Novel Methods for the Design of General Type-2 Fuzzy Sets based on Device Characteristics and Linguistic Labels Surveys

Fuzzy Logic Systems are widely recognized to be successful at modelling uncertainty in a large variety of applications. While recently interval type-2 fuzzy logic has been credited for the ability to better deal with large amounts of uncertainty, general type- 2 fuzzy logic has been a steadily growing research area. All fuzzy logic systems require the accurate specification of the membership functions' (MFs) parameters. While some work for automatic or manual design of these parameters has been proposed for type-1 and interval type-2 fuzzy logic, the problem has not yet been widely addressed for general type-2 fuzzy logic. In this paper we propose two methods which allow the automatic design of general type-2 MFs using either data gathered through a survey on the linguistic variables required or, in the case of physical devices (e.g. sensors, actuators), using data directly gathered from the specific devices. As such, the proposed methods allow for the creation of general type-2 MFs which directly model the uncertainty incorporated in the respective applications. Additionally, we demonstrate how interval type-2, type-1 and the recently introduced zSlices based general type- 2 MFs can be extracted from the automatically designed general type-2 MFs. We also present a recursive algorithm that computes the convex approximation of generated fuzzy sets. Keywords— Type-2 fuzzy systems, general type-2 fuzzy sets, specification of fuzzy sets.