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An approach for solving fully fuzzy multi-objective linear fractional optimization problems

  • Rubi Arya
  • Pitam Singh
  • Saru KumariEmail author
  • Mohammad S. Obaidat
Methodologies and Application
  • 26 Downloads

Abstract

This article presents an algorithm for solving fully fuzzy multi-objective linear fractional (FFMOLF) optimization problem. Some computational algorithms have been developed for the solution of fully fuzzy single-objective linear fractional optimization problems. Veeramani and Sumathi (Appl Math Model 40:6148–6164, 2016) pointed out that no algorithm is available for solving a single-objective fully fuzzy optimization problem. Das et al. (RAIRO-Oper Res 51:285–297, 2017) proposed a method for solving single-objective linear fractional programming problem using multi-objective programming. Moreover, it is the fact that no method/algorithm is available for solving a FFMOLF optimization problem. In this article, a fully fuzzy MOLF optimization problem is considered, where all the coefficients and variables are assumed to be the triangular fuzzy numbers (TFNs). So, we are proposing an algorithm for solving FFMOLF optimization problem with the help of the ranking function and the weighted approach. To validate the proposed fuzzy intelligent algorithm, three existing classical numerical problems are converted into FFMOLF optimization problem using approximate TFNs. Then, the proposed algorithm is applied in an asymmetric way. Since there is no algorithm available in the existing literature for solving this difficult problem, we compare the obtained efficient solutions with corresponding existing methods for deterministic problems.

Keywords

Multi-objective optimization Linear fractional optimization Fuzzy multi-criteria decision making Fuzzy optimization Triangular fuzzy number (TFNs) 

Notes

Compliance with ethical standards

Conflict of interest

All the authors declare that they have no conflict of interest.

Ethical approval

This article does not contain any studies with human participants or animals performed by any of the authors.

