A weighted inference engine based on interval-valued fuzzy relational theory

• Extend the BK subproduct from Type-1 fuzzy sets to interval-valued fuzzy sets.
• Weight parameter is introduced to the BK subproduct.
• Develop a novel method that automatically constructs knowledge base from examples.
• The proposed method outperforms state-of-the-art solutions in medical data.

The study of fuzzy relations forms an important fundamental of fuzzy reasoning. Among all, the research on compositional fuzzy relations by Bandler and Kohout, or the Bandler–Kohout (BK) subproduct gained remarkable success in developing inference engines for numerous applications. Despite of its successfulness, we notice that there are limitations associated in the current implementations of the BK subproduct. In this paper, the BK subproduct, which originally based on the ordinary fuzzy set theory, is extended to the interval-valued fuzzy sets. This is because studies had claimed that ordinary fuzzy set theory has its limitation in addressing uncertainties using the crisp membership functions. Secondly, with the understanding that some features might have higher influence compare to the others, a weight parameter is introduced in the BK subproduct-based inference engines. Finally, a fuzzification method that able to fuzzify the input data and also train the inference engines is also developed. So, the BK subproduct-based inference systems can be built without human intervention, which are cumbersome and time consuming. Experiments on three public datasets and a comparison with state-of-art solutions have shown the efficiency and robustness of the proposed method.