A New Uncertain Modeling of Production Project Time and Cost Based on Atanassov Fuzzy Sets

Document Type: Research Paper


1 Shahed University

2 Faculty of Industrial & Mechanical Engineering, Qazvin Branch, Islamic Azad University


Uncertainty plays a major role in any project evaluation and management process. One of the trickiest parts of any production project work is its cost and time forecasting. Since in the initial phases of production projects uncertainty is at its highest level, a reliable method of project scheduling and cash flow generation is vital to help the managers reach successful implementation of the project. In the recent years, some scholars have tried to address uncertainty of projects in time and cost by using basic uncertainty modeling tools such as fuzzy sets theory. In this paper, a new approach is introduced to model project cash flow under uncertain environments using Atanassov fuzzy sets or intuitionistic fuzzy sets (IFSs). The IFSs are presented to calculate project scheduling and cash flow generation. This modern approach enhances the ability of managers to use their intuition and lack of knowledge in their decision-makings. Moreover, unlike the recent studies in this area, this model uses a more sophisticated tool of uncertain modeling which is highly practical in real production project environments. Furthermore, a new effective IFS-ranking method is introduced. The methodology is exemplified by estimating the working capital requirements in an activity network. The proposed model could be useful for both project proposal evaluation during feasibility studies and for performing earned value analysis for project monitoring and control.


 1. Atanassov, K. T. (2008). My personal view on intuitionistic fuzzy sets theory. InFuzzy Sets and Their Extensions: Representation, Aggregation & Models (pp. 23-43). Springer Berlin Heidelberg.

2. Atanassov, K. T. Intuitionistic fuzzy sets. Central Tech Library, Bulgarian Academy Science, Sofia, Bulgaria, 1983.

3. Atkinson, R., Crawford, L., & Ward, S. (2006). Fundamental uncertainties in projects and the scope of project management. International journal of project management, 24(8), 687-698.

4. Barbosa, P. S., & Pimentel, P. R. (2001). A linear programming model for cash flow management in the Brazilian construction industry. Construction management and Economics, 19(5), 469-479.

5. Bhattacharyya, R. (2015). A Grey Theory Based Multiple Attribute Approach for R&D Project Portfolio Selection.

Fuzzy Information and Engineering, 7(2), 211-225.

6. Blyth, K. & Kaka, A. (2006). A novel multiple linear regression model for forecasting S-curves, Engineering, Construction and Architectural Management, 13(1): 82–95.

7. Boran, F. E., Boran, K., & Menlik, T. (2012). The evaluation of renewable energy technologies for electricity generation in Turkey using intuitionistic fuzzy TOPSIS. Energy Sources, Part B: Economics, Planning, and Policy, 7(1), 81-90.

8. Boussabaine A.H. & Kaka, A. (1998). A neural networks approach for cost-flow forecasting. Construction Management and Economics Journal, 16, 471-479.

9. Caron, F., & Comandulli, M. (2014). A cash flow-based approach for assessing expansion options stemming from project modularity. International Journal of Project Organization and Management, 6(1-2), 157-178.

10. Chai, J., Liu, J. N., & Xu, Z. (2012). A new rule-based SIR approach to supplier selection under intuitionistic fuzzy environments. International Journal of Uncertainty, Fuzziness and Knowledge-based Systems, 20(3), 451-471.

11. Chanas, S., & Kamburowski, J. (1981). The use of fuzzy variables in PERT. Fuzzy sets and systems, 5(1), 11-19.

12. Chen, C. C., & Zhang, Q. (2014). Applying quality function deployment techniques in lead production project selection and assignment. In Advanced Materials Research (Vol. 945, pp. 2954-2959).

13. Chen, H. L., Chen, C. I., Liu, C. H., & Wei, N. C. (2013). Estimating a project's profitability: A longitudinal approach.

International Journal of Project Management, 31(3), 400-410.

14. Cheng, M. Y., & Roy, A. F. (2011). Evolutionary fuzzy decision model for cash flow prediction using time-dependent support vector machines. International Journal of Project Management, 29(1), 56-65.

15. Cheng, M. Y., Hoang, N. D., and Wu, Y. W. (2015). Cash flow prediction for construction project using a novel adaptive time-dependent least squares support vector machine inference model. Journal of Civil Engineering and Management, 21(6), 679-688.

16. Cioffi, D.F., (2005). A tool for managing projects: an analytic parameterization of the S-curve. International Journal of Project Management, 23(3), 215–222.

17. Cooke, B., & Jepson, W. B. (1979). Cost and financial control for construction firms. Macmillan.

18. Deng, H. (2014). Comparing and ranking fuzzy numbers using ideal solutions. Applied Mathematical Modelling, 38(5), 1638-1646.

19. Duong, A. N. (2011). Rate-decline analysis for fracture-dominated shale reservoirs. SPE Reservoir Evaluation and Engineering, 14(3), 377.

20. Gerogiannis, V. C., Fitsilis, P., & Kameas, A. D. (2011). Using a combined intuitionistic fuzzy set-TOPSIS method for evaluating project and portfolio management information systems. In Artificial Intelligence Applications and Innovations (pp. 67-81), Springer Berlin Heidelberg.

21. Gormley, F.M., & Meade, N., 2007. The utility of cash flow forecasts in the management of corporate cash balances.

European Journal of Operational Research 182(2), 923–935 .

