Abstract—Multi-component data envelopment analysis (MC- DEA) is a popular technique for measuring aggregate performance of the decision making units (DMUs) along with their components. However, the conventional MC-DEA is limited to crisp input and output data which may not always be available in exact form. In real life problems, data may be imprecise or fuzzy. Therefore, in this paper, we propose (i) a fuzzy MC-DEA (FMC-DEA) model in which shared and undesirable fuzzy resources are incorporated, (ii) the proposed FMC-DEA model is transformed into a pair of crisp models using   cut approach, (iii) fuzzy aggregate performance of a DMU and fuzzy efficiencies of components are defined to be fuzzy numbers, and (iv) a numerical example is illustrated to validate the proposed approach. Keywords—Multi-component DEA, fuzzy multi-component DEA, fuzzy resources. I. INTRODUCTION HE data envelopment analysis (DEA) is a non-parametric technique for evaluating the relative efficiencies of decision making units (DMUs) with multiple inputs and outputs [1]. It has been applied to wide range of organizations such as banks, hospitals, schools, etc. However, in many real life instances, DMUs can be separated into different components, also known as decision making sub-units (DMSUs). A DMU with such structure is known as multi- component DMU. The study of the aggregate performance of multi-component DMUs along with their components is known as multi-component DEA (MC-DEA) [2]-[4]. The standard DEA and MC-DEA models are typically based on the assumption that inputs have to be minimized and outputs have to be maximized. However, undesirable and shared resources can also be present in the production process which needs to be included while measuring aggregate and component-wise performances. Thus, in this study, both shared and undesirable resources are incorporated into the production process of MC- DEA. The conventional MC-DEA is limited to crisp input and output data which may not always be available in exact form. In real life applications, data might be available in fuzzy or imprecise form. Therefore, in such situations, fuzzy MC-DEA (FMC-DEA) approach is more preferable as compared to traditional MC-DEA. In this paper, we extend traditional MC- DEA to FMC-DEA and propose FMC-DEA model. In order to J. Puri is with the Indian Institute of Technology Roorkee, Roorkee- 247667, India (corresponding author, Tel: +91-7500766529; e-mail: puri.jolly@ gmail.com). S. P. Yadav is with the Indian Institute of Technology Roorkee, Roorkee- 247667, India (e-mail: spyorfma@gmail.com). evaluate fuzzy performance of DMUs along with their DMSUs in fuzzy environment, we use   cut approach to solve FMC-DEA model. Further, proposed methodology is illustrated with a numerical example. The paper is organized as follows: Section II presents an overview of DEA and MC-DEA with shared and undesirable resources. Section III presents the proposed FMC-DEA model with shared and undesirable fuzzy resources followed by the methodology to solve it. A numerical illustration is presented in Section IV. Section V concludes the findings of our study. II. DEA AND MULTI-COMPONENT DEA A. DEA (Data Envelopment Analysis) To describe DEA efficiency evaluation, assume that the performance of a set of n homogeneous DMUs be measured. The performance of DMU k is characterized by a production process of m inputs x ik ; i = 1, …, m to yield s 1 desirable outputs 1 ; 1, 2, , g rk y r s   and s 2 undesirable outputs 2 ; 1, 2, , . b pk y p s   Assume that input-output data are positive. In DEA, the efficiency E k of DMU k in the presence of undesirable outputs is defined as 1 2 1 1 1 . s s m g g b b k rk rk pk pk ik ik r p i E u y u y vx                 Then, the relative efficiency of DMU k is evaluated from the following mathematical model presented by Puri and Yadav [5]: Max subject to 0 1, 1, ,, , , , k j g b rk pk ik E E j n u ru pv i              Model - 1  where , g ik rk v u and b pk u are the weights corresponding to the i th input, r th desirable output and p th undesirable output of DMU k respectively. B. Multi-Component DEA with Shared and Undesirable Resources Nomenclature: Let n: Number of DMUs, d: Number of DMSUs. For DMU k and 1, 2, , , i d   let  : S I Number of shared inputs consumed by DMSU i .  : i I Number of external inputs consumed by DMSU i .  : g i K Number of desirable outputs produced by DMSU i . Jolly Puri, Shiv Prasad Yadav Fuzzy Multi-Component DEA with Shared and Undesirable Fuzzy Resources T World Academy of Science, Engineering and Technology International Journal of Computer and Information Engineering Vol:8, No:9, 2014 1207 International Scholarly and Scientific Research & Innovation 8(9) 2014 scholar.waset.org/1307-6892/9999243 International Science Index, Computer and Information Engineering Vol:8, No:9, 2014 waset.org/Publication/9999243