Interval-valued fuzzy inference systems based on the bandler-kohout subproduct / Lim Chee Kau - Lim , Chee Kau (2015)
The studies of fuzzy relations by Bandler and Kohout, which are also known as the BK products, are well known in the literature as tools to study the composition of relations. In the past, BK products, particularly the BK subproduct, gained remarkable success in developing inference engines for numerous applications. Though successful, there are still some limitations. First of all, this research starts with a survey on a set of inference structures formed by the BK subproduct in previous researches. The survey finds shortcomings in some inference structures. With excluding these candidates, a set of robust inference structures are obtained from the analysis. Secondly, with the understanding that the ordinary type-1 fuzzy sets have limited ability in modeling uncertainty, a more general fuzzy set framework is proposed to improve the performance of BK products. Thus, extending BK products to interval-valued fuzzy sets is another contribution of this thesis. Since the subsethood measure is fundamental to the BK products, two interval-valued fuzzy subsethood measures are also developed in this research. Moreover, this research suggests that, among all the features involved in inferences, certain features should have higher influence compared to the others. Therefore, to distinguish the influence of features towards inference results, a weight parameter is added. The computation of this weighted inference engine is also discussed. In order to test the proposed inference engine, this research also proposes a new method to define membership degrees from statistical data. With this method, the BK subproduct is tested with 3 publicly available data sets. The results are compared. Experimental results show that the extension to interval-valued fuzzy sets and the additional weight parameter improve the quality of inferences.