Advertisement

A Solving Method for Fuzzy Linear Programming Problem with Interval Type-2 Fuzzy Numbers

  • Moslem Javanmard
  • Hassan Mishmast NehiEmail author
Article
  • 26 Downloads

Abstract

Thus far, many methods have been suggested to solve the fuzzy linear programming (FLP) problems with interval type-2 fuzzy numbers (IT2FNs) ambiguous of kind Vagueness (uncertainty at the satisfaction level of the objective function and constraints), while studies on models of the interval type-2 FLP problems with uncertainty of kind Ambiguity in which all or part of the parameters are ambiguous (all or part of the coefficients in FLP problem are IT2FNs) are very limited. In this paper, first, an interval type-2 FLP problem with uncertainty of kind Ambiguity was considered generally and all the coefficients in the problem were interval type-2 triangular fuzzy numbers. Next, a method for solving it based on the nearest interval approximation was proposed. Finally, the method was illustrated using some numerical examples.

Keywords

Best–worst cases (BWC) Fuzzy linear programming (FLP) Interval linear programming (ILP) Interval type-2 fuzzy number (IT2FN) Membership function (MF) 

Notes

Acknowledgements

We would like to thank the anonymous referees for their constructive comments and suggestions that have helped to improve this paper.

References

  1. 1.
    Allahdadi, M., Mishmast Nehi, H., Ashayerinasab, H.A., Javanmard, M.: Improving the modified interval linear programming method by new techniques. Inf. Sci. 339, 224–236 (2016)CrossRefGoogle Scholar
  2. 2.
    Ashayerinasab, H.A., Mishmast Nehi, H., Allahdadi, M.: Solving the interval linear programming problem: a new algorithm for a general case. Expert Syst. Appl. 93, 39–49 (2018)CrossRefGoogle Scholar
  3. 3.
    Ashayerinasab, H.A., Mishmast Nehi, H., Allahdadi, M.: A generalized method for solving interval linear programming problem. Int. J. Adv. Soft Comput. Appl. (IJASCA) (2017) (Submitted)Google Scholar
  4. 4.
    Fan, Y.R., Huang, G.H.: Robust two-step method for solving interval linear programming problems within an environmental management context. J. Environ. Inf. 19(1), 1–9 (2012)CrossRefGoogle Scholar
  5. 5.
    Figueroa, J.C.: Linear programming with interval type-2 fuzzy right hand side parameters. In: 2008 Annual Meeting of the North American Fuzzy Information Processing Society (NAFIPS), vol. 27. IEEE, pp. 16 (2008)Google Scholar
  6. 6.
    Figueroa, J.C.: Solving fuzzy linear programming problems with interval type-2 RHS. In: Proceedings of the 2009 IEEE International Conference on Systems, Man, and Cybernetics San Antonio, TX, USA (2009)Google Scholar
  7. 7.
    Figueroa, J.C.: Interval type-2 fuzzy linear programming: uncertain constraints. In: 2011 IEEE Symposium Series on Computational Intelligence (2011)Google Scholar
  8. 8.
    Figueroa, J.C.: An Appraximation Method for Type Reduction of an Interval Type-2 Fuzzy Set based on \(\alpha\)-Cuts. IEEE, pp. 49–54 (2012)Google Scholar
  9. 9.
    Figueroa, J.C.: A General Model for Linear Programming with Interval Type-2 Fuzzy technological Coefficients. IEEE (2012)Google Scholar
  10. 10.
    Figueroa, J.C., Hernandez, G.: Computing optimal solution of a linear programming problem with interval type-2 fuzzy constraints. In: HAIS, part 1, LNCS 7208, pp. 567–576 (2012)Google Scholar
  11. 11.
