RESEARCH ARTICLE Restricting the relative weights in data envelopment analysis Hosein Arman 1 | Abdollah Hadi-Vencheh 2 1 Department of Management, Najafabad Branch, Islamic Azad University, Najafabad, Iran 2 Department of Mathematics, Isfahan (Khorasgan) Branch, Islamic Azad University, Isfahan, Iran Correspondence Hosein Arman, Department of Management, Najafabad Branch, Islamic Azad University, Najafabad, Iran. Email: hosein.arman@yahoo.com, hosein. arman@phu.iaun.ac.ir Abstract In this paper, we address the problem of relative weight restriction in data envelopment analysis (DEA). A fuzzy-based approach to restricting the relative weights is proposed in this study. Unlike the classical weight restriction methods, the proposed approach has an interactive orientation. That is, similar to analytical hierarchy process, the proposed method shares the decision maker (DM) in weight restriction process. Here, the preferences of DM are asked via pairwise comparison matrices. Then, the weights of factors (inputs/ outputs) are extracted from these matrices. These weights, finally, are incorpo- rated in multiplier DEA models as the parametric triangular fuzzy numbers, in which, the parameter value indicates the degree of conformity of the relative weights according to DM views. To best of our knowledge, no one has been yet utilized fuzzy set theory to control the relative weights in DEA. Putting in another word, the contribution of this study is that the authors propose a new approach based on fuzzy set theory to weight restriction in DEA. A last, a real case on financial banking efficiency is used to illustrate the proposed approach. KEYWORDS analytical hierarchy process, data envelopment analysis, fuzzy number, relative weight, α-cut 1 | INTRODUCTION Data envelopment analysis (DEA), proposed by Charnes, Cooper, and Rhodes (1978) to measure the relative effi- ciency of a set of decision-making units (DMUs). For this purpose, DEA determines a set of weights for each DMU. These weights are, typically, different for each DMU, because DEA is applied separately for each DMU to max- imize its efficiency. In fact, DEA is value-free and does not require any priori weights of the factors (Thompson, Langemeier, Lee, Lee, & Thrall, 1990). The flexibility of the inputs (outputs) weights in DEA models may result in some drawbacks. First, the same factor may be assigned different weights, when DEA is applied to measure the efficiency of different DMUs (Roll & Golany, 1993). Second, the weights of factors derived from conventional DEA models are usually unac- ceptable in real world applications (Roll & Golany, 1993) and do not reflect the DM's preferences. Third, unreason- able weights may be assigned to some factors. This will be more highlighted when DEA allocates a weight of zero to some inputs (outputs) and therefore neglects them, leading to unsatisfactory result (Wong & Beasley, 1990). In fact, the classical DEA models are totally flexible to assign the weights to factors that may result in an over- estimation of technical efficiency (Puig-Junoy, 2000). Therefore, some DMUs may be assessed on only a subset of their factors, while the rest are all ignored (Dyson & Thanassoulis, 1988). Indeed, introducing the easy and applicable approaches for restricting the weights in DEA Received: 28 February 2020 Revised: 24 June 2020 Accepted: 24 June 2020 DOI: 10.1002/ijfe.2007 Int J Fin Econ. 2020;1–10. wileyonlinelibrary.com/journal/ijfe © 2020 John Wiley & Sons, Ltd. 1