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A New Approach for Solving Fuzzy Maximal Flow Problems

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Rough Sets, Fuzzy Sets, Data Mining and Granular Computing (RSFDGrC 2009)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 5908))

Abstract

In conventional maximal flow problems, it is assumed that decision maker is certain about the flows between different nodes. But in real life situations, there always exist uncertainty about the flows between different nodes. In such cases, the flows may be represented by fuzzy numbers. In literature, there are several methods to solve such type of problems. Till now, no one has used ranking function to solve above type of problems. In this paper, a new algorithm is proposed to find fuzzy maximal flow between source and sink by using ranking function. To illustrate the algorithm a numerical example is solved and result is explained. 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.

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References

  1. Ahuja, R.K., Magnanti, T.L., Orlin, J.B.: Network Flows, Theory, Algorithms and Applications. Prentice Hall, New Jersey (1993)

    Google Scholar 

  2. Campos, L., Verdegay, J.L.: Linear Programming Problems and Ranking of Fuzzy Numbers. Fuzzy Sets and Systems 32, 1–11 (1989)

    Article  MATH  MathSciNet  Google Scholar 

  3. Chanas, S., Kolodziejczyk, W.: Maximum Flow in a Network with Fuzzy Arc Capacities. Fuzzy Sets and Systems 8, 165–173 (1982)

    Article  MATH  MathSciNet  Google Scholar 

  4. Chanas, S., Kolodziejczyk, W.: Real-valued Flows in a Network with Fuzzy Arc Capacities. Fuzzy Sets and Systems 13, 139–151 (1984)

    Article  MATH  MathSciNet  Google Scholar 

  5. Chanas, S., Kolodziejczyk, W.: Integer Flows in Network with Fuzzy Capacity Constraints. Networks 16, 17–31 (1986)

    Article  MATH  MathSciNet  Google Scholar 

  6. Dubois, D., Prade, H.: Fuzzy Sets and Systems, Theory and Applications. Academic Press, New York (1980)

    MATH  Google Scholar 

  7. Fortemps, P., Roubens, M.: Ranking and Defuzzification Methods Based on Area Compensation. Fuzzy Sets and Systems 82, 319–330 (1996)

    Article  MATH  MathSciNet  Google Scholar 

  8. Kalir, G.J., Yuhan, B.: Fuzzy Sets and Fuzzy Logic, Theory and Applications. Prentice Hall, Englewood Cliffs (1995)

    Google Scholar 

  9. Kasana, H.S., Kumar, K.D.: Introductory Operations Research Theory and Application. Springer, Heidelberg (2008)

    Google Scholar 

  10. Kaufmann, A., Gupta, M.M.: Introduction to Fuzzy Arithmetics. Theory and Application, New York (1991)

    Google Scholar 

  11. Kim, K., Roush, F.: Fuzzy Flows on Network. Fuzzy Sets and Systems 8, 35–38 (1982)

    Article  MathSciNet  Google Scholar 

  12. Liou, T.S., Wang, M.J.: Ranking Fuzzy Numbers with Integral Value. Fuzzy Sets and Systems 50, 247–255 (1992)

    Article  MathSciNet  Google Scholar 

  13. Zadeh, L.: Fuzzy Sets. Inf. and Control 8, 338–353 (1965)

    Article  MATH  MathSciNet  Google Scholar 

  14. Zimmermann, H.J.: Fuzzy Sets Theory and Its Application, 2nd edn. Kluwer Academic Publisher, Boston (1991)

    Google Scholar 

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Author information

Authors and Affiliations

  1. School of Mathematics and Computer Applications, Thapar University, Patiala, 147004, India

    Amit Kumar, Neha Bhatia & Manjot Kaur

Authors
  1. Amit Kumar
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  2. Neha Bhatia
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  3. Manjot Kaur
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Editor information

Editors and Affiliations

  1. Department of Mathematics and Computer Aided Sciences, Kyushu Institute of Technology, 804-8550, Tobata, Kitakyushu, Japan

    Hiroshi Sakai

  2. Department of Pure Mathematics, University of Calcutta, 35 Ballygunge Circular Road, 700019, Kolkata, India

    Mihir Kumar Chakraborty

  3. Information Technology Department, University of Cairo, 5 Ahmed Zewal St. Orman, Giza, Egypt

    Aboul Ella Hassanien

  4. University of Warsaw & Infobright Inc., Poland

    Dominik Ślęzak

  5. University of Electronic Science and Technology of China, Chengdu, China

    William Zhu

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© 2009 Springer-Verlag Berlin Heidelberg

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Kumar, A., Bhatia, N., Kaur, M. (2009). A New Approach for Solving Fuzzy Maximal Flow Problems. In: Sakai, H., Chakraborty, M.K., Hassanien, A.E., Ślęzak, D., Zhu, W. (eds) Rough Sets, Fuzzy Sets, Data Mining and Granular Computing. RSFDGrC 2009. Lecture Notes in Computer Science(), vol 5908. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-10646-0_34

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  • DOI: https://doi.org/10.1007/978-3-642-10646-0_34

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-10645-3

  • Online ISBN: 978-3-642-10646-0

  • eBook Packages: Computer ScienceComputer Science (R0)

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