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Solving fuzzy multi-objective linear programming problems using deviation degree measures and weighted max–min method

Journal Article


Abstract


  • This paper proposes a method for solving fuzzy multi-objective linear programming (FMOLP) problems where all the coefficients are triangular fuzzy numbers and all the constraints are fuzzy equality or inequality. Using the deviation degree measures and weighted max–min method, the FMOLP problem is transformed into crisp linear programming (CLP) problem. If decision makers fix the values of deviation degrees of two side fuzzy numbers in each constraint, then the δ-pareto-optimal solution of the FMOLP problems can be obtained by solving the CLP problem. The bigger the values of the deviation degrees are, the better the objectives function values will be. So we also propose an algorithm to find a balance-pareto-optimal solution between two goals in conflict: to improve the objectives function values and to decrease the values of the deviation degrees. Finally, to illustrate our method, we solve a numerical example.

UOW Authors


  •   Cheng, Haifang (external author)
  •   Huang, Wei (external author)
  •   Zhou, Quan
  •   Cai, Jianhu (external author)

Publication Date


  • 2013

Citation


  • Cheng, H., Huang, W., Zhou, Q. & Cai, J. (2013). Solving fuzzy multi-objective linear programming problems using deviation degree measures and weighted max–min method. Applied Mathematical Modelling: simulation and computation for engineering and environmental systems, 37 (10-11), 6855-6869.

Scopus Eid


  • 2-s2.0-84878196377

Number Of Pages


  • 14

Start Page


  • 6855

End Page


  • 6869

Volume


  • 37

Issue


  • 10-11

Place Of Publication


  • United States

Abstract


  • This paper proposes a method for solving fuzzy multi-objective linear programming (FMOLP) problems where all the coefficients are triangular fuzzy numbers and all the constraints are fuzzy equality or inequality. Using the deviation degree measures and weighted max–min method, the FMOLP problem is transformed into crisp linear programming (CLP) problem. If decision makers fix the values of deviation degrees of two side fuzzy numbers in each constraint, then the δ-pareto-optimal solution of the FMOLP problems can be obtained by solving the CLP problem. The bigger the values of the deviation degrees are, the better the objectives function values will be. So we also propose an algorithm to find a balance-pareto-optimal solution between two goals in conflict: to improve the objectives function values and to decrease the values of the deviation degrees. Finally, to illustrate our method, we solve a numerical example.

UOW Authors


  •   Cheng, Haifang (external author)
  •   Huang, Wei (external author)
  •   Zhou, Quan
  •   Cai, Jianhu (external author)

Publication Date


  • 2013

Citation


  • Cheng, H., Huang, W., Zhou, Q. & Cai, J. (2013). Solving fuzzy multi-objective linear programming problems using deviation degree measures and weighted max–min method. Applied Mathematical Modelling: simulation and computation for engineering and environmental systems, 37 (10-11), 6855-6869.

Scopus Eid


  • 2-s2.0-84878196377

Number Of Pages


  • 14

Start Page


  • 6855

End Page


  • 6869

Volume


  • 37

Issue


  • 10-11

Place Of Publication


  • United States