A fully fuzzy approach to DEA and multi-component DEA for measuring fuzzy technical efficiencies in the presence of undesirable outputs

DEA is a non-parametric technique for measuring the relative technical efficiencies of similar decision making units (DMUs) with multiple inputs and multiple outputs. In smoe real life situations, DMUs may perform different types of functions and can be segregated into independent components such that each component has its own set of inputs and outputs. Owing the importance of the internal structure of the DMUs, DEA has been extended to multi-component DEA (MC-DEA) which is a technique for measuring the technical efficiencies of the DMUs and their components. The conventional DEA and MC-DEA approaches require crisp input and output data which may not always be available precisely. However, in real life problems, data might be imprecise or vague which can suitably be represented by fuzzy numbers. Many researchers have proposed methods to deal with fuzzy parameters in DEA and MC-DEA. However, in real situations, the decision variables can also take fuzzy forms. Therefore, the aim of the present paper is fourfold: (i) to extend DEA in the presence of undesirable outputs to fully fuzzy DEA (FFDEA) for measuring the fuzzy technical efficiencies of the DMUs in fully fuzzy environments where all decision variables and parameters are taken as fuzzy numbers, in particular triangular fuzzy numbers, (ii) to extend MC-DEA in the presence of undesirable outputs to multi-component fully fuzzy DEA (MC-FFDEA) for measuring the fuzzy technical efficiencies of DMUs and their components in fully fuzzy environments, (iii) to propose a new ranking function approach to transform both the FFDEA and MC-FFDEA models into crisp linear programming problems, and (iv) to present numerical examples in order to validate the effectiveness and advantages of the proposed approach over the existing ones. © 2015, The Society for Reliability Engineering, Quality and Operations Management (SREQOM), India and The Division of Operation and Maintenance, Lulea University of Technology, Sweden.