To date, because of the computational complexity of using a general type-2 fuzzy set (T2 FS) in a T2 fuzzy logic system (FLS), most people only use an interval T2 FS, the result being an interval T2 FLS (IT2 FLS). Unfortunately, there is a heavy educational burden even to using an IT2 FLS. This burden has to do with first having to learn general T2 FS mathematics, and then specializing it to an IT2 FSs. In retrospect, we believe that requiring a person to use T2 FS mathematics represents a barrier to the use of an IT2 FLS. In this paper, we demonstrate that it is unnecessary to take the route from general T2 FS to IT2 FS, and that all of the results that are needed to implement an IT2 FLS can be obtained using T1 FS mathematics. As such, this paper is a novel tutorial that makes an IT2 FLS much more accessible to all readers of this journal. We can now develop an IT2 FLS in a much more straightforward way

/pdf/interval-type-2-fuzzy-logic-systems-made-simple-as15zfz2h0.pdf

Interval Type-2 Fuzzy Logic Systems Made Simple

http://sipi.usc.edu/~mendel/publications/Mendel%20INS%202007%20AT2.pdf

Advances in type-2 fuzzy sets and systems

/pdf/analysis-of-observed-chaotic-data-3spe9uweeb.pdf

Analysis of observed chaotic data

Type-1 fuzzy logic controllers (FLCs) have been applied to date with great success to many different applications. However, for dynamic unstructured environments and many real-world applications, there is a need to cope with large amounts of uncertainties. The traditional type-1 FLC using crisp type-1 fuzzy sets cannot directly handle such uncertainties. A type-2 FLC using type-2 fuzzy sets can handle such uncertainties to produce a better performance. Hence, type-2 FLCs will have the potential to overcome the limitations of type-1 FLCs and produce a new generation of fuzzy controllers with improved performance for many applications, which require handling high levels of uncertainty. This paper introduces briefly the interval type-2 FLC and its benefits. We also present briefly the type-2 FLC application to three challenging domains: industrial control, mobile robots control and ambient intelligent environments control

Type-2 FLCs: A New Generation of Fuzzy Controllers

Higher order fuzzy logic systems (FLSs), such as interval type-2 FLSs, have been shown to be very well suited to deal with the high levels of uncertainties present in the majority of real-world applications. General type-2 FLSs are expected to further extend this capability. However, the immense computational complexities associated with general type-2 FLSs have, until recently, prevented their application to real-world control problems. This paper aims to address this problem by the introduction of a complete representation framework, which is referred to as zSlices-based general type-2 fuzzy systems. The proposed approach will lead to a significant reduction in both the complexity and the computational requirements for general type-2 FLSs, while it offers the capability to represent complex general type-2 fuzzy sets. As a proof-of-concept application, we have implemented a zSlices-based general type-2 FLS for a two-wheeled mobile robot, which operates in a real-world outdoor environment. We have evaluated the computational performance of the zSlices-based general type-2 FLS, which is suitable for multiprocessor execution. Finally, we have compared the performance of the zSlices-based general type-2 FLS against type-1 and interval type-2 FLSs, and a series of results is presented which is related to the different levels of uncertainty handled by the different types of FLSs.

Toward General Type-2 Fuzzy Logic Systems Based on zSlices

This article presents a recursive algorithm to compute the generalized centroid of an interval type-2 fuzzy set. First, a re-expression of the upper and lower limits of the generalized centroid is introduced. Then, the re-expressed formulas are solved by using a mixed approach of exhaustive search and recursive computations. This method is compared with the Karnik-Mendel iterative algorithm under the same computational principles. Experimental evidence shows that the recursive approach is computationally faster than the Karnik-Mendel method without loosing numeric precision.

A Fast Recursive Method to Compute the Generalized Centroid of an Interval Type-2 Fuzzy Set

This paper presents an improved iterative algorithm for computing the generalized centroid of an interval type-2 fuzzy set. The properties of the discrete centroid function provide a stop condition that speeds up the original algorithm. Experimental evidence observed from three cases of study reveals that the improved algorithm is faster than the enhanced Karnik-Mendel algorithm when running over a common computing platform.

Improved iterative algorithm for computing the generalized centroid of an interval type-2 fuzzy set

This paper presents a type-2 fuzzy logic controller for a robotic agent intended to track a mobile object in the context of robot soccer games The controller has two inputs and two outputs that are logically connected by four rules Image processing is used to estimate the angle between the agent and the target, which introduces uncertainty in the control loop Other sources of uncertainty related to defects in the control loop have been identified In this sense, the paper explores how the type-2 controller overcomes those sources without incrementing the computational cost of the application

A Type-2 Fuzzy Controller for Tracking Mobile Objects in the Context of Robotic Soccer Games

This article discusses some relevant methodological aspects for implementing IT2-FLS on hardware. First it describes a hardware architecture for an IT2-FP. In addition, it details particular considerations for the design of the different components of the architecture. As a study case, a simple implementation of an IT2-FP in FPGA technology is presented

Implementing Interval Type-2 Fuzzy Processors [Developmental Tools]

This paper presents an architectural proposal for a hardware-based interval type-2 fuzzy inference system. First, it presents a computational model which considers parallel inference processing and type reduction based on computing inner and outer bound sets. Taking into account this model, we conceived a hardware architecture with several pipeline stages for full parallel execution of type-2 fuzzy inferences. The architectural proposal is used for specifying a type-2 fuzzy processor with reconfigurable rule base, which is implemented over FPGA technology. Implementation results show that this processor performs more than 30 millions of type-2 fuzzy inferences per second.

Miguel Melgarejo

Papers

A Fast Recursive Method to Compute the Generalized Centroid of an Interval Type-2 Fuzzy Set

Improved iterative algorithm for computing the generalized centroid of an interval type-2 fuzzy set

A Type-2 Fuzzy Controller for Tracking Mobile Objects in the Context of Robotic Soccer Games

Implementing Interval Type-2 Fuzzy Processors [Developmental Tools]

Hardware architecture and FPGA implementation of a type-2 fuzzy system