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This paper develops a range directional distance data envelopment analysis (DEA) model to simultaneously deal with the problems of negative data and undesirable outputs in the study of performance measurement with two-stage DEA. We report on the development of this model to handle both positive and negative data in a DEA framework and accommodate the problem of undesirable intermediate outputs in the first stage of operational processes. Unlike previous two-stage DEA models we allow for a nonuniform abatement factor imposing on stage 1’ production technology. Such a model is then applied to evaluate Taiwanese bank efficiencies both at the operational stage and profitability stage in banking activities based on a data set consisting of 35 domestic banks in Taiwan in the period 2007. The results indicate that, by the range directional two-stage data envelopment analysis model, the operational efficiency was smaller than the profitability efficiency. Many banks generated too many performing loans in which independent banks should reduce more performing loans than financial holding company subsidiary banks. Both the ratio of investments to loans and the ratio of nonperforming loans to performing loans did not have significant contributions to the efficiency. This paper is able to provide information for bank operators and researchers on the managerial and strategic implications of how negative data and undesirable outputs affect efficiency and how to measure efficiency appropriately.

The objective of this paper is to provide a more comprehensive efficiency measure to estimate the performance of OECD and non-OECD countries. A Russell directional distance function that appropriately credits the decision-making unit not only for increase in desirable outputs but also for the decrease of undesirable outputs is derived from the proposed weighted Russell directional distance model. The method was applied to a panel of 116 countries from 1992 to 2010. This framework also decomposes the comprehensive efficiency measure into individual input/output components' inefficiency scores that are useful for policy making. The results reveal that the OECD countries perform better than the non-OECD countries in overall, goods, labor and capital efficiencies, but worse in bad and energy efficiencies.

An assessment of a set of alternatives under certain evaluation criteria has difficulty in dealing with the priority of these alternatives, especially with a lack of precise information in an uncertain environment. Fuzzy numbers are usually applied to represent the imprecise numerical measurements of different alternatives. In this study statistical data are used to derive level (1-α,1-β) interval-valued fuzzy numbers to represent unknown alternative effectiveness scores, after which, by using the compositional rule of inference and signed distance to transform the fuzzy decision making problem into crisp one, one can conveniently obtain the order of these different alternatives and subsequently obtain the best alternative. The approach presented is computationally efficiency, and its underlying concepts are simple and comprehensible. By using this extended generalized method, two cases of an organizational type of rapid-transit-system selection problem are presented as examples to illustrate the applicability of the interval-valued fuzzy numbers and ranking system for decision making. The key contribution of the method is the seamless integration of the statistical data, interval-valued fuzzy number and signed distance to analyze multicriteria decision making problem. The innovation introduced in the model concerns interval-valued fuzzy number which is recognized as a determinant of the effectiveness score in fuzzy relation matrix.

In this paper, we adopt statistical data from sixteen experts to derive effectiveness matrix with level 1-α fuzzy numbers and to obtain fuzzy weights of m evaluation criteria. In application of level 1-α numbers ranking, the centroids of level 1-α fuzzy numbers and centroids of fuzzy weights will be used in modification of concordance analysis, thereby providing a better choice of alternatives.