Title: Fuzzy stochastic input-oriented primal data envelopment analysis models with application to insurance industry
Authors: Seyed Hadi Nasseri; Ali Ebrahimnejad; Omid Gholami
Addresses: Department of Mathematics, Faculty of Mathematical Sciences, University of Mazandaran, Babolsar, Iran ' Department of Mathematics, Qaemshahr Branch, Islamic Azad University, P.O. Box 163, Qaemshahr, Iran ' Department of Mathematics, Faculty of Mathematical Sciences, University of Mazandaran, Babolsar, Iran
Abstract: Data envelopment analysis (DEA) is a widely used technique for measuring the relative efficiencies of decision making units (DMUs) with multiple inputs and multiple outputs. However, in real-world problems, the observed values of the input and output data are often vague or random. Indeed, decision makers (DMs) may encounter a hybrid uncertain environment where fuzziness and randomness coexist in a problem. This paper proposes a normal distribution with fuzzy components to deal with fuzziness and randomness of input and output data. The proposed normal distribution introduces a class of fuzzy random variables. We propose a DEA model problems characterised by fuzzy stochastic variables. Unlike the existing approaches, the proposed fuzzy stochastic DEA model is transformed into a deterministic model with linear constraints. A case study in the insurance industry is presented to exhibit the efficacy and the applicability of the proposed model.
Keywords: data envelopment analysis; fuzzy DEA; fuzzy random variables; normal distribution; efficiency scores; fuzzy logic; insurance industry; decision making units; DMUs; stochastic variables.
International Journal of Applied Decision Sciences, 2016 Vol.9 No.3, pp.259 - 282
Received: 30 Jun 2016
Accepted: 01 Aug 2016
Published online: 20 Dec 2016 *