Measuring efficiency of a hierarchical organization with fuzzy DEA method

The paper analyses how the data envelopment analysis (DEA) and fuzzy set theory can be used to measure and evaluate the efficiency of a hierarchical system with n decision making units and a coordinating unit. It is presented a model for determining the of activity levels of decision making units so as to achieve both fuzzy objectives of achieving global target levels of coordination unit on the inputs and outputs and individual target levels of decision making units, and then some methods to resolve fuzzy models are proposed.fuzzy DEA, policy making in multi-level organisations, efficiency analysis

A Simple Approximation of Productivity Scores of Fuzzy Production Plans

This paper suggests a simple approximation procedure for the assessment of productivity scores with respect to fuzzy production plans. The procedure has a clear economic interpretation and all the necessary calculations can be performed in a spreadsheet making it highly operational.rationing; inequality preservation; taxation; manipulation; proportional method

Fuzzy Efficiency Measure with Fuzzy Production Possibility Set

The existing data envelopment analysis (DEA) models for measuring the relative efficiencies of a set of decision making units (DMUs) using various inputs to produce various outputs are limited to crisp data. The notion of fuzziness has been introduced to deal with imprecise data. Fuzzy DEA models are made more powerful for applications. This paper develops the measure of efficiencies in input oriented of DMUs by envelopment form in fuzzy production possibility set (FPPS) with constant return to scale

Fuzzy data envelopment analysis:a discrete approach

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 a-cut. One drawback of the a-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 a-cut approach. We introduce the concept of "local a-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

Evaluating decision-making units under uncertainty using fuzzy multi-objective nonlinear programming

This paper proposes a new method to evaluate Decision Making Units (DMUs) under uncertainty using fuzzy Data Envelopment Analysis (DEA). In the proposed multi-objective nonlinear programming methodology both the objective functions and the constraints are considered fuzzy. The coefficients of the decision variables in the objective functions and in the constraints, as well as the DMUs under assessment are assumed to be fuzzy numbers with triangular membership functions. A comparison between the current fuzzy DEA models and the proposed method is illustrated by a numerical example

A geometrical approach for fuzzy DEA frontiers.

Interval DEA frontiers are here used in situation where one input or output is subject to uncertainty in its measurement and is presented as an interval data. We built an efficient frontier without any assumption about the probability distribution function of the imprecise variable. We take into account only the minimum and the maximum values of each imprecise variable. Two frontiers are constructed: the optimistic and the pessimistic ones. We use fuzszy relationships to introduce a new efficiency index based on a set of some Fuzzy T Norms. We will explore only the case where only on single variable presents a certain degree of uncertainty

An input relaxation model for evaluating congestion in fuzzy DEA

This paper develops a BCC input relaxation model for identifying input congestion as a severe form of inefficiency of decision-making units in fuzzy data envelopment analysis. The possibility approach is presented to obtain the models equivalent to fuzzy models. We use a one-model approach to determine input congestion based on the BCC input relaxation model. A numerical example is given to illustrate the proposed model and identify the congestion with precise and imprecise data. The proposed model is also used to determine the congestion in 16 hospitals using four fuzzy inputs and two fuzzy outputs with a symmetrical triangular membership function

A scientometrics study on green building: A DEA application

Construction operations are blamed as one of important causes of green gas effects. During the past few decades, there has been tremendous efforts to reduce the negative effects of construction operations on environment. This paper presents an application of data envelopment analysis to measure the relative efficiencies of the researches accomplished by various countries around the world on green construction or green management. The study expects countries that produce higher amount of CO2 accomplish more quality research articles. To do this, the study performs a survey using three keywords; namely “green construction”, “green building” and “sustainable building” on Scopus database and found 8692 articles over the period 1965-2019 where one of these keywords, at least, was used in their abstracts, keywords or titles. We also use three measures of h-index, I-10 and total publications repre-sentative of quality and quantity of the outputs produced by researchers. The study considers 28 countries responsible for at least 90% of CO2 emission for measuring the relative efficiency program using data envelopment analysis. The results indicate that Hong Kong was the only efficient country followed by Singapore with relative efficiency of 0.67