The Design and Implementation of a Constrained Interval Type-2 Fuzzy System for Credit Card Fraud Detection

Fuzzy systems with type-1, interval type-2 and general type-2 fuzzy sets have been widely applied in various fields. Constrained Interval Type-2 (CIT2) fuzzy sets and systems are an approach designed to improve the interpretability of type-2 fuzzy inference systems (FISs) by preserving the semantic values throughout the modelling and decision process, including in the type-reduction and defuzzification stages. Whilst all the steps necessary for building CIT2 inference systems have been established, there is still a challenge for people to build data-driven models based on CIT2 sets and apply them in practice. This paper presents a step-by-step design of a CIT2 fuzzy inference system featuring a case study in credit card fraud detection, utilising the Juzzy Constrained toolkit. The framework contains three parts: creating CIT2 membership functions from data based on the K-means algorithm; deriving fuzzy rules by using a decision tree model; and implementing the CIT2 FIS with the Juzzy Constrained toolkit available online. This constitutes the first end-to-end demonstration of designing, creating and implementing a CIT2 FIS in a fresh application context. This will support other researchers to explore CIT2 fuzzy systems.