Trapezoidal Fuzzy Shortest Path (TFSP) Selection for Green Routing and Scheduling Problems

Conference paper
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 248)

Abstract

The routing of vehicles represents an important component of many distribution and transportation systems. Finding the shortest path is one of the fundamental and popular problems. In real life applications, like vehicle green routing and scheduling, transportation, etc. which are related to environmental issues the arc lengths could be uncertain due to the fluctuation with traffic conditions or weather conditions. Therefore finding the exact optimal path in such networks could be challenging. In this paper, we discuss and analyze different approaches for finding the Fuzzy Shortest Path. The shortest path is computed using the ranking methods based on i)Degree of Similarity ii) Acceptable Index, where the arc lengths are expressed as trapezoidal fuzzy numbers. The Decision makers can choose the best path among the various alternatives from the list of rankings by prioritizing the scheduling which facilitates Green Routing.

Keywords

Fuzzy Shortest Path Bellman’s Dynamic Programming Trapezoidal Fuzzy shortest path Degree of Similarity Acceptable Index 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Touati-Moungla, N., Jost, V.: On green routing and scheduling problem, hal-00674437, version 1 - 7 (March 2012)Google Scholar
  2. 2.
    Dubois, D., Prade, H.: Theory and Applications: Fuzzy Sets and Systems. Academic Press, New York (1980)MATHGoogle Scholar
  3. 3.
    Dubois, D., Prade, H.: Ranking fuzy numbers in the setting of possiblity theory. Information Sciences 30, 183–224 (1983)MathSciNetCrossRefMATHGoogle Scholar
  4. 4.
    Klein, C.M.: Fuzzy Shortest Paths. Fuzzy Sets and Systems 39, 27–41 (1991)MathSciNetCrossRefMATHGoogle Scholar
  5. 5.
    Lin, K., Chen, M.: The Fuzzy Shortest Path Problem and its Most Vital Arcs. Fuzzy Sets and Systems 58, 343–353 (1994)CrossRefGoogle Scholar
  6. 6.
    Okada, S., Soper, T.: A shortest path problem on a network with fuzzy arc lengths. Fuzzy Sets and Systems 109, 129–140 (2000)MathSciNetCrossRefMATHGoogle Scholar
  7. 7.
    Yao, J.S., Lin, F.T.: Fuzzy shortest-path network problems with unce -rtain edge weights. Journal of Information Science and Engineering 19, 329–351 (2003)MathSciNetGoogle Scholar
  8. 8.
    Chuang, T.N., Kung, J.Y.: The fuzzy shortest path length and the corresponding shortest path in a network. Computers and Operations Research 32, 1409–1428 (2005)MathSciNetCrossRefGoogle Scholar
  9. 9.
    De, P.K., Bhinchar, A.: Computation of Shortest Path in a Fuzzy Network: Case Study with Rajasthan Roadways Network. International Journal of Computer Applications (0975 – 8887) 11(12) (December 2010)Google Scholar
  10. 10.
    Sujatha, L., Elizabeth, S.: Fuzzy Shortest Path Problem Based on Index Ranking. Journal of Mathematics Research 3(4) (November 2011)Google Scholar

Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  1. 1.Dept. of CS & MathsBangalore UniversityBangaloreIndia
  2. 2.CMRIMSBangaloreIndia

Personalised recommendations