Skip to main content
SpringerLink
Log in

Constraint Shortest Path Problem in a Network with Intuitionistic Fuzzy Arc Weights

  • Conference paper
  • First Online:
Information Processing and Management of Uncertainty in Knowledge-Based Systems. Applications (IPMU 2018)

Part of the book series: Communications in Computer and Information Science ((CCIS,volume 855))

Abstract

The Shortest Path (SP) problem is one of the most widely used problems in network optimization which has a wide range of applications in various fields of science and engineering such as communication, transportation, routing and scheduling. The aim of this problem is to find a minimum cost path between two specified nodes. In the present communication, we consider a modified version of the SP known as constraint SP (CSP) problem with an additional constraint that establishes an upper limit on the travel time for the path. The objective of the CSP problem is to determine a minimum cost path between two specified nodes that the traversal time of the path does not exceed from a specified time. Traditional CSP problems assume the arc weights represented by time and cost are specified precisely. However, these weights can fluctuate with traffic conditions, weather, or payload. For this reason, being able to deal with vague and imprecise data may greatly contribute to the application of CSP problems. Here, we first formulate a CSP problem in a directed network where the arc weights represented by cost and time are intuitionistic trapezoidal fuzzy numbers. We then develop an approach for solving the intuitionistic fuzzy CSP problem under consideration. Finally, we present a small numerical example to illustrate the proposed approach.

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

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Biswas, S.S., Bashir, A., Doja, M.N.: An algorithm for extracting intuitionistic fuzzy shortest path in a graph. Appl. Comput. Intell. Soft Comput. 2013, 1–5 (2013)

    Article  Google Scholar 

  2. Chuang, T.N., Kung, J.Y.: The fuzzy shortest path length and the corresponding shortest path in a network. Comput. Oper. Res. 32(6), 1409–1428 (2005)

    Article  MathSciNet  Google Scholar 

  3. Dou, Y., Zhu, L., Wang, H.S.: Solving the fuzzy shortest path problem using multi-criteria decision method based on vague similarity measure. Appl. Soft Comput. 12(6), 1621–1631 (2012)

    Article  Google Scholar 

  4. Ebrahimnejad, A., Karimnejad, Z., Alrezaamiri, H.: Particle swarm optimization algorithm for solving shortest path problems with mixed fuzzy arc weights. Int. J. Appl. Decision Sci. 8(2), 203–222 (2015)

    Article  Google Scholar 

  5. Ebrahimnejad, A., Tavana, M., Alrezaamiri, H.: A novel artificial bee colony algorithm for shortest path problems with fuzzy arc weights. Measurement 93, 48–56 (2016)

    Article  Google Scholar 

  6. Ebrahimnejad, A., Verdegay, J.L.: An efficient computational approach for solving type–2 intuitionistic fuzzy numbers based transportation problems. Int. J. Comput. Intell. Syst. 9(6), 1154–1173 (2016)

    Article  Google Scholar 

  7. Geetharamani, G., Jayagowri, P.: Using similarity degree approach for shortest path in Intuitionistic fuzzy network. In: International Conference on Computing, Communication and Applications (ICCCA), pp. 1–6, IEEE, Dindigul (2012)

    Google Scholar 

  8. Hassanzadeh, R., Mahdavi, I., Mahdavi-Amiri, N., Tajdin, A.: A genetic algorithm for solving fuzzy shortest path problems with mixed fuzzy arc lengths. Math. Comput. Model. 57(1–2), 84–99 (2013)

    Article  MathSciNet  Google Scholar 

  9. Hernandes, F., Lamata, M.T., Verdegay, J.L., Yamakami, A.: The shortest path problem on networks with fuzzy parameters. Fuzzy Sets Syst. 158(14), 1561–1570 (2007)

    Article  MathSciNet  Google Scholar 

  10. Kumar, G., Bajaj, R.K., Gandotra, N.: Algorithm for shortest path problem in a network with interval–valued intuitionistic trapezoidal fuzzy number. Procedia Comput. Sci. 70, 123–129 (2015)

    Article  Google Scholar 

  11. Mahdavi, I., Nourifar, R., Heidarzade, A., Mahdavi Amiri, N.: A dynamic programming approach for finding shortest chains in a fuzzy network. Appl. Soft Comput. 9, 503–511 (2009)

    Article  Google Scholar 

  12. Moazeni, M.: Fuzzy shortest path problem with finite fuzzy quantities. Appl. Math. Comput. 183, 160–169 (2006)

    MathSciNet  MATH  Google Scholar 

  13. Mukherjee, S.: Dijkstra’s algorithm for solving the shortest path problem on networks under intuitionistic fuzzy environment. J. Math. Model. Algorithm 11(4), 345–359 (2012)

    Article  MathSciNet  Google Scholar 

  14. Okada, S., Super, T.: A shortest path problem on a network with fuzzy arc lengths. Fuzzy Sets Syst. 109, 129–140 (2000)

    Article  MathSciNet  Google Scholar 

  15. Olada, T.: Fuzzy shortest path problems incorporating interactivity among paths. Fuzzy Sets Syst. 142, 335–357 (2004)

    Article  MathSciNet  Google Scholar 

  16. Santos, L., Coutinho-Rodrigues, J., Current, J.R.: An improved solution algorithm for the constrained shortest path problem. Transp. Res. Part B 41, 756–771 (2007)

    Article  Google Scholar 

  17. Sujatha, L., Hyacinta, J.D.: The shortest path problem on networks with intuitionistic fuzzy edge weights. Global J. Pure Appl. Math. 13(7), 3285–3300 (2017)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Computer Engineering, Sari Branch, Islamic Azad University, Sari, Iran

    Homayun Motameni

  2. Department of Mathematics, Qaemshahr Branch, Islamic Azad University, Qaemshahr, Iran

    Ali Ebrahimnejad

Authors
  1. Homayun Motameni
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Ali Ebrahimnejad
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Homayun Motameni .

Editor information

Editors and Affiliations

  1. Universidad de Cádiz, Cádiz, Cadiz, Spain

    Jesús Medina

  2. Universidad de Málaga, Málaga, Málaga, Spain

    Manuel Ojeda-Aciego

  3. Universidad de Granada, Granada, Spain

    José Luis Verdegay

  4. Institute for Research and Applications, University of Ostrava, Ostrava, Czech Republic

    Irina Perfilieva

  5. LIP6, Université Pierre et Marie Curie, CNRS, Paris, France

    Bernadette Bouchon-Meunier

  6. Iona College, New Rochelle, New York, USA

    Ronald R. Yager

Rights and permissions

Reprints and permissions

Copyright information

© 2018 Springer International Publishing AG, part of Springer Nature

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Motameni, H., Ebrahimnejad, A. (2018). Constraint Shortest Path Problem in a Network with Intuitionistic Fuzzy Arc Weights. In: Medina, J., Ojeda-Aciego, M., Verdegay, J., Perfilieva, I., Bouchon-Meunier, B., Yager, R. (eds) Information Processing and Management of Uncertainty in Knowledge-Based Systems. Applications. IPMU 2018. Communications in Computer and Information Science, vol 855. Springer, Cham. https://doi.org/10.1007/978-3-319-91479-4_26

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-91479-4_26

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-91478-7

  • Online ISBN: 978-3-319-91479-4

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation