Application of Grey Numbers to Assessment of Case-Based Reasoning Systems

Case-Based Reasoning (CBR) is the process of solving new problems (usually with the help of computers) by adapting the solutions of similar (analogous) problems solved in the past. The CBR approach has got a lot of attention over the last 30-40 years, because as an intelligent-systems method enables information managers to increase efficiency and reduce cost by substantially automating processes. In the present work a method is developed using Grey Numbers (GNs) as a tool for accessing the effectiveness of CBR systems and examples are provided illustrating it. This new assessment method is proved to be equivalent with an analogous method using Triangular Fuzzy Numbers that has been developed in earlier author's works, but it has the advantage of reducing significantly the required computational burden. GNs, which are defined with the help of the closed intervals of real numbers, are indeterminate numbers whose range is known, but not their exact value, and they have found nowadays many and important applications in science, engineering and in the everyday life for handling approximate data.