usnig lr-fuzzy numbers data to measure the eciency and the malmquist productivity index in data envelopment analysis , and its application in insurance organizations

in many real applications, the data of production processes can't be precisely measured.we develop some fuzzy versions of the classical dea models (in particular, the ccrmodel) by using some ranking methods based on the comparison of cuts. our approachescan be seen as an extension of the dea methodology. the provides users and practitionerswith models which represent some real life processes more appropriately. dea- basedmalmquist productivity index measures the productivity change over time. in this paperwe provide an extension to the dea- based malmquist productivity index for all dmuswith fuzzy data.