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


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.


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


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.


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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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