Skip to main content
Log in

Realistic solution of fuzzy critical path problems, case study: the airport’s cargo ground operation systems

  • Original Paper
  • Published:
Granular Computing Aims and scope Submit manuscript

Abstract

In fact, this research is executed in an environment where uncertainty is the principal feature of it. One of these uncertainties in the project planning process is estimating the duration of activities. This paper presents a methodology for implementing an extended method of critical path based on the application of fuzzy expert systems to manage schedule uncertainties. To represent the uncertainty involved we have considered the generalized quasi-geometric fuzzy numbers to represent the activity times. Moreover, TA-based fuzzy operations are used to have real solutions for the parameters. Meanwhile, a new approach to ranking generalized quasi-geometric fuzzy numbers and their distance is proposed in detail. Finally, the proposed concepts are applied in the field of critical path analysis and a relevant case study of it is also included to justify the notion.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7

Similar content being viewed by others

Data availability

Data sharing not applicable to this article as no datasets were generated or analyzed during the current study.

References

  • Abbasi F, Allahviranloo T, Abbasbandy S (2015). A new attitude coupled with fuzzy thinking to fuzzy rings and fields. Journal of intelligent fuzzy systems, 29(2)(2):851–861

  • Abbasi F, Allahviranloo T, Abbasbandy S (2016) A new attitude coupled with the basic fuzzy thinking to distance between two fuzzy numbers. Iran J Fuzzy Syst 13(6):21–39

    MathSciNet  MATH  Google Scholar 

  • Adilakshmi S, Shankar N (2021) A new ranking in hexagonal fuzzy number by centroid of centroids and application in fuzzy critical path. Reliability 16(2(62)):124–135

    Google Scholar 

  • Ahmood RZ, Abdulahad FN (2022) Probabilistic approach for identifying longest fuzzy critical path. Al-Nahrain J Sci 25(2):29–33

    Article  Google Scholar 

  • Alizdeh S, Saeidi S (2020) Fuzzy project scheduling with critical path including risk and resource constraints using linear programming. Int J Adv Intell Paradigms 16(1):4–17

    Article  Google Scholar 

  • Ambika G, Nagalakshmi T (2022). Application of pentagonal fuzzy number in cpm and pert network with algorithm. In Proceedings of 2nd International Conference on Mathematical Modeling and Computational Science, https://doi.org/10.1007/978-981-19-0182-9-46

  • Ammar MA, Abdelkhalek SI (2022) Criticality measurement in fuzzy project scheduling. Int J Construction Manag 22(2):252–261

    Article  Google Scholar 

  • Beaula T, Vijaya V (2013) A study on exponential fuzzy numbers using a-cuts. Int J Appl Oper Res 3(2):1–13

    MATH  Google Scholar 

  • Boukezzoula R, Foulloy L, Coquin D, Galichet S (2021) Gradual interval arithmetic and fuzzy interval arithmetic. Granular Comput 6(2):451–471

    Article  MATH  Google Scholar 

  • Chanas S, Zielinski P (2001) Critical path analysis in the network with fuzzy activity times. Fuzzy Sets Syst 122(2):195–204

    Article  MathSciNet  MATH  Google Scholar 

  • Chen SH (1985) Operations on fuzzy numbers with function principal. J Manag Sci 6(1):13–26

    MATH  Google Scholar 

  • Chen SM, Chang TH (2001) Finding multiple possible critical paths using fuzzy pert. IEEE Trans Syst Man Cybernet Part B (Cybernetics) 31(6):930–937

    Article  Google Scholar 

  • Chen SM, Ke JS, Chang JF (1990) Knowledge representation using fuzzy petri nets. IEEE Trans Knowl Data Eng 2(3):311–319

    Article  Google Scholar 

  • Chen SP (2007) Analysis of critical paths in a project network with fuzzy activity times. Euro J Oper Res 183(1):442–459

    Article  MathSciNet  MATH  Google Scholar 

  • Chen SP, Hsueh YJ (2008) A simple approach to fuzzy critical path analysis in project networks. Appl Math Model 32(7):1289–1297

    Article  MathSciNet  MATH  Google Scholar 

  • Deza MM, Deza E (2009) Encyclopedia of distances. In Encyclopedia of distances. https://doi.org/10.1007/978-3-642-00234-2-1

  • Dinagar DS, Abirami D (2016) A note on fuzzy critical path in project scheduling using topsis ranking method. Int J Appl Fuzzy Sets Artificial Intell 6(2016):5–15

    Google Scholar 

  • Dorfeshan Y, Mousavi SM, Vahdani B (2022) A new analysis of critical paths in mega projects with interval type-2 fuzzy activities by considering time, cost, risk, quality, and safety factors. J Opti Ind Eng 15(1):145–160

    Google Scholar 

  • Dorfeshan Y, Mousavi SM, Vahdani B, Siadat A (2018) 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. Sci Arts Métiers 26(4):2579–2600

    Google Scholar 

  • Dorfeshan Y, Mousavi SM, Zavadskas EK, Antucheviciene J (2021) A new enhanced aras method for critical path selection of engineering projects with interval type-2 fuzzy sets. Int J Inform Technol Decision Making 20(1):37–65

    Article  Google Scholar 

  • Dutta P, Saikia B (2021) Arithmetic operations on normal semi elliptic intuitionistic fuzzy numbers and their application in decision-making. Granular Comput 6(1):163–179

    Article  Google Scholar 

  • Elizabeth S, Sujatha L (2013) Fuzzy critical path problem for project network. Int J Pure Appl Math 85(2):223–240

