Interval type-2 fuzzy c-control charts using likelihood and reduction methods

Control charts, used in many areas, are important for providing information about the status of the product control. Control charts allow us observation of abnormal conditions about a product and/or a process. These situations usually need to be interpreted by an expert. At this point, fuzzy numbers can be beneficial in reducing the differences between experts’ opinions and information loss. This is especially true for qualitative data, and for this reason, fuzzy numbers can be used to transform linguistic expressions into data. Although some recent studies have created control charts with fuzzy sets, most focused on type-1 fuzzy sets. Nevertheless, in real life, it may not always be possible to express these data as type-1 fuzzy sets; it may be more realistic to express some data as type-2 fuzzy sets. The purpose of this study is to create control charts using interval type-2 fuzzy numbers. Interval type-2 fuzzy control charts can be obtained by using different approaches, including defuzzification, centroid, type reduction and likelihood approaches. Comparisons are made between the interval type-2 fuzzy control charts and classical control charts. This study introduces likelihood method as a new approach to generate fuzzy control charts. The significant contribution of this paper to the relevant literature is that interval type-2 fuzzy set methods applied to different areas—such as likelihood, centroid, type reduction—are adapted to c-control charts for the first time.