A Fuzzy Goal Programming Formulation with Multiple Target Levels

The essential activity of a manager is decision making, which is becoming more and more complex, mainly in the multi‐criteria problems. Multi‐choice goal programming (MCGP) is considered as a robust tool in operational research to solve this type of problem. However, in real world problems, determining precise targets for the goals is a difficult task. To deal with such situation, Tabrizi introduced and used in 2012 the concept of membership functions in the MCGP model in order to model the targets fuzziness of each goal. In their model, they considered just only one type of functions (triangular form), which does not reflect adequately the decision maker's preferences that are considered as an essential element for modelling the goal's fuzziness. Their model is called Fuzzy MCGP. In this paper, new ideas are presented to reformulate MCGP model to tackle all types of functions by introducing the (decision maker's) preferences. The concept of indifference thresholds is used in the new formulation for characterizing the imprecision and the preferences associated with all types of the goals. The proposed formulation provides useful insight about the solution of a new class of problems. A numerical example is given to demonstrate the validity and strength of the new formulation.