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

Keywords: Fuzzy relations BK subproduct Inference engine Interval-valued fuzzy sets Fuzzy sets and systems Membership functions a b s t r a c t 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 successful-ness, we notice that there are limitations associated in the current implementations of the BK subprod-uct. 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. Reasoning with fuzzy sets theory has been widely studied in the literature. Some common directions of studies include finding soft cluster centers of data (Roh, Pedrycz, & Ahn, 2014; Son, 2015), integrate the fuzzy sets theory with other technologies such as artifi-In all these fuzzy inference systems, fuzzy rules are the core of the inference processes. However, the popularity of these rule based fuzzy inference systems dispute the necessity of developing other inference schemes. to those popular rule based fuzzy inference systems, a special characteristic of BK subproduct based inference systems is it does not require rules. Certainly, it is an advantage in the cases which rules are hardly define (Kolodner, 1992). While some theoretical researches on BK subproduct are in advancement, empirical works have also been carried out to prove its advantages in many expert systems, such as medical Despite of its successfulness, we notice that there are still some limitations associated in the current implementations of the BK subproduct. First of all, the implementations of the BK subproduct in the literature are still based on the classical Type-1 Fuzzy Set (T1FS) theory, which address uncertainties with point-values. …