Fuzzy integer-valued data envelopment analysis^★

¹ Department of Mathematics, Lahijan Branch, Islamic Azad University, Lahijan, Iran
² Department of Applied Mathematics, Rasht Branch, Islamic Azad University, Rasht, Iran

^* Corresponding author: sohrabkordrostami@gmail.com

Received: 8 September 2016
Accepted: 30 October 2017

Abstract

In conventional data envelopment analysis (DEA) models, the efficiency of decision making units (DMUs) is evaluated while data are precise and continuous. Nevertheless, there are occasions in the real world that the performance of DMUs must be calculated in the presence of vague and integer-valued measures. Therefore, the current paper proposes fuzzy integer-valued data envelopment analysis (FIDEA) models to determine the efficiency of DMUs when fuzzy and integer-valued inputs and/or outputs might exist. To illustrate, fuzzy number ranking and graded mean integration representation methods are used to solve some integer-valued data envelopment analysis models in the presence of fuzzy inputs and outputs. Two examples are utilized to illustrate and clarify the proposed approaches. In the provided examples, two cases are discussed. In the first case, all data are as fuzzy and integer-valued measures while in the second case a subset of data is fuzzy and integer-valued. The results of the proposed models indicate that the efficiency scores are calculated correctly and the projections of fuzzy and integer factors are determined as integer values, while this issue has not been discussed in fuzzy DEA, and projections may be estimated as real-valued data.