Identification of Fuzzy Rule-Based Models With Output Space Knowledge Guidance

Abstract

In this article, we advocate that a knowledge tidbit residing in the output space could be helpful in improving the performance (accuracy) of the fuzzy rule-based model. It states that <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">if two outputs are far apart from each other</i> , <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">it is advisable to place their corresponding inputs in different clusters when forming subspaces of the input space</i> . Considering this knowledge guidance mechanism, we propose two different methods to partition the input space. In the first method, input data are first partitioned with the use of the standard clustering algorithm, say fuzzy C-means; here, a constructed partition matrix is reflective of the structure present in the input space. Then, the knowledge tidbit is used to adjust the entries of the original partition matrix in such a way that those input data whose corresponding output data are far apart from each other are assigned with low values of proximity. In the second method, we propose two strategies to modify the distance between input data and a prototype (cluster center) identified in the input space. The crux of this method is that if there are many input data (which, in virtue of the knowledge tidbit, are regarded as being far-apart from the input data of interest) around a certain prototype, the distance between the input data of interest and this prototype should be penalized. Thus, the membership of these input data to the prototype is reduced. The comprehensive experimental studies carried out on both synthetic and publicly available data are used to examine the usefulness of the proposed methods.