References

  1. Arya R, Singh P (2017) Fuzzy parametric iterative method for multi-objective linear fractional optimization problems. J Intell Fuzzy Syst 32:421–433CrossRefGoogle Scholar
  2. Arya R, Singh P (2018) Bhati D A fuzzy based branch and bound approach for multi-objective linear fractional (MOLF) optimization problems. J Comput Sci 24:54–64MathSciNetCrossRefGoogle Scholar
  3. Arya R, Singh P (2019) Fuzzy efficient iterative method for multi-objective linear fractional programming problems. Math Comput Simul 160:39–54MathSciNetCrossRefGoogle Scholar
  4. Bellman RE, Zadeh LA (1970) Decision making in a fuzzy environment. Manag Sci 17(4):141–164MathSciNetCrossRefGoogle Scholar
  5. Bhati D, Singh P (2017) Branch and bound computational method for multi-objective linear fractional optimization problem. Neural Comput Appl 28:3341–3351 CrossRefGoogle Scholar
  6. Chakraborty M, Gupta S (2002) Fuzzy mathematical programming for multi-objective linear fractional programming problem. Fuzzy Sets Syst 125:335–342MathSciNetCrossRefGoogle Scholar
  7. Chang C-T (2017) Fuzzy linearization strategy for multiple objective linear fractional programming with binary utility functions. Comput Ind Eng 112:437–446CrossRefGoogle Scholar
  8. Charnes A, Cooper WW (1962) Programming with linear fractional functional. Nav Res Logist Q 9:181–186MathSciNetCrossRefGoogle Scholar
  9. Costa JP (2005) An interactive method for multiple objective linear fractional programming problems. OR Spectr 27:633–652CrossRefGoogle Scholar
  10. Costa JP (2007) Computing non-dominated solutions in MOLFP. Eur J Oper Res 181:1464–1475CrossRefGoogle Scholar
  11. Craven BD (1988) Fractional programming. Heldermann Verlag, BerlinzbMATHGoogle Scholar
  12. Das SK, Mandal T, Edalatpanah SA (2017) A new approach for solving fully fuzzy linear fractional programming problems using the multi-objective linear programming. RAIRO-Oper Res 51(1):285–297MathSciNetCrossRefGoogle Scholar
  13. Das SK, Edalatpanah SA, Mandal T (2018) A proposed model for solving fuzzy linear fractional programming problem: numerical Point of View. J Comput Sci 25:367–375MathSciNetCrossRefGoogle Scholar
  14. Deb M (2018) A study of fully fuzzy linear fractional programming problems by signed distance ranking technique in optimization techniques for problem solving in uncertainty. IGI Global, pp 73–115Google Scholar
  15. Dutta D, Rao JR, Tiwari RN (1992) Sensitivity analysis in fractional programming-the tolerance approach. Int J Syst Sci 23(5):823–832MathSciNetCrossRefGoogle Scholar
  16. Ezzati R, Khorram E, Enayati R (2013) A new algorithm to solve fully fuzzy linear programming problems using the MOLP problem. Appl Math Model 39:3183–3193MathSciNetCrossRefGoogle Scholar
  17. Guzel N (2013) A proposal to the solution of multi-objective linear fractional programming. Hindawi Publishing Corporation Abstract and Applied Volume. Article ID 435030:1–4Google Scholar
  18. Guzel N, Sivri M (2005) Taylor series application of multi-objective linear fractional programming problem. Trakya Univ J Sci 6(2):80–87Google Scholar
  19. Kauffmann A, Gupta MM (1991) Introduction to fuzzy arithmetic: theory and applications. Van Nostrand Reinhold, New YorkGoogle Scholar
  20. Kumar A, Kaur J, Singh P (2011) A new method for solving fully fuzzy linear programming problems. Appl Math Model 35:817–823MathSciNetCrossRefGoogle Scholar
  21. Liou TS, Wang MJ (1992) Ranking fuzzy number with integral value. Fuzzy Set Syst 50:247–255MathSciNetCrossRefGoogle Scholar
  22. Lotfi FH, Allahviranloo T, Jondabeha MA, Alizadeh L (2009) Solving a fully fuzzy linear programming using lexicography method and fuzzy approximate solution. Appl Math Model 33:1464–1475Google Scholar
  23. Luhandjula MK (1984) Fuzzy approches for multiple objective linear fractional optimization. Fuzzy Sets Syst 13:11–23CrossRefGoogle Scholar
  24. Najafi HS, Edalatpanah SA (2013) A note on “A new method for solving fully fuzzy linear programming problems”. Appl Math Model 37(14–15):7865–7867MathSciNetCrossRefGoogle Scholar
  25. Najafi HS, Edalatpanah SA, Dutta H (2016) A nonlinear model for fully fuzzy linear programming with fully unrestricted variables and parameters. Alex Eng J 55(3):2589–2595CrossRefGoogle Scholar
  26. Pal BB, Moitra BN, Maulik U (2003) A goal programming procedure for fuzzy multi-objective linear fractional programming problem. Fuzzy Sets Syst 139:395–405CrossRefGoogle Scholar
  27. Pop B, Stancu-Minasian IM (2008) A method of solving fully fuzzified linear fractional programming problem. J Appl Math Comput 27:227–242MathSciNetCrossRefGoogle Scholar
  28. Schaible S (1976) Fractional programming I: duality. Manag Sci 22:658–667MathSciNetzbMATHGoogle Scholar
  29. Schaible S (1978) Analyse and Anwendungen von Quotientenprogrammen. Verlag Anton Hain, Meisenheim am GlanzbMATHGoogle Scholar
  30. Sharma U, Aggarwal S (2018) Solving fully fuzzy multi-objective linear programming problem using nearest interval approximation of fuzzy number and interval programming. Int J Fuzzy Syst 20(2):488–499MathSciNetCrossRefGoogle Scholar
  31. Valipour A, Yaghoobi MA, Mashinchi M (2014) An iterative approach to solve multiobjective linear fractional programming problems. Appl Math Model 38:38–49MathSciNetCrossRefGoogle Scholar
  32. Veeramani C, Sumathi M (2014) Fuzzy mathematical programming approach for solving fuzzy linear programming problem. RAIRO-Oper Res 48:109–122MathSciNetCrossRefGoogle Scholar
  33. Veeramani C, Sumathi M (2016) Solving the linear fractional programming problem in a fuzzy environment: numerical approach. Appl Math Model 40:6148–6164MathSciNetCrossRefGoogle Scholar
  34. Zimmerman HJ (1978) Fuzzy programming and linear programming with several objective functions. Fuzzy Sets Syst 1:45–55MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  • Rubi Arya
    • 1
  • Pitam Singh
    • 1
  • Saru Kumari
    • 2
    Email author
  • Mohammad S. Obaidat
    • 3
    • 4
  1. 1.Department of MathematicsMotilal Nehru National Institute of Technology AllahabadPrayagrajIndia
  2. 2.Department of MathematicsChaudhary Charan Singh UniversityMeerutIndia
  3. 3.ECE DepartmentNazarbayev UniversityAstanaKazakhstan
  4. 4.King Abdullah II School of Information TechnologyThe University of Jordan, Jordan and University of Science and TechnologyBeijingChina

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