Sadhana

, Volume 39, Issue 1, pp 189–206 | Cite as

A new method for solving single and multi-objective fuzzy minimum cost flow problems with different membership functions

Article
  • 180 Downloads

Abstract

Several authors have proposed different methods for solving fuzzy minimum cost flow (MCF) problems. In this paper, some single and multi-objective fuzzy MCF problems are chosen which cannot be solved by using any of the existing methods and a new method is proposed for solving such type of problems. The main advantage of the proposed method over existing methods is that the fuzzy MCF problems which can be solved by using the existing methods can also be solved by the proposed method. But, there exist several fuzzy MCF problems which can be solved only by using the proposed method i.e., it is not possible to solve these problems by using the existing methods. To illustrate the proposed method and also to show the advantages of the proposed method over existing methods some single and multi-objective fuzzy MCF problems which cannot be solved by using the existing methods are solved by using the proposed method and the obtained results are discussed.

Keywords

Single and multi-objective fuzzy MCF problems fuzzy linear programming LR fuzzy numbers ranking function 

Notes

Acknowledgements

The authors would like to thank the Editor-in-Chief and anonymous referees for various suggestions which have led to an improvement in both the quality and clarity of the paper. I, Dr. Amit Kumar, want to acknowledge the adolescent inner blessings of Mehar. I believe that Mehar is an angel for me and without Mehar’s blessing it was not possible to think the idea proposed in this paper. Mehar is a lovely daughter of Parmpreet Kaur (Research Scholar under my supervision).

References

  1. Ahuja R K, Magnanti T L and Orlin J B 1993 Network flows. Englewood Cliffs: Prentice-Hall MATHGoogle Scholar
  2. Chanas S and Kuchta D 1998 Fuzzy integer transportation problem. Fuzzy Set Syst. 98: 291–298CrossRefMathSciNetGoogle Scholar
  3. Chen S P 2007 Analysis of critical paths in a project network with fuzzy activity times. Eur. J. Oper. Res. 183: 442–459CrossRefMATHGoogle Scholar
  4. Chen S P and Hsueh Y J 2008 A simple approach to fuzzy critical path analysis in project networks. Appl. Math. Model 32: 1289–1297CrossRefMathSciNetGoogle Scholar
  5. Ching K L and Cheng C H 2009 A novel general approach to evaluating the PCBA for components with different membership function. Appl. Soft Comp. 9: 1044–1056CrossRefGoogle Scholar
  6. Dubois D and Prade H 1980 Fuzzy sets and systems: Theory and applications. Academic Press, New YorkMATHGoogle Scholar
  7. Ghatee M and Hashemi S M 2007 Ranking function-based solutions of fully fuzzified minimal cost flow problem. Inform. Sci. 177: 4271–4294CrossRefMATHMathSciNetGoogle Scholar
  8. Ghatee M and Hashemi S M 2008 Generalized minimal cost flow problem in fuzzy nature: an application in bus network planning problem. Appl. Math. Model 32: 2490–2508CrossRefMATHMathSciNetGoogle Scholar
  9. Ghatee M and Hashemi S M 2009 Application of fuzzy minimum cost flow problems two network design under uncertainty. Fuzzy Set Syst. 160: 3263–3289CrossRefMATHMathSciNetGoogle Scholar
  10. Ghatee M, Hashemi S M, Hashemi B and Dehghan M 2008 Solution and duality of imprecise network problems. Comput. Math. Appl. 55: 2767–2790CrossRefMATHMathSciNetGoogle Scholar
  11. Ghatee M, Hashemi S M, Zarepisheh M and Khorram E 2009 Preemptive priority-based algorithms for fuzzy minimal cost flow problem: An application in hazardous materials transportation. Comput. Ind. Eng. 57: 341–354CrossRefGoogle Scholar
  12. Hamacher H W, Pedersen C R and Ruzika S 2007 Multiple objective minimum cost flow problems: A review. Eur. J. Oper. Res. 176: 1404–1422CrossRefMATHMathSciNetGoogle Scholar
  13. Kumar A, Yadav S P and Kumar S 2008 Fuzzy system reliability using different types of vague sets. Int. J. Appl. Sci. Eng. 6: 71–83Google Scholar
  14. Liu S T and Kao C 2004 Network flow problems with fuzzy arc lengths. IEEE T. Syst. Man. Cy. B 34: 765–769CrossRefGoogle Scholar
  15. Mon D L and Cheng C H 1994 Fuzzy system reliability analysis for components with different membership functions. Fuzzy Set Syst. 64: 145–157CrossRefMathSciNetGoogle Scholar
  16. Shih H S and Lee E S 1999 Fuzzy multi-level minimum cost flow problems. Fuzzy Set Syst. 107: 159–176CrossRefMATHMathSciNetGoogle Scholar
  17. Verma R , Biswal M P and Biswas A 1997 Fuzzy programming technique to solve multi-objective transportation problems with some non-linear membership functions. Fuzzy Set Syst. 91: 37–43CrossRefMATHMathSciNetGoogle Scholar
  18. Yager R R 1981 A procedure for ordering fuzzy subsets of the unit interval. Inform. Sci. 24: 143–161CrossRefMATHMathSciNetGoogle Scholar
  19. Zadeh L A 1965 Fuzzy sets. Inform. Control 8: 338–353CrossRefMATHMathSciNetGoogle Scholar
  20. Zareei A, Zaerpour F, Bagherpour M, Noora A and Vencheh A H 2011 A new approach for solving fuzzy critical path problem using analysis of events. Expert Syst. Appl. 38: 87–93CrossRefGoogle Scholar

Copyright information

© Indian Academy of Sciences 2014

Authors and Affiliations

  1. 1.School of Mathematics and Computer ApplicationsThapar UniversityPatialaIndia
  2. 2.Department of MathematicsDr BR Ambedkar National Institute of TechonologyJalandharIndia

Personalised recommendations