To overcome the complexities in Type-2 Fuzzy Sets (T2FSs) and to present a general model for chaotic FSs, this paper introduces new FSs called Bifurcating FSs (BFSs). The BFS is inspired from human brain. Mathematically, it is equivalent to the coupled chaotic map in which one of the variables is a fuzzy membership function. Biologically, it is equivalent to the oscillatory neuron in which a fu...

This paper investigates the stabilization problem of interval type-2 (IT2) Takagi-Sugeno (T-S) fuzzy fractional order systems (FOSs). Firstly, IT2 model is constructed to approximate subject actuator saturation systems. Then, sufficient conditions output feedback control FOSs in terms linear matrix inequalities (LMIs) are presented by using method involving singular value decomposition (SVD). F...

This article is devoted to event-triggered stabilization for a class of interval type-2 (IT2) fuzzy systems with aperiodic sampling. First, the IT2 Takagi-Sugeno model and sampled-data controllers are established subject mismatched membership functions. Second, considering nonuniform sampling case, refined adaptive communication scheme proposed in hierarchy form dynamically adjust direction rat...

Interval type-2 fuzzy sets, each of which is characterized by the footprint of uncertainty, are a very useful means to depict the linguistic information in the process of decision making. In this article, we investigate the group decision making problems in which all the linguistic information provided by the decision makers is expressed as interval type-2 fuzzy decision matrices where each of ...

Most decision making methods used to evaluate a system or demonstrate the weak and strength points are based on fuzzy sets and evaluate the criteria with words that are modeled with fuzzy sets. The ambiguity and vagueness of the words and different perceptions of a word are not considered in these methods. For this reason, the decision making methods that consider the perceptions of decision...

Abstract: In this paper, a new hierarchical data-driven modelling strategy based on Interval Type-2 Fuzzy Clustering is elicited for the Interval Type-2 Takagi-Sugeno-Kang (TSK) Fuzzy Logic System. This framework which we have called the IT2-Squared framework uses interval type-2 fuzzy clustering for initial antecedent parameters and structures determination and least-squares algorithm for deri...

In this paper, the interval type-2 fuzzy proportional-integral-derivative controller (IT2F-PID) is proposed for controlling an inverted pendulum on a cart system with an uncertain model. The proposed controller is designed using a new method of type-reduction that we have proposed, which is called the simplified type-reduction method. The proposed IT2F-PID controller is able to handle the effec...

it is firstly proved that the multi-input-single-output (miso) fuzzy systems based on interval-valued $r$- and $s$-implications can approximate any continuous function defined on a compact set to arbitrary accuracy.  a formula to compute the lower upper bounds on the number  of interval-valued fuzzy sets needed to achieve a pre-specified approximation  accuracy for an arbitrary multivariate con...