1. MMC
  2. All Volumes and Issues
  3. Volume 10, Number 1, 2023
  4. On modeling a lexicographic weighted maxmin–minmax approach for fuzzy linear goal programming

On modeling a lexicographic weighted maxmin–minmax approach for fuzzy linear goal programming

MMC.
2023;
Volume 10, Number 1
: pp. 186–194
https://doi.org/10.23939/mmc2023.01.186
Received: September 20, 2022
Revised: December 01, 2020
Accepted: December 06, 2022

Mathematical Modeling and Computing, Vol. 10, No. 1, pp. 186–194 (2023)

Authors:
  1. M. G. Iskander
1
Department of Business Administration, The British University in Egypt

In this paper, a novel approach for solving fuzzy goal programming is proposed.  This approach utilizes the weighted maxmin and weighted minmax methods simultaneously.  Relative weight is assigned to each fuzzy goal according to the preference of the decision maker.  A model for each of the two methods is separately stated; hence the two models are merged into one.  Moreover, the lexicographic maximization technique is applied to guarantee efficient solutions.  Therefore, the proposed approach allows the decision maker to compromise between the two methods.  Furthermore, the proposed approach can be implemented to concave piecewise linear membership functions.  This type of membership function is represented using the min-operator.  The effectiveness of the proposed approach is illustrated by a numerical example.

fuzzy goal programming
weighted maxmin
weighted minmax
lexicographic maximization
efficiency
  1. Zimmermann H. J.  Fuzzy programming and linear programming with several objective functions.  Fuzzy Sets and Systems.  1 (1), 45–55  (1978).
  2. Hannan E. L.  On fuzzy goal programming.  Decision Sciences.  12 (3), 522–531 (1981).
  3. Yaghoobi M. A., Tamiz M.  A method for solving fuzzy goal programming problems based on MINMAX approach.  European Journal of Operational Research.  177 (3), 1580–1590 (2007).
  4. Yang T., Ignizio J. P., Kim H.-J.  Fuzzy programming with nonlinear membership functions: Piecewise linear approximation.  Fuzzy Sets and Systems.  41 (1), 39–53 (1991).
  5. Kim J. S., Whang K.-S.  A tolerance approach to the fuzzy goal programming problems with unbalanced triangular membership function.  European Journal of Operational Research.  107 (3), 614–624 (1998).
  6. Lin C.-C.  A weighted max–min model for fuzzy goal programming.  Fuzzy Sets and Systems.  142 (3), 407–420 (2004).
  7. Iskander M. G.  Using the weighted max–min approach for stochastic fuzzy goal programming: A case of fuzzy weights.  Applied Mathematics and Computation.  188 (1), 456–461 (2007).
  8. Amid A., Ghodsypour S. H., O'Brien C.  A weighted max–min model for fuzzy multi-objective supplier selection in a supply chain.  International Journal of Production Economics.  131 (1), 139–145 (2011).
  9. Iskander M. G.  A suggested approach for solving weighted goal programming problem.  American Journal of Computational and Applied Mathematics.  2 (2), 55–57 (2012).
  10. Cheng H., Huang W., Zhou Q., Cai J.  Solving fuzzy multi-objective linear programming problems using deviation degree measures and weighted max–min method.  Applied Mathematical Modelling.  37 (10–11), 6855–6869 (2013).
  11. Iskander M. G.  A joint maxmin-lexicographic maximisation approach in fuzzy goal programming using dominance possibility and necessity criteria.  International Journal of Multicriteria Decision Making.  8 (1), 1–12 (2019).
  12. Umarusman N.  Min–max goal programming approach for solving multi-objective de novo programming problems.  International Journal of Operations Research.  10 (2), 92–99 (2013).
  13. Banik S., Bhattacharya D.  A note on min–max goal programming approach for solving multi-objective de novo programming problems.  International Journal of Operational Research.  37 (1), 32–47 (2020).
  14. Umarusman N.  Fuzzy goal programming problem based on minmax approach for optimal system design.  Alphanumeric Journal.  6 (1), 177–192  (2018).
  15. Zangiabadi M., Maleki H. R.  Fuzzy goal programming for multiobjective transportation problems.  Journal of Applied Mathematics and Computing.  24 (1), 449–460 (2007).
  16. Venkatasubbaiah K., Acharyulu S. G., Mouli K. C.  Fuzzy goal programming method for solving multi-objective transportation problems.  Global Journal of Research in Engineering.  11 (3), 4–10 (2011).
  17. Ikeagwuani C. C., Nwonu D. C., Onah H. N.  Min–max fuzzy goal programming – Taguchi model for multiple additives optimization in expansive soil improvement.  International Journal for Numerical and Analytical Methods in Geomechanics.  45 (4), 431–456 (2021).
  18. Raskin L., Sira O., Sagaydachny D.  Multi-criteria optimization in terms of fuzzy criteria definitions.  Mathematical Modeling and Computing.  5 (2), 207–220 (2018).
  19. Aköz O., Petrovic D.  A Fuzzy goal programming method with imprecise goal hierarchy.  European Journal of Operational Research.  181 (3), 1427–1433 (2007).
  20. Ogryczak W.  Comments on properties of the minmax solutions in goal programming.  European Journal of Operational Research.  132 (1), 17–21 (2001).