE/CAA Journal of Automatica Sinica, Article in press, Doi: 10.1109/JAS.2020.1003444.
Madhuri, K. U., Siresha, S., & Shankar, N. R. (2012). A new approach for solving fuzzy critical path problem using LL fuzzy numbers. Applied Mathematical Sciences, 6(27), 1303-1324.
Mehlawat, M. K., & Gupta, P. (2016). A new fuzzy group multi-criteria decision making method with an application to the critical path selection. The International Journal of Advanced Manufacturing Technology, 83(5-8), 1281-1296.
Mendel, J. M., & Wu, H. (2006). Type-2 fuzzistics for symmetric interval type-2 fuzzy sets: Part 1, forward problems. IEEE Transactions on Fuzzy Systems, 14(6), 781-792.
Mendel, J. M., John, R. I., & Liu, F. (2006). Interval type-2 fuzzy logic systems made simple. IEEE transactions on fuzzy systems, 14(6), 808-821.
Mohagheghi, V., & Mousavi, S.M., (2019). An analysis approach to handle uncertain multi-criteria group decision problems in the framework of interval type-2 fuzzy sets theory, Neural Computing and Applications, 31(8),  3543–3557.
Mohagheghi, V., Mousavi, S.M. and Vahdani, B., (2015). A new optimization model for project portfolio selection under interval-valued fuzzy environment. Arabian Journal for Science and Engineering, 40(11),  3351-3361.
Mohagheghi, V., Mousavi, S.M. and Vahdani, B., (2017). Analyzing project cash flow by a new interval type-2 fuzzy model with an application to construction industry. Neural Computing and Applications, 28(11),  3393-3411.
Mon, D. L., Cheng, C. H., & Lu, H. C. (1995). Application of fuzzy distributions on project management. Fuzzy sets and systems, 73(2), 227-234.
Moradi, N.,  Mousavi, S.M., & Vahdani, B., (2018). An interval type-2 fuzzy model for project-earned value analysis under uncertainty, Journal of Multiple-Valued Logic and Soft Computing, 30, 79–103.
Mousavi, S. M., Antuchevičienė, J., Zavadskas, E. K., Vahdani, B., & Hashemi, H. (2019). A new decision model for cross-docking center location in logistics networks under interval-valued intuitionistic fuzzy uncertainty. Transport, 34(1), 30-40.
Mousavi, S.M. and Vahdani, B., (2016). Cross-docking location selection in distribution systems: a new intuitionistic fuzzy hierarchical decision model. International Journal of computational intelligence Systems, 9(1),  91-109.
Mousavi, S.M., Vahdani, B., Tavakkoli-Moghaddam, R. and Tajik, N., (2014). Soft computing based on a fuzzy grey group compromise solution approach with an application to the selection problem of material handling equipment. International Journal of Computer Integrated Manufacturing, 27(6), 547-569.
Mousavi, S.M., Vahdani, B., Tavakkoli-Moghaddam, R., Ebrahimnejad, S. and Amiri, M., (2013). A multi-stage decision-making process for multiple attributes analysis under an interval-valued fuzzy environment. The International Journal of Advanced Manufacturing Technology, 64(9-12),  1263-1273.
Nasir, D., McCabe, B., & Hartono, L. (2003). Evaluating risk in construction–schedule model (ERIC–S): construction schedule risk model. Journal of construction engineering and management, 129(5), 518-527.
Ock, J. H., & Han, S. H. (2010). Measuring risk-associated activity’s duration: A fuzzy set theory application. KSCE Journal of Civil Engineering, 14(5), 663-671.
San Cristobal, J. R. (2012). Critical path definition using multicriteria decision making: PROMETHEE method. Journal of Management in Engineering, 29(2), 158-163.
Sari, I. U., & Kahraman, C. (2015). Interval type-2 fuzzy capital budgeting. International Journal of Fuzzy Systems, 17(4), 635-646.
Shukla, A. K., & Muhuri, P. K. (2019). General type-2 fuzzy decision making and its application to travel time selection. Journal of Intelligent & Fuzzy Systems, 36(6), 5227-5244.
Vahdani, B. and Zandieh, M., (2010). Selecting suppliers using a new fuzzy multiple criteria decision model: the fuzzy balancing and ranking method. International Journal of Production Research, 48(18),  5307-5326.
Vahdani, B., Mousavi, S.M. and Ebrahimnejad, S., (2014). Soft computing-based preference selection index method for human resource management. Journal of Intelligent & Fuzzy Systems, 26(1),  393-403.
Vahdani, B., Razmi, J. and Tavakkoli-Moghaddam, R., (2012). Fuzzy possibilistic modeling for closed loop recycling collection networks. Environmental Modeling & Assessment, 17(6), pp.623-637.
Vahdani, B., Zandieh, M. and Roshanaei, V., (2011). A hybrid multi-stage predictive model for supply chain network collapse recovery analysis: a practical framework for effective supply chain network continuity management. International Journal of Production Research, 49(7),  2035-2060.
Yılmaz, H., & Kabak, Ö. (2020). Prioritizing distribution centers in humanitarian logistics using type-2 fuzzy MCDM approach. Journal of Enterprise Information Management, 33(5), 1199-1232.
Zadeh, L. A. (1965). Fuzzy sets. Information and control, 8(3), 338-353.
Zadeh, L. A. (1975). The concept of a linguistic variable and its application to approximate reasoning—I. Information sciences, 8(3), 199-249.
Zadeh, L. A. (1978). Fuzzy sets as a basis for a theory of possibility. Fuzzy sets and systems, 1(1), 3-28.
Zammori, F. A., Braglia, M., & Frosolini, M. (2009). A fuzzy multi-criteria approach for critical path definition. International Journal of Project Management, 27(3), 278-291.
Zamri, N., & Abdullah, L. (2013). A new linguistic variable in interval type-2 fuzzy entropy weight of a decision making method. Procedia Computer Science, 24, 42-53.
Zareei, A., Zaerpour, F., Bagherpour, M., Noora, A. A., & Vencheh, A. H. (2011). A new approach for solving fuzzy critical path problem using analysis of events. Expert Systems with Applications, 38(1), 87-93.
Zhang, Z., & Zhang, S. (2013). A novel approach to multi attribute group decision making based on trapezoidal interval type-2 fuzzy soft sets. Applied Mathematical Modelling, 37(7), 4948-4971.