This page has only limited features, please log in for full access.
Cross-efficiency evaluation effectively distinguishes a set of decision-making units (DMUs) via self- and peer-evaluations. In constant returns to scale, this evaluation technique is usually applied for data envelopment analysis (DEA) models because negative efficiencies will not occur in this case. For situations of variable returns to scale, the negative cross-efficiencies may occur in this evaluation method. In the real world, the observations could be uncertain and difficult to measure precisely. The existing fuzzy cross-evaluation methods are restricted to production technologies with constant returns to scale. Generally, symmetry is a fundamental characteristic of binary relations used when modeling optimization problems. Additionally, the notion of symmetry appeared in many studies about uncertain theories employed in DEA problems, and this approach can be considered an engineering tool for supporting decision-making. This paper proposes a fuzzy cross-efficiency evaluation model with fuzzy observations under variable returns to scale. Since all possible weights of all DMUs are considered, a choice of weights is not required. Most importantly, negative cross-efficiencies are not produced. An example shows that this paper’s fuzzy cross-efficiency evaluation method has discriminative power in ranking the DMUs when observations are fuzzy numbers.
Shun-Cheng Wu; Tim Lu; Shiang-Tai Liu. A Fuzzy Approach to Support Evaluation of Fuzzy Cross Efficiency. Symmetry 2021, 13, 882 .
AMA StyleShun-Cheng Wu, Tim Lu, Shiang-Tai Liu. A Fuzzy Approach to Support Evaluation of Fuzzy Cross Efficiency. Symmetry. 2021; 13 (5):882.
Chicago/Turabian StyleShun-Cheng Wu; Tim Lu; Shiang-Tai Liu. 2021. "A Fuzzy Approach to Support Evaluation of Fuzzy Cross Efficiency." Symmetry 13, no. 5: 882.
The selection of advanced manufacturing technologies (AMTs) is an essential yet complex decision that requires careful consideration of various performance criteria. In real-world applications, there are cases that observations are difficult to measure precisely, observations are represented as linguistic terms, or the data need to be estimated. Since the growth of engineering sciences has been the key reason for the increased utilization of AMTs, this paper develops a fuzzy network data envelopment analysis (DEA) to the selection of AMT alternatives considering multiple decision-makers (DMs) and weight restrictions when the input and output data are represented as fuzzy numbers. By viewing the multiple DMs as a network one, the data provided by each DM can then be taken into account in evaluating the overall performances of AMT alternatives. In the solution process, we obtain the overall and DMs efficiency scores of each AMT alternative at the same time, and a relationship in which the former is a weighted average of the latter is also derived. Since the final evaluation results of AMTs are fuzzy numbers, a ranking procedure is employed to determine the most preferred one. An example is used to illustrate the applicability of the proposed methodology.
Tim Lu. A Fuzzy Network DEA Approach to the Selection of Advanced Manufacturing Technology. Sustainability 2021, 13, 4236 .
AMA StyleTim Lu. A Fuzzy Network DEA Approach to the Selection of Advanced Manufacturing Technology. Sustainability. 2021; 13 (8):4236.
Chicago/Turabian StyleTim Lu. 2021. "A Fuzzy Network DEA Approach to the Selection of Advanced Manufacturing Technology." Sustainability 13, no. 8: 4236.
The quality of a product produced by a manufacturing process should be able to lie within an acceptable variability around its target value. The signal-to-noise (S/N) ratio, served as the objective function for optimization in Taguchi methods, is a useful tool for the evaluation of manufacturing processes. Most studies and applications focus on the calculation of S/N ratios with deterministic observations, and the literature receives little attention to the consideration of S/N ratio with fuzzy observations. This paper develops a fuzzy nonlinear programming model to calculate the fuzzy S/N ratio for the assessment of the manufacturing processes with fuzzy observations. A pair of nonlinear fractional programs is formulated to calculate the lower and upper bounds of the fuzzy S/N ratio. By model reduction and variable substitutions, this pair of nonlinear fractional programs is transformed into quadratic programs. Solving the transformed quadratic programs, we obtain the optimum solutions of the lower bound and upper bound fuzzy S/N ratio. By deriving the ranking indices of the fuzzy S/N ratios of manufacturing process alternatives, the evaluation result of the alternatives is obtained.
Tim Lu; Shiang-Tai Liu. Fuzzy nonlinear programming approach to the evaluation of manufacturing processes. Engineering Applications of Artificial Intelligence 2018, 72, 183 -189.
AMA StyleTim Lu, Shiang-Tai Liu. Fuzzy nonlinear programming approach to the evaluation of manufacturing processes. Engineering Applications of Artificial Intelligence. 2018; 72 ():183-189.
Chicago/Turabian StyleTim Lu; Shiang-Tai Liu. 2018. "Fuzzy nonlinear programming approach to the evaluation of manufacturing processes." Engineering Applications of Artificial Intelligence 72, no. : 183-189.
Cross-efficiency evaluation, an extension of data envelopment analysis (DEA), can eliminate unrealistic weighing schemes and provide a ranking for decision making units (DMUs). In the literature, the determination of input and output weights uniquely receives more attentions. However, the problem of choosing the aggressive (minimal) or benevolent (maximal) formulation for decision-making might still remain. In this paper, we develop a procedure to perform cross-efficiency evaluation without the need to make any specific choice of DEA weights. The proposed procedure takes into account the aggressive and benevolent formulations at the same time, and the choice of DEA weights can then be avoided. Consequently, a number of cross-efficiency intervals is obtained for each DMU. The entropy, which is based on information theory, is an effective tool to measure the uncertainty. We then utilize the entropy to construct a numerical index for DMUs with cross-efficiency intervals. A mathematical program is proposed to find the optimal entropy values of DMUs for comparison. With the derived entropy value, we can rank DMUs accordingly. Two examples are illustrated to show the effectiveness of the idea proposed in this paper.
Tim Lu; Shiang-Tai Liu. Ranking DMUs by Comparing DEA Cross-Efficiency Intervals Using Entropy Measures. Entropy 2016, 18, 452 .
AMA StyleTim Lu, Shiang-Tai Liu. Ranking DMUs by Comparing DEA Cross-Efficiency Intervals Using Entropy Measures. Entropy. 2016; 18 (12):452.
Chicago/Turabian StyleTim Lu; Shiang-Tai Liu. 2016. "Ranking DMUs by Comparing DEA Cross-Efficiency Intervals Using Entropy Measures." Entropy 18, no. 12: 452.