The numerous studies on comparing and ranking fuzzy numbers clear that this task is still young. However, the observation that many papers do not hesitate to use some incorrect ranking methods in risk analysis problems, encouraged the author to point out the shortcoming of some of these methods. In this note, we review briefly the methods for ranking fuzzy number in risk analysis.

Integrated supply chain includes different components of order, production and distribution and it plays an important role on reducing the cost of manufacturing system. In this paper, an integrated supply chain in a form of multi-objective decision-making problem is presented. The proposed model of this paper considers different parameters with uncertainty using trapezoid numbers. We first implement a ranking method to covert the fuzzy model into a crisp one and using multi-objective particle swarm optimization, we solve the resulted model. The results are compared with the performance of NSGA-II for some randomly generated problems and the preliminary results indicate that the proposed model of the paper performs better than the alternative method.