Attribute Weighting and Weighted Fuzzy Rule Bases

In conventional fuzzy inference systems, the if-then rules available are typically represented in a flat form without differing the importance levels amongst the antecedent attributes, and therefore, all attributes are treated equally. Little attempt has been made to systematically integrate different attribute weights within the process of approximate knowledge interpolative reasoning. This is largely due to the difficulty of explicitly evaluating individual weights from limited data while it can be challenging to request domain experts to provide weighted linguistic rules. Nonetheless, as indicated in Chap. 3 , computational methods are available to generate weights of the rule antecedents. Intuitively, such methods often follow a two-step approach, by first collecting data that help evaluate the rule antecedent attributes, and then looking for an appropriate and applicable technique to assess the relative significance of attributes using the data gathered. However, this is difficult for domains where only restricted data is available, which is the case when a sparse knowledge base is concerned that requires interpolative reasoning. Without any information other than the given (sparse) rule base, the question is whether such a two-step procedure can still be implemented. That is, can weights of rule conditional attributes be generated using the rule bases only? Addressing this important question, the present chapter introduces a novel idea named reverse engineering to artificially create training data for attribute evaluation from a given sparse rule base. A practical case study is provided to illustrate how the underlying theoretical mechanism functions. In addition, provided with such learned attribute weights, the chapter presents a systematic method for constructing weighted fuzzy rule base, ready to support weighted approximate knowledge interpolation.