Skip to main content
SpringerLink
Log in

On FGP Approach to Multiobjective Quadratic Fractional Programming Problem

  • Original Paper
  • Published:
International Journal of Applied and Computational Mathematics Aims and scope Submit manuscript

Abstract

Multiobjective quadratic fractional programming models involve optimization of many conflicting objective functions in the mathematical form of quadratic fractional with subject to the constraints. In this paper, we present an alternate new procedure for solving multiobjective quadratic fractional programming problem (MOQFPP) based on fuzzy goal programming (FGP) approach. In the proposed alternate modified technique, separate linear membership functions for each numerator and denominator function of each objective function of MOQFPP are defined. Then achievement of the maximum value of each of fuzzy goals in terms of membership functions is formulated by minimizing the sum of the negative deviational variables. The proposed modified approach is comparatively more efficient, less computational and simpler than earlier FGP technique for MOQFPP. Comparative analysis is also carried out with the help of numerical example to demonstrate the efficiency and simplicity of proposed modified approach over earlier method.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1

Similar content being viewed by others

References

  1. Balbas, A., Galperin, E., Guerra, P.J.: Sensitivity in multiobjective optimization: the generalized evolvent theorem. Nonlinear Anal. 63, 725–733 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  2. Baky, I.A.: Fuzzy goal programming algorithm for solving decentralized bi- level multiobjective programming problem. Fuzzy Sets Syst. 160, 2701–2713 (2009)

    Article  MATH  MathSciNet  Google Scholar 

  3. Chanas, S.: Fuzzy programming in multiobjective linear programming: a parametric approach. Fuzzy Sets Syst. 29, 303–313 (1989)

    Article  MATH  MathSciNet  Google Scholar 

  4. Chakraborty, M., Gupta, S.: Fuzzy mathematical programming for multiobjective linear fractional programming problem. Fuzzy Sets Syst. 125, 335–342 (2005)

    Article  MATH  Google Scholar 

  5. Gupta, S., Chakraborty, M.: Multiobjective linear programming: a fuzzy programming approach. Int. J. Manag. Syst. 13(2), 207–214 (1997)

    Google Scholar 

  6. Hanan, E.L.: On the efficiency of the product operator in fuzzy programming with multiple objective. Fuzzy Sets Syst. 2, 259–263 (1979)

    Article  Google Scholar 

  7. Jain, S., Lachhwani, K.: Multiobjective programming problem with fuzzy relational equations. Int. J. Oper. Res. 6(2), 55–63 (2009)

    MathSciNet  Google Scholar 

  8. Jain, S., Lachhwani, K.: Solution of a multiobjective fractional programming problem using fuzzy programming approach. Proc. Natl. Acad. Sci. India Sect. A 79, 267–272 (2009)

    Google Scholar 

  9. Li, S., Hu, C.: Satisfying optimization method based on goal programming for fuzzy multiple objective optimization problem. Eur. J. Oper. Res. 193, 329–341 (2009)

    Article  MATH  MathSciNet  Google Scholar 

  10. Lachhwani, K.: FGP approach to multiobjective quadratic fractional programming problem. Int. J. Ind. Math. 6(1), (2014) Article ID IJIM-00438, 49-57

  11. Lachhwani, K.: Fuzzy goal programming approach to multiobjective quadratic programming problem. Proc. Natl. Acad. Sci. India Sect. A 82(4), 317–322 (2012)

    Article  MathSciNet  Google Scholar 

  12. Lachhwani, K.: On solving multi level multiobjective linear programming problems through fuzzy goal programming approach. Opsearch 51(4), 624–637 (2014)

    Article  MATH  MathSciNet  Google Scholar 

  13. Lachhwani, K.: Modified FGP approach for multi level multiobjective linear fractional programming problems. Appl. Math. Comput. 266, 1038–1049 (2015)

    MathSciNet  Google Scholar 

  14. Lachhwani, K.: Fuzzy goal programming approach applied to multiobjective programming problem with FREs as constraints. Decis. Sci. Lett. 4, 465–476 (2015)

    Article  Google Scholar 

  15. Lachhwani, K., Nehra, S.: Modified FGP approach and MATLAB program for solving multi level linear fractional programming problems. J. Ind. Eng. Int. 11(1), 15–36 (2015)

    Article  Google Scholar 

  16. Lachhwani, K., Poonia, M.P.: Mathematical solution of multi level fractional programming problem with fuzzy goal programming approach. J. Ind. Eng. Int. 11(1), 15–26 (2015)

    Article  Google Scholar 

  17. Mohamed, R.H.: The relationship between goal programming and fuzzy programming. Fuzzy Sets Syst. 89, 215–222 (1997)

    Article  MathSciNet  Google Scholar 

  18. Narasimhan, R.: Goal programming in fuzzy environment. Decision Sci. 11, 325–336 (1980)

    Article  Google Scholar 

  19. Pramanik, S., Roy, T.K.: Fuzzy goal programming approach to multi level programming problem. Eur. J. Oper. Res. 176, 1151–1166 (2007)

    Article  MATH  Google Scholar 

  20. Rubin, P.A., Narasimhan, R.: Fuzzy goal programming with nested priorities. Fuzzy Sets Syst. 14, 115–129 (1984)

    Article  MATH  MathSciNet  Google Scholar 

  21. Rommelfanger, H.: Interactive decision making in fuzzy linear optimization problems. Eur. J. Oper. Res. 41, 210–217 (1989)

    Article  MATH  MathSciNet  Google Scholar 

  22. Wallenius, J.: Comparative evaluation of some interactive approaches to multicriteria optimization. Manag. Sci. 21, 1387–1396 (1975)

    Article  MATH  Google Scholar 

  23. Wolfe, P.: The simplex method for quadratic programming. Econometrica 27, 382–389 (1959)

    Article  MATH  MathSciNet  Google Scholar 

  24. Yager, R.R.: Mathematical programming with fuzzy constraints and preference on the objective. Kybernates 8, 258–291 (1979)

    MathSciNet  Google Scholar 

  25. Ying-Yung, F.: A method using fuzzy mathematical programming to solve vector maximum problem. Fuzzy Sets Syst. 9, 129–136 (1983)

    Article  Google Scholar 

  26. Yan, H., Wei, Q., Wang, J.: Constructing efficient solution structure of multiobjective linear programming. J. Math. Anal. Appl. 307, 504–523 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  27. Zimmermann, H.J.: Fuzzy programming and linear programming with several objectives function. Fuzzy Sets Syst. 1, 46–55 (1978)

    Article  MathSciNet  Google Scholar 

  28. Zimmermann, H.J.: Fuzzy mathematical programming. Comput. Oper. Res. 4, 291–298 (1981)

    MathSciNet  Google Scholar 

  29. Zeleny, M.: Multiple Criteria Decision Making. McGraw-Hill, New York (1982)

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Applied Science, National Institute of Technical Teachers Training and Research, Chandigarh, 160 019, India

    Kailash Lachhwani

Authors
  1. Kailash Lachhwani
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Kailash Lachhwani.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Lachhwani, K. On FGP Approach to Multiobjective Quadratic Fractional Programming Problem. Int. J. Appl. Comput. Math 3, 3443–3453 (2017). https://doi.org/10.1007/s40819-017-0307-7

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s40819-017-0307-7

Keywords

Search

Navigation