# A brief tutorial on interval type 2 fuzzy sets and systems pdf

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Abdurrehman, S.

Type-II fuzzy sets are used to convey the uncertainties in the membership function of type-I fuzzy sets. Linguistic information in expert rules does not give any information about the geometry of the membership functions. These membership functions are mostly constructed through numerical data or range of classes. But there exists an uncertainty about the shape of the membership, that is, whether to go for a triangle membership function or a trapezoidal membership function.

## A Brief Tutorial on Interval Type-2 Fuzzy Sets and Systems

The trend to accelerate the learning process in neural and fuzzy systems has led to the design of hardware implementations of different types of algorithms. In this paper we explore type-2 fuzzy logic systems acceleration, which can be applied to fuzzy logic control methods, signal processing, etc. Due to the three dimensional membership functions in the input of the system, different algorithms for the output processing stage have been developed. In order to have a fast response in type-2 fuzzy logic systems, in this paper we explore the Karnik-Mendel algorithms KM , which are used to calculate the centroid at the output processing stage of the interval type-2 fuzzy system, through the application of iterative procedures. Because of the computation complexity of the iterative process, we propose a Hardware implementation of the KM algorithm using a High Level Synthesis tool, making possible to explore different types of implementation in order to obtain a significant reduction in computation time, and a reduction in hardware resources. Skip to main content.

## Hardware Implementation of Karnik-Mendel Algorithm for Interval Type-2 Fuzzy Sets and Systems

Updated 16 Dec View Version History. This package contains the following files: example. Dongrui Wu Retrieved March 13, But now, If there are the system two inputs and one output.

One obstacle in learning IT2 fuzzy logic is its complex notations. In this tutorial we try to avoid these notations and give the reader some intuitive understanding of IT2 FLSs. In contrast, for a crisp set, the membership degree of each element in it can be either 0 or 1; there is no value e. The membership function MF , X x , of a T1 FS can either be chosen based on the users opinion hence, the MFs from two individuals could be quite different depending upon their experiences, perspectives, cultures, etc. This tutorial can be distributed freely.

One obstacle in learning IT2 fuzzy logic is its complex notations. In this tutorial we try to avoid these notations and give the reader some intuitive understanding of IT2 FLSs. In contrast, for a crisp set, the membership degree of each element in it can be either 0 or 1; there is no value e. The membership function MF , X x , of a T1 FS can either be chosen based on the users opinion hence, the MFs from two individuals could be quite different depending upon their experiences, perspectives, cultures, etc. This tutorial can be distributed freely. T1 FS is certain in the sense that its membership grades are crisp values.

Interval type-2 (IT2) FSs1 [36], a special case of type-2 FSs, are currently the most widely used for their reduced computational cost. An example of an IT2 FS, ˜X, is shown in Fig. 1(b). Observe that unlike a T1 FS, whose membership for each x is a number, the membership of an IT2 FS is an interval.

## Type-2 Fuzzy Sets and Systems: a Retrospective

Type-2 fuzzy sets and systems generalize standard Type-1 fuzzy sets and systems so that more uncertainty can be handled. From the beginning of fuzzy sets, criticism was made about the fact that the membership function of a type-1 fuzzy set has no uncertainty associated with it, something that seems to contradict the word fuzzy , since that word has the connotation of much uncertainty. So, what does one do when there is uncertainty about the value of the membership function?

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