An improved general type-2 fuzzy sets type reduction and its application in general type-2 fuzzy controller design

The Karnik–Mendel (KM) or the enhanced Karnik–Mendel (EKM) algorithm is widely used for interval type-2 fuzzy sets type reduction in many applications. Compared with iterative procedures of KM/EKM, an iterative algorithm with a stop condition or an enhanced iterative algorithm with a stop condition based on the KM algorithm that converges monotonically is more efficient. In this article, a new iterative algorithm with stop condition type reduction for interval type-2 fuzzy sets is proposed, in which switch points are initialized and unidirectional search is performed based on monotone properties of the KM algorithm. Furthermore, the proposed algorithm is applied to general type-2 fuzzy sets type reduction based on α-plane representation. The experimental results of a triangular and gaussian secondary membership function show practicality and efficiency of this method. In accordance with the conventional PI, type-1 or interval type-2 fuzzy controller is difficult to achieve a desired control effect for steam temperature at collector outlet of trough solar thermal power generation system with large time delay, strong inertia and parameter time-variation, and a general type-2 fuzzy controller with more adjustable controller parameters is proposed in this article. In different working conditions, the proposed controller can reduce system overshoot and ensure system stability. Moreover, when the working condition changes, the controller can solve a model mismatch problem under same controller parameters and has faster response.