Title: Convex and non-convex approaches for cost efficiency models with fuzzy data

Authors: Khalil Paryab; Madjid Tavana; Rashed Khanjani Shiraz

Addresses: School of Mathematics, Iran University of Science and Technology, Tehran 13114-16846, Iran ' Lindback Distinguished Chair of Information Systems and Decision Sciences, La Salle University, Philadelphia, PA 19141, USA ' School of Mathematics, Iran University of Science and Technology, Tehran 13114-16846, Iran

Abstract: Classical cost efficiency (CE) measurement models require exact and accurate knowledge of the input and output values for each decision making unit (DMU). However, the observed values of the input and output data in real-world problems are often imprecise or vague. In recent years, fuzzy data envelopment analysis (DEA) has been successfully used to deal with imprecise or vague data in efficiency measurement. In this paper, we incorporate fuzzy set theory into the traditional CE measurement. We propose two approaches based on the convex DEA and non-convex free disposable hull (FDH) approach with fuzzy variables. The purpose of this paper is two-fold: 1) we develop a CE analysis for non-parametric convex methods based on fuzzy set theory; 2) we further develop a non-convex CE analysis model where the non-convexity is formulated based on the FDH approach. We also present a numerical example to demonstrate the applicability of the proposed models and exhibit the efficacy of the procedures and algorithms.

Keywords: data envelopment analysis; fuzzy DEA; cost efficiency; fuzzy set theory; free disposable hull; non-parametric convex; convex approaches; non-convex approaches; fuzzy data; efficiency measurement.

DOI: 10.1504/IJDMMM.2015.071450

International Journal of Data Mining, Modelling and Management, 2015 Vol.7 No.3, pp.213 - 238

Received: 08 May 2021
Accepted: 12 May 2021

Published online: 28 Aug 2015 *

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