    Figueroa-Garca, J.C., Hernndez, G.: A method for solving linear programming models with Interval type-2 fuzzy constraints. Pesqui. Oper. 34(1), 73–89 (2014)CrossRefGoogle Scholar
  12. 12.
    Golpayegani, Z., Mishmast Nehi, H.: Interval type-2 fuzzy linear programming: general uncertainty model. In: 44th Annual Iranian Mathematics Conference, Mashhad, Iran, pp. 85–88 (2013)Google Scholar
  13. 13.
    Grzegorzewski, P.: Nearest interval approximation of a fuzzy number. Fuzzy Sets Syst. 130, 321–330 (2002)MathSciNetCrossRefGoogle Scholar
  14. 14.
    Hisdal, E.: The If THEN ELSE statement and interval-valued fuzzy sets of higher type. Int. J. Man Mach. Stud. 15, 385–455 (1981)MathSciNetCrossRefGoogle Scholar
  15. 15.
    Javanmard, M., Mishmast Nehi, H.: Rankings and operations for interval type-2 fuzzy numbers: a review and some new methods. J. Appl. Math. Comput. (2018).  https://doi.org/10.1007/s12190-018-1193-9
  16. 16.
    Javanmard, M., Mishmast Nehi, H.: Interval type-2 triangular fuzzy numbers; new ranking method and evaluation of some reasonable properties on it. In: 5th Iranian Joint Congress on Fuzzy and Intelligent Systems, CFIS, vol. 8003587, pp. 4–6 (2017)Google Scholar
  17. 17.
    Javanmard, M., Mishmast Nehi, H.: Solving interval type-2 fuzzy linear programming problem with a new ranking function method. In: 5th Iranian Joint Congress on Fuzzy and Intelligent Systems, CFIS, vol. 8003586, pp. 1–3 (2017)Google Scholar
  18. 18.
    Liang, Q., Mendel, J.M.: Interval type-2 fuzzy logic systems: theory and design. IEEE Trans. Fuzzy Syst. 8, 535–550 (2000)CrossRefGoogle Scholar
  19. 19.
    Melgarejo, M.A.: A fast recursive method to compute the generalized centroid of an interval type-2 fuzzy set. In: Annual Meeting of the North American Fuzzy Information Processing Society (NAFIPS). IEEE, pp. 190194 (2007)Google Scholar
  20. 20.
    Mendel, J.M., John, R.I., Liu, F.L.: Interval type-2 fuzzy logical systems made simple. IEEE Trans. Fuzzy Syst. 14(6), 808–821 (2006)CrossRefGoogle Scholar
  21. 21.
    Tong, S.C.: Interval number, fuzzy number linear programming. Fuzzy Sets Syst. 66, 301–306 (1994)MathSciNetCrossRefGoogle Scholar
  22. 22.
    Wang, X., Huang, G.: Violation analysis on two-step method for interval linear programming. Inf. Sci. 281, 8596 (2014)MathSciNetGoogle Scholar
  23. 23.
    Zadeh, L.A.: Fuzzy sets. Inf. Control 8(3), 338–353 (1965)CrossRefGoogle Scholar
  24. 24.
    Zadeh, L.A.: The concept of a linguistic variable and its application to approximate reasoning. Inf. Sci. 8(3), 199–249 (1975)MathSciNetCrossRefGoogle Scholar
  25. 25.
    Zeng, J., Liu, Z.-Q.: Enhanced Karnik–Mendel algorithms for interval Type-2 fuzzy sets and systems. In: Annual Meeting of the North American Fuzzy Information Processing Society (NAFIPS), vol. 26. IEEE, pp. 184189 (2007)Google Scholar
  26. 26.
    Zhou, F., Huang, G.H., Chen, G.X., Guo, H.C.: Enhanced-interval linear programming. Eur. J. Oper. Res. 199, 323333 (2009)MathSciNetCrossRefGoogle Scholar
  27. 27.
    Zimmermann, H.J., Fuller, R.: Fuzzy reasoning for solving fuzzy mathematical programming problems. Fuzzy Sets Syst. 60, 121133 (1993)MathSciNetzbMATHGoogle Scholar

Copyright information

© Taiwan Fuzzy Systems Association 2019

Authors and Affiliations

  1. 1.Mathematics DepartmentUniversity of Sistan and BaluchestanZahedanIran

Personalised recommendations