22. Hsu, K. (2003). Estimation of a double S-curve model, AACE International Transactions IT13.1– IT13.5.

23. Hwee, N. G. & Tiong, R. L. K., (2002). Model on cash flow forecasting and risk analysis for contracting firms, International Journal of Project Management, 20, 351-363.

24. Jarrah, R., Kulkarni, D., & O’Connor, J.T., (2007). Cash flow projections for selected TxDoT highway projects. Journal of Construction Engineering and Management, 133(3), 235–241.

25. Jiang, A., Issa, R. R., & Malek, M. (2011). Construction project cash flow planning using the Pareto optimality efficiency network model. Journal of Civil Engineering and Management, 17(4), 510-519.

26. Khosrowshahi, F., & Kaka, A. P. (2007). A decision support model for construction cash flow management. ComputerAided Civil and Infrastructure Engineering, 22(7), 527-539.

27. Kumar, V. S., Hanna, A. S., & Adams, T. (2000). Assessment of working capital requirements by fuzzy set theory.

Engineering, Construction and Architectural Management, 7(1), 93-103.

28. Lam, K. C., et al. (2001). An integration of the fuzzy reasoning technique and the fuzzy optimization method in construction project management decision-making. Construction Management and Economics, 19(1), 63-76.

29. Lawson, C. P., Longhurst, P. J., & Ivey, P. C. (2006). The application of a new research and development project selection model in SMEs. Technovation, 26(2), 242-250.

30. Lee F. (1998). Fuzzy information processing system. Peking University Press Inc., 118–132. 31. Li, H., & Yen, V. C. (1995). Fuzzy sets and fuzzy decision-making. CRC press.

32. Liang, C., Zhao, S., & Zhang, J. (2014). Aggregation Operators on Triangular Intuitionistic Fuzzy Numbers and its Application to Multi-Criteria Decision Making Problems. Foundations of Computing and Decision Sciences, 39(3), 189-208.

33. Maravas, A., & Pantouvakis, J. P. (2012). Project cash flow analysis in the presence of uncertainty in activity duration and cost. International journal of project management, 30(3), 374-384.

34. McCahon, C. S., & Lee, E. S. (1988). Project network analysis with fuzzy activity times. Computers & Mathematics with applications, 15(10), 829-838.

35. Mohagheghi, V., Mousavi, S. M., & Vahdani, B. (2015). A new optimization model for project portfolio selection under interval-valued fuzzy environment. Arabian Journal for Science and Engineering, 40, 3351–3361.

36. Mousavi, S. M., Jolai, F., & Tavakkoli-Moghaddam, R. (2013). A fuzzy stochastic multi-attribute group decision-making approach for selection problems. Group Decision and Negotiation, 22(2), 207-233.

37. Neog, T. J., & Sut, D. K. (2011). An application of fuzzy soft sets in medical diagnosis using fuzzy soft complement.

International Journal of Computer Applications, 33(9).

38. Ning, X., Lam, K. C., & Lam, M. C. K. (2011). A decision-making system for construction site layout planning. Automation in Construction, 20(4), 459-473.

39. Prade, H. (1979). Using fuzzy set theory in a scheduling problem: a case study. Fuzzy sets and systems, 2(2), 153-165.

40. Rostamy, A. A., Takanlou, F., & AnvaryRostamy, A. (2013). A fuzzy statistical expert system for cash flow analysis and management under uncertainty. Advances in Economics and Business, 1(2), 89-102.

41. Santamaría, L., Barge-Gil, A., & Modrego, A. (2010). Public selection and financing of R&D cooperative projects: Credit versus subsidy funding. Research Policy, 39(4), 549-563.

42. Shu, M. H., Cheng, C. H., & Chang, J. R. (2006). Using intuitionistic fuzzy sets for fault-tree analysis on printed circuit board assembly. Microelectronics Reliability, 46(12), 2139-2148.

43. Szmidt, E., & Kacprzyk, J. (2001). Intuitionistic fuzzy sets in some medical applications. In Computational Intelligence. Theory and Applications (pp. 148-151). Springer Berlin Heidelberg.

44. Szmidt, E., Kacprzyk, J., & Bujnowski, P. (2014). How to measure the amount of knowledge conveyed by Atanassov’s intuitionistic fuzzy sets. Information Sciences, 257, 276-285.

45. Touran, A., Atgun, M., & Bhurisith, I., (2004). Analysis of the United States department of transportation prompt pay provisions. Journal of Construction Engineering and Management, 130(5), 719–725.

46. Ungureanu, D., & Vernic, R. (2014). On a fuzzy cash flow model with insurance applications. Decisions in Economics and Finance, 1-16.

47. Wang, Y. (2012). An Approach to Software Selection with Triangular Intuitionistic Fuzzy Information. International Journal of Advancements in Computing Technology, 4(2).

48. Xu, Z., & Liao, H. (2014). Intuitionistic Fuzzy Analytic Hierarchy Process, IEEE Transactions on Fuzzy Systems, 22(4),749-761.

49. Zadeh, L. A. (1965). Fuzzy sets. Information and control, 8(3), 338-353.

50. Zimmermann, H. J. (2001).Fuzzy set theoryand its applications. Springer Science & Business Media.