A type-2 fuzzy-statistical clustering approach for estimating the multiple change points in a process mean with monotonic change

Abstract

Identifying the real time of the change in a process, recognized as change point problem, simplifies the removal of change causes. In most of the change point models, the existence of different uncertainty levels is either ignored or paid a little attention to. This paper tries to address an appropriate model to estimate the multiple change points in a monotonic change process in an uncertain condition and for a known number of change points. In this regard, a novel set of membership functions and a novel objective function, based on using interval type-2 fuzzy sets, are introduced in a fuzzy-statistical clustering approach. The proposed approach, in addition to the ability of managing various amount of uncertainty, is free from the distribution of the process variables, and in the case of existence, a certain variable distribution, it is independent from it. Finally, extensive simulation studies are conducted to evaluate the performance of the proposed approach in simple step change, multiple step change, and linear trend change in the presence of isotonic change in the process mean. The results are compared with some of the powerful change point approaches.