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An extension principle based solution approach for shortest path problem with fuzzy arc lengths

Author

Listed:
  • Sadegh Niroomand

    (Firouzabad Institute of Higher Education)

  • Ali Mahmoodirad

    (Islamic Azad University)

  • Ahmad Heydari

    (Firouzabad Institute of Higher Education)

  • Fatemeh Kardani

    (Islamic Azad University)

  • Abdollah Hadi-Vencheh

    (Islamic Azad University)

Abstract

A shortest path problem on a network in the presence of fuzzy arc lengths is focused in this paper. The aim is to introduce the shortest path connecting the first and last vertices of the network which has minimum fuzzy sum of arc lengths among all possible paths. In this study a solution algorithm based on the extension principle of Zadeh is developed to solve the problem. The algorithm decomposes the fuzzy shortest path problem into two lower bound and upper bound sub-problems. Each sub-problem is solved individually in different $$\alpha$$ α levels to obtain the shortest path, its fuzzy length and its associated membership function value. The proposed method contains no fuzzy ranking function and also for each $$\alpha$$ α -cut, it gives a unique lower and upper bound for the fuzzy length of the shortest path. The algorithm is examined over some well-known networks from the literature and its performance is superior to the existent methods.

Suggested Citation

  • Sadegh Niroomand & Ali Mahmoodirad & Ahmad Heydari & Fatemeh Kardani & Abdollah Hadi-Vencheh, 2017. "An extension principle based solution approach for shortest path problem with fuzzy arc lengths," Operational Research, Springer, vol. 17(2), pages 395-411, July.
    • Handle: RePEc:spr:operea:v:17:y:2017:i:2:d:10.1007_s12351-016-0230-4
    DOI: 10.1007/s12351-016-0230-4
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    References listed on IDEAS

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    1. Liu, Shiang-Tai & Kao, Chiang, 2004. "Solving fuzzy transportation problems based on extension principle," European Journal of Operational Research, Elsevier, vol. 153(3), pages 661-674, March.
    2. Paola Cappanera & Maria Paola Scaparra, 2011. "Optimal Allocation of Protective Resources in Shortest-Path Networks," Transportation Science, INFORMS, vol. 45(1), pages 64-80, February.
    3. Sengupta, Atanu & Pal, Tapan Kumar, 2000. "On comparing interval numbers," European Journal of Operational Research, Elsevier, vol. 127(1), pages 28-43, November.
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    Cited by:

    1. Tanveen Kaur Bhatia & Amit Kumar & Srimantoorao S. Appadoo & Yuvraj Gajpal & Mahesh Kumar Sharma, 2021. "Mehar Approach for Finding Shortest Path in Supply Chain Network," Sustainability, MDPI, vol. 13(7), pages 1-14, April.
    2. Tina Verma, 2022. "Solving the shortest path problem on networks with fuzzy arc lengths using the complete ranking method," Operational Research, Springer, vol. 22(4), pages 3607-3631, September.

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