Fuzziness in Performance Evaluation Problems Using Data Envelopment Analysis

Efficiency evaluation is an important part of decision making in many areas particularly in management and manufacturing sectors. Uncertainty and fuzziness of the real world problems have increased utilization of fuzzy sets theory in many research areas and data envelopment analysis is one of them. Utilizing data envelopment analysis to evaluate efficiency scores of decision making units in fuzzy environment requires fuzzy models and mathematical methods for solving fuzzy models with minimum calculation and maximum precision. Since current fuzzy data envelopment analysis models are not able to solve some problems in fuzzy environment, our attempt is to provide fuzzy data envelopment analysis models related to following various problems. Some problems include uncontrollable data (for manager) that regularly have fuzzy essence. An uncontrollable fuzzy data envelopment analysis model is represented for these types of problems. The advantages of the proposed model are in capability of it in including uncontrollable factors particularly those with fuzzy nature in problems with fuzzy data and controlling factor weights by additional constraints which can avoid the model to become infeasibility. The disadvantage of the method is in using too many restrictions (one restriction for each fuzzy data) which makes the model complicated and expensive to solve. For cases that interval efficiency scores are helpful, a method for solving fuzzy data envelopment analysis models is represented which interval efficiency scores can be achieved without adding restrictions to the model for each fuzzy data. In comparison with other methods, this method is simple, easy and with no additional constraint for each fuzzy data. In addition a fuzzy weights data envelopment analysis model is proposed to determine effect of data on the efficiency score. The model is informative in problems that the manager needs to know about uncertain effects of factors on efficiency score. The method of solving the model is simple and informative. By suggesting categorical data envelopment analysis method for problems with uncertain membership in various categories, we can help the decision maker to recognize the efficient decision making units fairly. In comparison with available method for categorical problems, our method is more informative and the traditional categorical method is a special case of our method. Finally, we provide a solution to comparison of production methods by utilizing fuzzy non-discretionary data envelopment analysis model. The proposed technique is more capable and informative while it includes factors with fuzzy essence that have effect on efficiency of production methods which is a real problem and may be its performance be effected by many fuzzy issues. categorical method is a special case of our method. Finally, we provide a solution to comparison of production methods by utilizing fuzzy non-discretionary data envelopment analysis model. The proposed technique is more capable and informative while it includes factors with fuzzy essence that have effect on efficiency of production methods which is a real problem and may be its performance be effected by many fuzzy issues

An efficiency evaluation problem including fuzzy weights

This paper presents a procedure to dissolve a fuzzy weights CCR model with numerical input and output data in the objective function. This technique is a combination of utilizing fuzzy operations arithmetic and traditional method in DEA in order to convert the model into two simple linear programming problems with the purpose of detecting the effect of uncertain factors on the efficiency scores of decision making units (DMUs). It is in accordance with our determination to provide a method based on data envelopment analysis (DEA), supporting efficiency evaluation problems in fold fuzziness in factor weights to assist decision making issues

Fuzzy weights in data envelopment analysis.

In many real problems of evaluating efficiency score for decision making units (DMUs) using data envelopment analysis (DEA) factor weights related to the data may have fuzzy essence and it is required to create methods for solving these problems. In this paper we have provided a method to solve a CCR model with fuzzy weights in the objective function. This method is based on parametric linear programming which is transformed using t-cut concept for fuzzy numbers. Besides our method is based on two steps to find the triangular fuzzy number as weights of the objective function