Non-stationary type-2 fuzzy sets

In this paper, we introduce non-stationary type-2 fuzzy set (NST2FS), which is the important extension of its type-1 counterpart. NST2FS has distinct characteristics with uncertain membership function and alteration over time. According to different mathematical formalizations of its instantaneous T2FS (IT2FS), NST2FS can be divided into two categories, i.e. homogeneous and heterogeneous counterparts. The paper concentrates on homogeneous continuous NST2FS (HCNST2FS), of which each IT2FS is continuous. A plane representation theorem is the cogent tool to deal with these basic set operators (intersection, union and complement) and approximate fuzzy reasoning. Some selected important properties are also proved in the process. On this basis, homogeneous continuous non-stationary type-2 fuzzy logic system (HCNST2FLS) is discussed in the following section, which focuses on the elaboration of its calculation procedure. One numerical case, that is, blurred `or´ logic operator, is carried out in order to evaluate the superior performance of our proposing system.