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

2013; Elsevier BV; Volume: 37; Issue: 10-11 Linguagem: Inglês

10.1016/j.apm.2013.01.048

1872-8480

Haifang Cheng, Weilai Huang, Quan Zhou, Jianhu Cai,

Optimization and Variational Analysis

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.