    Article  Google Scholar 

  • Gazdik I (1983) Fuzzy network planning-fnet. IEEE Trans Reliab 32(3):304–313

    Article  MATH  Google Scholar 

  • Han TC, Chung CC, Liang GS (2006) Application of fuzzy critical path method to airports cargo ground operation systems. J Marine Sci Technol 14(3):139–146

    Article  Google Scholar 

  • He LH, Zhang LY (2014) An improved fuzzy network critical path method. Syst Eng Theory Pract 34(1):190–196

    Google Scholar 

  • Hu C, Liu D (2018) Improved critical path method with trapezoidal fuzzy activity durations. J Construction Eng Manag 144(009):04018090(1)-04018090(2)

    Article  Google Scholar 

  • Jayagowri P, Geetharamani G (2014) A critical path problem using intuitionistic trapezoidal fuzzy number. Appl Math Sci 8(52):2555–2562

    Google Scholar 

  • Kelley JE Jr, Walker MR (1959) Critical-path planning and scheduling. Eastern joint IRE-AIEE-ACM computer conference, https://doi.org/10.1145/1460299.1460318

  • Kumar A, Kaur P (2011) A new method for fuzzy critical path analysis in project networks with a new representation of triangular fuzzy numbers. J Fuzzy Set Valued Anal 5(10):1442–1466

    MathSciNet  MATH  Google Scholar 

  • Liang GS, Han TC (2004) Fuzzy critical path for project network. Int J Inform Manag Sci 15(4):29–40

    MathSciNet  MATH  Google Scholar 

  • Lin FT, Yao JS (2003) Fuzzy critical path method based on signed-distance ranking and statistical confidence interval estimates. J Supercomput 24(3):305–325

    Article  MATH  Google Scholar 

  • Marchwicka E, Kuchta D (2021) Critical path method for z-fuzzy numbers. In International Conference on Intelligent and Fuzzy Systems. https://doi.org/10.1007/978-3-030-85577-2-100

  • McCahon CS, Lee ES (1988) Project network analysis with fuzzy activity times. Comput Math Appl 15(10):829–838

    MATH  Google Scholar 

  • Mitlif RJ, Sadiq FA (2021) Finding the critical path method for fuzzy network with development ranking function. J Al-Qadisiyah Comput Sci Math 13(3):98–106

    Google Scholar 

  • Narayanamoorthy S, Maheswari S (2014) Finding fuzzy critical path by metric distance ranking method using fuzzy numbers. Int J Appl Eng Res 9(20):6843–6854

    Google Scholar 

  • Narayanamoorthy S, Maheswari S (2016). The intelligence of octagonal fuzzy number to determine the fuzzy critical path: a new ranking method. Scientific Programming, https://doi.org/10.1155/2016/6158208

  • Nasution SH (1994) Fuzzy critical path method. IEEE Trans Syst Man Cybernet 24(1):48–57

    Article  Google Scholar 

  • Oladeinde MH, Oladeinde CA (2014) An investigation into the decision makers’ risk attitude index ranking technique for fuzzy critical path analysis. Nigerian J Technol 33(3):345–350

    Article  Google Scholar 

  • Phani BRP, Ravi Shankar N (2012) Fuzzy critical path method based on lexicographic ordering. Pakistan J Stat Oper Res 8(1):139–154

    Article  MathSciNet  Google Scholar 

  • Priyadharshini S, Deepa G (2022) Critical path interms of intuitionistic triangular fuzzy numbers using maximum edge distance method. Reliability 17(67):382–390

    Google Scholar 

  • Ravi Shankar N, Sireesha V, Phani BRP (2010) An analytical method for finding critical path in a fuzzy project network. Int J Contemporary Math Sci 5(20):953–962

    MathSciNet  MATH  Google Scholar 

  • Samayan N, Sengottaiyan M (2017) Fuzzy critical path method based on ranking methods using hexagonal fuzzy numbers for decision making. J Intell Fuzzy Syst 32(1):157–164

    Article  MATH  Google Scholar 

  • Usha Madhuri K, Pardha Saradhi B, Ravi Shankar N (2013) Fuzzy linear programming model for critical path analysis. Int J Contemporary Math Sci 8(1):93–116

    Article  MathSciNet  MATH  Google Scholar 

  • Vimala S, Krishna Prabha S (2015) Solving fuzzy critical path problem using method of magnitude. Int J Sci Eng Res 6(11):1362–1370

    Google Scholar 

  • Yao JS, Lin FT (2000) Fuzzy critical path method based on signed distance ranking of fuzzy numbers. IEEE Trans Syst Man Cybernet Part A Syst Hum 30(1):76–82

    Article  Google Scholar 

  • Zareei A, Zaerpour F, Bagherpour M, Noora AA, Vencheh AH (2011) A new approach for solving fuzzy critical path problem using analysis of events. Expert Syst Appl 38(1):87–93

    Article  Google Scholar 

Download references

Acknowledgements

The authors are grateful to anonymous referees whose valuable comments helped to improve the content of this paper.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Fazlollah Abbasi.

Ethics declarations

Conflict of interest

The authors do not have any conflict of interest to declare.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Springer Nature or its licensor holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Abbasi, F., Allahviranloo, T. Realistic solution of fuzzy critical path problems, case study: the airport’s cargo ground operation systems. Granul. Comput. 8, 617–632 (2023). https://doi.org/10.1007/s41066-022-00347-w

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s41066-022-00347-w

Keywords

Navigation