Multi-Attribute Decision Making Based on Stochastic DEA Cross-Efficiency with Ordinal Variable and Its Application to Evaluation of Banks’ Sustainable Development

Abstract

Multi-attribute decision making (MADM) is a cognitive process for evaluating data with different attributes in order to select the optimal alternative from a finite number of alternatives. In the real world, a lot of MADM problems involve some random and ordinal variables. Therefore, in this paper, a MADM method based on stochastic data envelopment analysis (DEA) cross-efficiency with ordinal variable is proposed. First, we develop a stochastic DEA model with ordinal variable, which can derive self-efficiency and the optimal weight of each attribute for all decision making units (DMUs). To further improve its discrimination power, cross-efficiency as a significant extension is proposed, which utilizes peer DMUs' optimal weight to evaluate the relative efficiency of each alternative. Then, based on self-efficiency and cross-efficiency of all DMUs, we construct corresponding fuzzy preference relations (FPRs) and consistent fuzzy preference relations (FPRs). In addition, we obtain the priority weight vector of all DMUs by utilizing the row wise summation technique according to the consistent FPRs. Finally, we provide a numerical example for evaluating operation performance of sustainable development of 15 listed banks in China, which illustrates the feasibility and applicability of the proposed MADM method based on stochastic DEA cross-efficiency with ordinal variable.Sustainability 2020, 12, 2375 2 of 15 two parts: classifying and ranking. Classifying can be considered as the grouping of the alternatives based on the similarities of attributes. Ranking is defined as the rank of alternatives from the optimal to the worst [8]. In recent years, some methods have been proposed to handle MADM problems, such as total sum (TS) method [9], simple additive weighting (SAW) method [10], the analytic hierarchy process (AHP) method [11], multiplicative analytic hierarchy process (MAHP) method [12], the technique for order preference by similarity to ideal solution (TOPSIS) method [13], and data envelopment analysis (DEA) method [14].In MADM problems, we need some decision making information including attribute values and attribute weights, which denote the characteristics of alternatives and relative importance of attributes, respectively [7]. Nevertheless, attribute values are known, so we have to obtain attribute weights by the aforementioned approaches. However, DEA is a nonparametric programming efficiency rating technique for evaluating the relative efficiency of DMUs with multiple inputs and outputs, whose evaluation results come from input and output data [15][16][17]. Compared with other methods, attribute weights derived by DEA is relatively objective. Therefore, DEA has been widely applied in many fields for different purposes [18][19][20], such as assessment of environmental sustainability [21,22], supplier selection [23][24][25], and evaluation of the influence of E-marketing on hotel performance [26].Due to the inherent complexity and competition of the real world, MADM problems often involve some random and ordina...

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