On new quasi-type-2 fuzzy logic systems

Abstract

Abstract-This paper provides an answer to the question that the type-2 fuzzy logic community is now asking: "What comes after interval type-2 fuzzy logic systems (IT2 FLSs)?" It demonstrates, through a geometrical understanding of the type-reduced set, that logical next steps in the progression from type-1 to interval type-2 to type-2 FLSs are quasi-T2 FLSs, either an interconnection of a T1 FLS and an IT2 FLS, or an interconnection of two IT2 FLSs, in which both FLSs are designed simultaneously. The quasi-T2 FLSs overcome the computational difficulties that are associated with set theoretic operations and type-reduction (TR) for general T2 FSs and FLSs, because all set theoretic operations can be performed as in existing T1 or IT2 FLSs, and because TR for an IT2 FLS can be performed using existing KM Algorithms.

Toward General Type-2 Fuzzy Logic Systems Based on zSlices

“…While there are some areas that offer potential for parallel execution and, thus, performance increase such as the evaluation of individual rules in parallel as well as the computation of the centroids of individual wavy slices during type reduction, the general type-2 FLS in its standard form is not suitable for real-world control applications today. Hence, as mentioned earlier, new forms of representations have been devised in order to enable the use of general type-2 FLSs in real-world applications, such as the geometric representation of general type-2 sets [4] and the quasitype-2 fuzzy systems, which are based on alpha planes [5], [6]. Furthermore, several other advances have been made in trying to reduce the complexity associated with general type-2 fuzzy sets [2], [7], [8], [10].…”

“…Coupland and John [4] have presented a geometric representation of general type-2 sets, and, recently, other forms of representation have been introduced, where Mendel and Liu [5], [6] have put forward a representation based on alpha planes, while Wagner and Hagras [9] have introduced the zSlices-based representation. Furthermore, several other advances have been made in trying to reduce the complexity associated with general type-2 fuzzy systems [2], [7], [8], [11].…”

Type-2 fuzzy linear systems

“…Definition 2 (Mendel 2008;Coupland and John 2007) A T2FS, Ã , can be characterized by the so-called point-valued representation as follows:…”

Optimization of the Fuzzy Integrators in Ensembles of ANFIS Model for Time Series Prediction: The case of Mackey-Glass

“…When; we have an interval type-2 membership function. The uniform shading for the FOU represents the entire interval type-2 fuzzy set [19][20][21][22][23] and it can be described in terms of an upper and a lower membership function.…”