A novel algorithm for complete ranking of DMUs dealing with negative data using Data Envelopment Analysis and Principal Component Analysis: Pharmaceutical companies and another practical example.

When there is an extensive number of inputs and outputs compared to the number of DMUs, one of the drawbacks of Data Envelopment Analysis appears, which incorrectly classifies inefficient DMUs, as efficient ones. Accordingly, the DEA ranking power becomes further moderated. To improve the ranking power, this paper renders the details of an algorithm that presents a model combining the Principal Component Analysis and the Slacks-Based Measure (PCA-SBM) which reduces the number of the incorrectly determined efficient DMUs. Also to complete ranking of DMUs, the algorithm presents a Super-Efficiency model integrated with PCA (PCA-Super SBM) which can rank the efficient DMUs (extreme and non-extreme). Whereas the most important previous models for ranking efficient units cannot rank non-extreme ones. Additionally, in most previous studies, DEA models combined with PCA fail to handle negative data, while, the presented models can cover this data. Two case studies (pharmaceutical companies listed on the Iranian stock market and bank branches) are manipulated to demonstrate the applicability and performance of the algorithm. To show the superiority of the presented models, the SBM model without PCA and the Super SBM model without PCA have been implemented on the data of both cases. In comparing the two methods (PCA-SBM and SBM), the PCA-SBM model has higher ranking power (five efficient DMUs versus nineteen in the case of pharmaceutical companies and four efficient DMUs versus twenty-nine in the case of bank branches). Also in comparing the PCA-Super SBM and Super SBM, the PCA-Super SBM model works more powerfully in complete ranking. As the Super SBM model cannot rank non-extreme units unlike the PCA-Super SBM. Consequently, the presented algorithm works successfully in ranking the DMUs completely (inefficient, extreme, and non-extreme efficient) with low complexity.

An improved approach for fault detection by simultaneous overcoming of high-dimensionality, autocorrelation, and time-variability.

The control charts with the Principal Component Analysis (PCA) approach and its extension are among the data-driven methods for process monitoring and the detection of faults. Industrial processing data involves complexities such as high dimensionality, auto-correlation, and non-stationary which may occur simultaneously. An efficient fault detection technique is an approach that is robust against data training, sensitive to all the feasible faults of the process, and agile to the detection of the faults. To date, approaches such as the recursive PCA (RPCA) model and the moving-window PCA (MWPCA) model have been proposed when data is high-dimensional and non-stationary or dynamic PCA (DPCA) model and its extension have been suggested for autocorrelation data. But, using the techniques listed without considering all aspects of the process data increases fault detection indicators such as false alarm rate (FAR), delay time detection (DTD), and confuses the operator or causes adverse consequences. A new PCA monitoring method is proposed in this study, which can simultaneously reduce the impact of high-dimensionality, non-stationary, and autocorrelation properties. This technique utilizes DPCA property to decrease the effect of autocorrelation and adaptive behavior of MWPCA to control non-stationary characteristics. The proposed approach has been tested on the Tennessee Eastman Process (TEP). The findings suggest that the proposed approach is capable of detecting various forms of faults and comparing attempts to improve the detection of fault indicators with other approaches. The empirical application of the proposed approach has been implemented on a turbine exit temperature (TET). The results demonstrate that the proposed approach has detected a real fault successfully.

Linguistic Z-number weighted averaging operators and their application to portfolio selection problem.

Z-numbers can generate a more flexible structure to model the real information because of capturing expert's reliability. Moreover, various semantics can flexibly be reflected by linguistic terms under various circumstances. Thus, this study aims to model the portfolio selection problems based on aggregation operators under linguistic Z-number environment. Therefore, a multi-stage methodology is proposed and linguistic Z-numbers are applied to describe the assessment information. Moreover, the weighted averaging (WA) aggregation operator, the ordered weighted averaging (OWA) aggregation operator and the hybrid weighted averaging (HWA) aggregation operator are developed to fuse the input arguments under the linguistic Z-number environment. Then, using the max-score rule and the score-accuracy trade-off rule, three qualitative portfolio models are presented to allocate the optimal assets. These models are suitable for general investors and risky investors. Finally, to illustrate the validity of the proposed qualitative approach, a real case including 20 corporations of Tehran stock exchange market in Iran is provided and the obtained results are analyzed. The results show that combining linguistic Z-numbers with portfolio selection processes can increase the tendencies and capabilities of investors in the capital market and it helps them manage their portfolios efficiently.