A generalization of fuzzy goal programming with preemptive structure

This article proposes an alternative method that utilizes a penalty cost to solve an FGP problem with preemptive structure. By investing the properties of this FGP, we have transformed an FGP into a simpler form which can be solved with 1 iteration. Besides, the proposed method allows the mix-use of the linguistic terms of ‘around’, ‘at least’, and ‘at most’ with different types of membership functions. With designed operations of dilation and contraction of these membership functions, the preference attitude of a decision maker in uncertain environment can also be described.