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Hatami-Marbini, A., M. Tavana, A. Emrouznejad and S. Saati (2012). “Efficiency measurement in fuzzy additive Data Envelopment Analysis.” International Journal of Industrial and Systems Engineering 10(1): 1-20.

Performance evaluation in conventional data envelopment analysis (DEA) requires crisp numerical values. However, the observed values of the input and output data in real-world problems are often imprecise or vague. These imprecise and vague data can be represented by linguistic terms characterised by fuzzy numbers in DEA to reflect the decision-makers’ intuition and subjective judgements. This paper extends the conventional DEA models to a fuzzy framework by proposing a new fuzzy additive DEA model for evaluating the efficiency of a set of decision-making units (DMUs) with fuzzy inputs and outputs. The contribution of this paper is threefold: (1) we consider ambiguous, uncertain and imprecise input and output data in DEA, (2) we propose a new fuzzy additive DEA model derived from the ?-level approach and (3) we demonstrate the practical aspects of our model with two numerical examples and show its comparability with five different fuzzy DEA methods in the literature.

Zerafat Angiz L, M., A. Emrouznejad and A. Mustafa (2012). “Fuzzy Data Envelopment Analysis: A Discrete Approach.” Expert Systems with Applications 39(3): 2263–2269.

Data envelopment analysis (DEA) as introduced by Charnes, Cooper, and Rhodes (1978) is a linear programming technique that has widely been used to evaluate the relative efficiency of a set of homogenous decision making units (DMUs). In many real applications, the input–output variables cannot be precisely measured. This is particularly important in assessing efficiency of DMUs using DEA, since the efficiency score of inefficient DMUs are very sensitive to possible data errors. Hence, several approaches have been proposed to deal with imprecise data. Perhaps the most popular fuzzy DEA model is based on ?-cut. One drawback of the ?-cut approach is that it cannot include all information about uncertainty. This paper aims to introduce an alternative linear programming model that can include some uncertainty information from the intervals within the ?-cut approach. We introduce the concept of “local ?-level” to develop a multi-objective linear programming to measure the efficiency of DMUs under uncertainty. An example is given to illustrate the use of this method.

Emrouznejad, A., M. Zerafat Angiz L. and W. Ho (2012). “An alternative formulation for the fuzzy assignment problem.” Journal of the Operational Research Society 63(1): 59–63.

he existing assignment problems for assigning n jobs to n individuals are limited to the considerations of cost or profit measured as crisp. However, in many real applications, costs are not deterministic numbers. This paper develops a procedure based on Data Envelopment Analysis method to solve the assignment problems with fuzzy costs or fuzzy profits for each possible assignment. It aims to obtain the points with maximum membership values for the fuzzy parameters while maximizing the profit or minimizing the assignment cost. In this method, a discrete approach is presented to rank the fuzzy numbers first. Then, corresponding to each fuzzy number, we introduce a crisp number using the efficiency concept. A numerical example is used to illustrate the usefulness of this new method.