Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 30172
Solution of Fuzzy Maximal Flow Problems Using Fuzzy Linear Programming

Authors: Amit Kumar, Manjot Kaur

Abstract:

In this paper, the fuzzy linear programming formulation of fuzzy maximal flow problems are proposed and on the basis of the proposed formulation a method is proposed to find the fuzzy optimal solution of fuzzy maximal flow problems. In the proposed method all the parameters are represented by triangular fuzzy numbers. By using the proposed method the fuzzy optimal solution of fuzzy maximal flow problems can be easily obtained. To illustrate the proposed method a numerical example is solved and the obtained results are discussed.

Keywords: Fuzzy linear programming, Fuzzy maximal flow problem, Ranking function, Triangular fuzzy number

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1330009

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1597

References:


[1] D. R. Fulkerson and G. B. Dantzig, Computation of Maximum Flow in Network, Naval Research Logisics Quarterly, vol. 2, 1955, pp. 277-283.
[2] L. R. Ford, and D. R. Fulkerson, Maximal Flow Through a Network, Canadian Journal of Mathematics, vol. 8, 1956, pp. 399-404.
[3] R. K. Ahuja, T. L. Magnanti and J. B. Orlin, Network Flows, Theory, Algorithms and Applications, New Jersey, Prentice Hall, 1993.
[4] M. Bazaraa, J. Jarvis and H. F. Sherali, Linear Programming and Network Flows, John Wiley, 1990.
[5] L. A. Zadeh, Fuzzy Sets, Information and Control, vol. 8, 1965, pp. 338-353.
[6] K. Kim and F. Roush, Fuzzy Flows on Network, Fuzzy Sets and Systems, vol. 8, 1982, pp. 35-38.
[7] S. Chanas andW. Kolodziejczyk, Maximum Flow in a Network with Fuzzy Arc Capacities, Fuzzy Sets and Systems, vol. 8, 1982, pp. 165-173.
[8] S. Chanas and W. Kolodziejczyk, Real-valued Flows in a Network with Fuzzy Arc Capacities, Fuzzy Sets and Systems, vol. 13, 1984, pp. 139- 151.
[9] S. Chanas and W. Kolodziejczyk, Integer Flows in Network with Fuzzy Capacity Constraints, Networks, vol. 16, 1986, pp. 17-31.
[10] S. Chanas, M. Delgado, J. L. Verdegay and M. Vila, Fuzzy Optimal Flow on Imprecise Structures, European Journal of Operational Research, vol. 83, 1995, pp. 568-580.
[11] A. Diamond, A Fuzzy Max-flow Min-cut Theorem, Fuzzy Sets and Systems, vol. 119, 2001, pp. 139-148.
[12] S. T. Liu and C. Kao, Network Flow Problems with Fuzzy Arc Lengths, IEEE Transactions on Systems, Man and Cybernetics, vol. 34, 2004, pp. 765-769.
[13] X. Ji, L. Yang and Z. Shao, Chance Constrained Maximum Flow Problem with Arc Capacities, Lecture Notes in Computer Science, Springer- Verlag, Berlin, Heidelberg, vol. 4114, 2006, pp. 11-19.
[14] F. Hernandes, M. T. Lamata, M. T. Takahashi, A. Yamakami, and J. L. Verdegay, An Algorithm for the Fuzzy Maximum Flow Problem, IEEE International Fuzzy Systems Conference, 2007, pp. 1-6.
[15] A. Kaufmann and M. M. Gupta, Introduction to Fuzzy Arithmetics: Theory and Applications, New York, Van Nostrand Reinhold, 1985.
[16] T. S. Liou and M. J. Wang, Ranking Fuzzy Numbers with Integral Value, Fuzzy Sets and Systems, vol. 50, 1992, pp. 247-255.
[17] A. Kumar, J. Kaur and P. Singh, Fuzzy Optimal Solution of Fully Fuzzy Linear Programming Problems with Inequality Constraints, International Journal of Applied Mathematics and Computer Sciences, vol. 6, 2010, pp. 37-41.