All companies face problems in their operation, just like human body. Yet, most problems elicit warning signals during the early stage. If we could conduct simple diagnosis or measurement for the company, we could early detect the problem before they become unmanageable, and could map out corresponding plans to cope with it. In this paper, we applied two mathematical tools, Grey Relation Analysis (GRA) and Data Envelopment Analysis (DEA), to evaluate the performance of commercial banks newly reorganized from trust businesses in Taiwan. Both methods have limitations in application as well as respective advantages and disadvantages. Analysis and comparison of the GRA and DEA when applied to the evaluation of performance are discussed. The empirical result shows that the rankings of the three firms in the empirical study by using DEA and GRA are the same: first, the United World Chinese Bank, second, China Trust Commercial Bank, and third, Chinfon Bank.

Decision Analysis has been adopted by the discipline of management science in a rapid speed during the past few years. If the management of the small and medium enterprises in Taiwan could take the concept of a “system” given by this approach, and take management issues as a “system”, they could quantitify the data for analysis. In doing so, they could easily control the problems in management, and improve the quality of decision-making. All companies face problems in their operation, just like human beings. Yet, most problems elicit warning signals during the early stage. If we could conduct simple diagnosis or measurement for the company, we could detect the problem before they become unmanageable, and could map out corresponding measures to cope with it. In this study, two approaches that were widely used for performance measurement and decision analysis were discussed. They are Data Envelopment Analysis and Grey Relation Analysis. Each of the two approaches has its limitation in application. Yet, each of them has its strength. This study aims at finding out the difference of the two approaches in application on performance measurement, their respective “characteristics”, and “appropriateness in application”. Basing on the result of this study, the owners of small and medium enterprises in Taiwan may be able to find out an approach appropriate for their respective diagnosis and measuring of performance of the firms.