Data driven fuzzy membership function generation for increased understandability

Fuzzy Logic Systems (FLS) are a well documented proven method for various applications such as control classification and data mining. The major advantage of FLS is the use of human interpretable linguistic terms and rules. In order to capture the uncertainty inherent to linguistic terms, Fuzzy Membership Functions (MF) are used. Therefore, membership functions are essential for improving the understandability of fuzzy systems. Optimizing FLS for improved accuracy in terms of classification or control can reduce the understandability of fuzzy MFs. Expert knowledge can be used to derive MFs, but it has been shown that this might not be optimal, and acquiring expert knowledge is not trivial. Therefore, this paper presents a data driven method using statistical methods to generate membership functions that describe the data while maintaining the understandability. The presented method calculates key points such as membership function centers, intersections and slopes using data driven statistical methods. Furthermore, the presented method utilizes several understandability metrics to adjust the generated MFs. The presented method was tested on several benchmark datasets and a real-world dataset and was shown to be able to generate MFs that describe the dataset, while maintaining high levels of understandability.