A Novel Method for Finding the Shortest Path With Two Objectives Under Trapezoidal Intuitionistic Fuzzy Arc Costs

Main Article Content

K. Vidhya; A. Saraswathi


The Shortest Path Problem is a core problem in network optimization, with applications in various scientific and engineering fields, such as communication, transportation, routing, scheduling, and computer networks. Many studies and algorithms have been proposed to solve the traditional shortest path problem, but they often fail to provide optimal solutions when dealing with the uncertainties and vagueness that exist in real-world situations. This study aims to address the Bi-objective Shortest Path Problem using intuitionistic fuzzy arc numbers. The main goal is to find the path that minimizes both cost and time between a given source node and destination node. To handle the complexities introduced by trapezoidal intuitionistic fuzzy numbers, an accuracy function is used. The study suggests a simple yet effective method to solve this problem and shows its efficiency through a numerical example. The research tries to offer innovative solutions for optimizing paths in scenarios where cost and time factors are important, navigating the complex landscape of uncertainty inherent in practical applications.

Article Details


  1. L.A. Zadeh, Fuzzy Sets, Inf. Control. 8 (1965), 338–353. https://doi.org/10.1016/s0019-9958(65)90241-x.
  2. K.T. Atanassov, Interval Valued Intuitionistic Fuzzy Sets, in: Intuitionistic Fuzzy Sets, Physica-Verlag HD, Heidelberg, 1999: pp. 139–177. https://doi.org/10.1007/978-3-7908-1870-3_2.
  3. J.A. Goguen, L. A. Zadeh. Fuzzy Sets. Information and Control, vol. 8 (1965), pp. 338–353. - L. A. Zadeh. Similarity Relations and Fuzzy Orderings. Information Sciences, vol. 3 (1971), pp. 177-200, J. Symb. Log. 38 (1973), 656–657. https://doi.org/10.2307/2272014.
  4. D. Çoker, Fuzzy Rough Sets Are Intuitionistic L-Fuzzy Sets, Fuzzy Sets Syst. 96 (1998), 381–383. https://doi.org/10.1016/s0165-0114(97)00249-2.
  5. A. Ebrahimnejad, J.L. Verdegay, An Efficient Computational Approach for Solving Type-2 Intuitionistic Fuzzy Numbers Based Transportation Problems, Int. J. Comput. Intell. Syst. 9 (2016), 1154–1173. https://doi.org/10.1080/18756891.2016.1256576.
  6. S. Okada, T. Soper, A Shortest Path Problem on a Network With Fuzzy Arc Lengths, Fuzzy Sets Syst. 109 (2000), 129–140. https://doi.org/10.1016/s0165-0114(98)00054-2.
  7. D. Dubois, H.M. Prade, Fuzzy sets and systems: theory and applications, Academic Press, New York, 1980.
  8. C.M. Klein, Fuzzy Shortest Paths, Fuzzy Sets Syst. 39 (1991), 27–41. https://doi.org/10.1016/0165-0114(91)90063-v.
  9. T.N. Chuang, J.Y. Kung, The Fuzzy Shortest Path Length and the Corresponding Shortest Path in a Network, Comput. Oper. Res. 32 (2005), 1409–1428. https://doi.org/10.1016/j.cor.2003.11.011.
  10. S. Okada, Fuzzy Shortest Path Problems Incorporating Interactivity Among Paths, Fuzzy Sets Syst. 142 (2004), 335–357. https://doi.org/10.1016/s0165-0114(03)00225-2.
  11. I. Mahdavi, R. Nourifar, A. Heidarzade, N.M. Amiri, A Dynamic Programming Approach for Finding Shortest Chains in a Fuzzy Network, Appl. Soft Comput. 9 (2009), 503–511. https://doi.org/10.1016/j.asoc.2008.07.002.
  12. S. Mukherjee, Dijkstra’s Algorithm for Solving the Shortest Path Problem on Networks Under Intuitionistic Fuzzy Environment, J. Math. Model. Algor. 11 (2012), 345–359. https://doi.org/10.1007/s10852-012-9191-7.
  13. L. Sujatha, J.D. Hyacinta, The Shortest Path Problem on Networks With Intuitionistic Fuzzy Edge Weights, Glob. J. Pure Appl. Math 13 (2017), 3285–3300.
  14. G. Geetharamani, P. Jayagowri, Using Similarity Degree Approach for Shortest Path in Intuitionistic Fuzzy Network, in: 2012 International Conference on Computing, Communication and Applications, IEEE, Dindigul, Tamilnadu, India, 2012: pp. 1–6. https://doi.org/10.1109/ICCCA.2012.6179147.
  15. M. Arana-Jiménez, V. Blanco, On a Fully Fuzzy Framework for Minimax Mixed Integer Linear Programming, Comput. Ind. Eng. 128 (2019), 170–179. https://doi.org/10.1016/j.cie.2018.12.029.
  16. C. Mohamed, J. Bassem, L. Taicir, A Genetic Algorithms to Solve the Bicriteria Shortest Path Problem, Elec. Notes Discr. Math. 36 (2010), 851–858. https://doi.org/10.1016/j.endm.2010.05.108.
  17. L. Zero, C. Bersani, M. Paolucci, R. Sacile, Multi-Objective Shortest Path Problem With Deterministic and Fuzzy Cost Functions Applied to Hazmat Transportation on a Road Network, in: 2017 5th IEEE International Conference on Models and Technologies for Intelligent Transportation Systems (MT-ITS), IEEE, Naples, Italy, 2017: pp. 238–243. https://doi.org/10.1109/MTITS.2017.8005673.
  18. H. Motameni, A. Ebrahimnejad, Constraint Shortest Path Problem in a Network with Intuitionistic Fuzzy Arc Weights, in: J. Medina, M. Ojeda-Aciego, J.L. Verdegay, I. Perfilieva, B. Bouchon-Meunier, R.R. Yager (Eds.), Information Processing and Management of Uncertainty in Knowledge-Based Systems. Applications, Springer International Publishing, Cham, 2018: pp. 310–318. https://doi.org/10.1007/978-3-319-91479-4_26.
  19. V. Kannan, S. Appasamy, G. Kandasamy, Comparative study of fuzzy Floyd Warshall algorithm and the fuzzy rectangular algorithm to find the shortest path, AIP Conf. Proc. 2516 (2022), 200029. https://doi.org/10.1063/5.0110337.