The time-varying shortest path problem with fuzzy transit costs and speedup

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In this paper, we focus on the time-varying shortest path problem, where the transit costs are fuzzy numbers. Moreover, we consider this problem in which the transit time can be shortened at a fuzzy speedup cost. Speedup may also be a better decision to find the shortest path from a source vertex to a specified vertex.

[1] X. Cai X, D. Sha, C. K. Wong, Time-varying network optimization, Springer Science Press. New York, USA, 2007.

[2] L. Campos, J. L. Verdegay, Linear programming problems and ranking of fuzzy numbers, Fuzzy Sets and Systems, 32 (1989), 1–11.

[3] M. Gent, R. Cheng, D. Wang, Genetic algorithms for solving shortest path problems, Proceedings of the IEEE International Conference on Evolutionary Computation, (1997), 401–406.

[4] X. Ji, K. Iwamura, Z. Shao, New models for shortest path problem with problem with fuzzy arc lengths, Applied Mathematical Modeling, 31 (2007), 259–269.

[5] A. Kaufmann, M. M. Gupta, Fuzzy mathematical models in engineering and management science, Elsevier, Amsterdam, The Netherland, 1988.

[6] A. Kaur, A. Kumar, A new approach for solving fuzzy transportation problems using generalized trapezoidal fuzzy numbers, Applied Soft Computing, 12 (2012), 1201–1213.

[7] C. M. Klein, Fuzzy shortest path, Fuzzy Sets and Systems, 39 (1991), 27–41.

[8] A. Kumar, K. Manjot, A new algorithm for solving network ow problems with fuzzy arc lengths, Turkish Journal of Fuzzy Systems, 1 (2011), 1–13.

[9] Y. Li, M. Gen, K. Ida, Solving fuzzy shortest path problems by neural networks, Computers and Industrial Engineering, 31 (1996), 861–865.

[10] K. C. Lin, M. S. Chern, The fuzzy shortest path problem and its most vital arcs, Fuzzy Sets and Systems, 58 (1993), 343–353.

[11] I. Mahdavi, R. Nourifar, A. Heidarzade, N. M. Amiri, A dynamic programming approach for finding shortest chains in fuzzy network, Applied Soft Computing, 9 (2009), 503–511.

[12] S. Moazeni, Fuzzy shortest path problem with finite fuzzy quantities, Applied Mathematics and Computation, 183 (2006), 160–169.

[13] S. Okada, M. Gen, Fuzzy shortest path problems, Computers and Industrial Engineering, 27 (1994), 465–468.

[14] S. Okada, T. Soper, A shortest path problem on a network with fuzzy arc lengths, Fuzzy Sets and Systems, 109 (2000), 129–140.

[15] Gh. Shirdel, H. Rezapour, K-Objective Time-Varying Shortest Path Problem with Zero Waiting Times at Vertices, Trends in Applied Science Research, 5 (2015), 278–285.

Acta Universitatis Sapientiae, Mathematica

The Journal of Sapientia Hungarian University of Transylvania

Journal Information

CiteScore 2017: 0.31

SCImago Journal Rank (SJR) 2017: 0.380
Source Normalized Impact per Paper (SNIP) 2017: 0.434

Mathematical Citation Quotient (MCQ) 2017: 0.10

Target Group

researchers in all fields of mathematics


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