Framework of Approximate Knowledge Interpolation

Fuzzy interpolative reasoning plays an important role in fuzzy rule-based inference systems, facilitating the extension of the capability of approximate reasoning when dealing with incomplete knowledge. This is supported by fuzzy rule interpolation (FRI) which is able to produce an approximate interpolated outcome using limited fuzzy rules that collectively fail to match a certain input observation and hence are unable to directly derive a conclusion through traditional computational mechanisms. FRI techniques have been continuously investigated for decades, resulting in various types of approach. In this chapter, the preliminary background knowledge of fuzzy interpolative reasoning mechanism is reviewed. The family of fundamental FRI techniques is presented through two representative groups of methods, where the scale and move transformation-based FRI (T-FRI) is particularly elaborated due to its popularity and wide applications. This offers a comprehensive tutorial for this important computational intelligence approach to rule-based inference. A comparative analysis of different FRI techniques is also provided, highlighting the main strengths and limitations while applying these methods to different problems. To facilitate the demonstration of the relevant methodology, basic notations that will be subsequently utilised in the rest of this book are described.