On a generalized fuzzy goal optimization for solving fuzzy multi-objective linear programming problems

Many organizational decision problems can be formulated by multi-objective linear programming (MOLP) models. Referring to the imprecision inherent in human judgments, uncertainty may be incorporated in the parameters of an MOLP model when it is established, which is called a Fuzzy MOLP (FMOLP) problem. What is an optimal solution for an FMOLP problem is the first issue to deal with in this study. The second issue is how to effectively derive an optimal solution for an FMOLP problem since uncertainty is also reflected in a solution process of an FMOLP problem. By introducing three types of comparison of fuzzy numbers and an adjustable satisfactory degree α in this study, a new solution concept of FMOLP is given. For handling the second issue, this study develops an interactive fuzzy goal optimization method which provides an interactive fashion with decision makers during their solution process and allows decision makers to give their fuzzy goals in any forms of membership functions. An illustrative example gives the details of the solution concept and the proposed method.