An algorithm for solving fuzzy maximal flow problems using generalized triangular fuzzy numbers

Issue title: Rough and Fuzzy Methods for Data Mining

Guest editors: A.E. Hassanienav, H. Sakaibw, D. Ślȩzakx, M.K. Chakrabortydy and W. Zhuz

Article type: Research Article

Authors: Kumar, Amit | Kaur, Manjot^{; *}

Affiliations: School of Mathematics and Computer Applications, Thapar University, Patiala-147 004, India | [v] Cairo University, Egypt | [w] Kyushu Institute of Technology, Japan | [x] University of Warsaw & Infobright Inc., Poland | [y] University of Calcutta, India | [z] UESTC, Chengdu, China

Correspondence: [*] Corresponding author. E-mail: [email protected]

Abstract: There are several papers in the literature in which generalized fuzzy numbers are used for solving real life problems but to the best of our knowledge, till now no one has used generalized fuzzy numbers for solving the maximal flow problems. In this paper, the existing algorithm is modified to find fuzzy maximal flow between source and sink by representing all the parameters as generalized triangular fuzzy numbers. To illustrate the modified algorithm a numerical example is solved and the obtained results are compared with the existing results. If there is no uncertainty about the flow between source and sink then the proposed algorithm gives the same result as in crisp maximal flow problems.

Keywords: Fuzzy maximal flow problem, ranking function, generalized triangular fuzzy numbers

DOI: 10.3233/HIS-2011-0127

Journal: International Journal of Hybrid Intelligent Systems, vol. 8, no. 1, pp. 15-24, 2011