Intuitionistic fuzzy DEA/AR and its application to flexible manufacturing systems

The concept of assurance region (AR) was proposed in Data Envelopment Analysis (DEA) literature to restrict the ratio of any two weights within a given lower and upper bounds so as to overcome the difficulty of ignoring or relying too much on any of the input or output while calculating the efficiency. Further, AR approach was extended to handle fuzzy input/output data. But, available information is not always sufficient to define the impreciseness in the input/output data using classical fuzzy sets. Intuitionistic Fuzzy Set (IFS) is a generalized fuzzy set to characterize the impreciseness by taking into account degree of hesitation also. In this paper, intuitionistic fuzzy DEA/AR approach has been proposed to evaluate the efficiency where input/output data are represented as intuitionistic fuzzy. Based on the expected value approach, classical cross efficiency has also been generalized to rank the DMUs for the case of intuitionistic fuzzy data. To the best of my knowledge, this is the first attempt to propose assurance region approach (DEA/AR) in DEA with intuitionistic fuzzy input/output data. This approach is useful for the experts and decision makers when they are hesitant about defining the degree of membership/non-membership of fuzzy data. Results have been illustrated and validated using a case of flexible manufacturing systems (FMS).