Mauricio A. Sanchez

Generalized Type-2 Fuzzy Systems for controlling a mobile robot and a performance comparison with Interval Type-2 and Type-1 Fuzzy Systems

A Generalized Type-2 Fuzzy Controller (GT2FC) was developed.Simulation of a GT2FC for a mobile robot is presented.Experiments support the notion that GT2FC handles more uncertainty. The aim of this paper is to show that a Generalized Type-2 Fuzzy Control System can outperform Type-1 and Interval Type-2 Fuzzy Control Systems when external perturbations are present. A Generalized Type-2 Fuzzy System can handle better uncertainty because of the nature of its membership functions, and as such, they are better tailored for situations where external noise is present. To test the noise resilience of Fuzzy Controllers, the design of a Fuzzy Controller for a mobile robot is presented in this paper, in conjunction with three types of external perturbations: band-limited white noise, pulse noise, and uniform random number noise. Noise resilience is measured through different performance indices, such as ITAE, ITSE, IAE, and ISE. Simulation results show that Generalized Type-2 Fuzzy Controllers outperform their Type-1 and Interval Type-2 Fuzzy Controller counterparts in the presence of external perturbations.

Information granule formation via the concept of uncertainty-based information with Interval Type-2 Fuzzy Sets representation and Takagi-Sugeno-Kang consequents optimized with Cuckoo search

Explanatory diagram of how the proposed approach measures and defines the uncertainty, and forms an IT2 Fuzzy Set with such uncertainty. A technique for forming information granules is presented in this paper.Based on the theory of uncertainty-based information, an approach which forms information granules is presented.Two implementations are proposed which form Interval Type-2 Fuzzy information granules.These approaches capture multiple evaluations of uncertainty from different samples and use these models to measure the uncertainty from the difference among them.The proposed approaches are tested with classification and curve identification benchmark datasets with very good results. A technique for forming information granules is shown in this paper. Based on the theory of uncertainty-based information, an approach toward a general base is given which forms information granules. Two implementations are proposed which form Interval Type-2 Fuzzy information granules, both with Takagi-Sugeno-Kang consequents optimized with Cuckoo search algorithm. These approaches capture multiple evaluations of uncertainty from taken samples and use these models to measure the uncertainty from the difference between them. The proposed approaches are tested with classification and curve identification datasets.

Fuzzy granular gravitational clustering algorithm for multivariate data

Abstract A new method for finding fuzzy information granules from multivariate data through a gravitational inspired clustering algorithm is proposed in this paper. The proposed algorithm incorporates the theory of granular computing, which adapts the cluster size with respect to the context of the given data. Via an inspiration in Newton’s law of universal gravitation, both conditions of clustering similar data and adapting to the size of each granule are achieved. This paper compares the Fuzzy Granular Gravitational Clustering Algorithm (FGGCA) against other clustering techniques on two grounds: classification accuracy, and clustering validity indices, e.g. Rand, FM, Davies–Bouldin, Dunn, Homogeneity, and Separation. The FGGCA is tested with multiple benchmark classification datasets, such as Iris, Wine, Seeds, and Glass identification.

A generalized type-2 fuzzy granular approach with applications to aerospace

In this paper a granular approach for intelligent control using generalized type-2 fuzzy logic is presented. Granularity is used to divide the design of the global controller into several individual simpler controllers. The theory of alpha planes is used to implement the generalized type-2 fuzzy systems. The proposed method for control is applied to a non-linear control problem to test the advantages of the proposed approach. Also an optimization method is used to efficiently design the generalized type-2 fuzzy system to improve the control performance.

Formation of general type-2 Gaussian membership functions based on the information granule numerical evidence

This paper shows a new technique for forming fuzzy Gaussian membership functions based on the numerical evidence which is found in its information granule. Inspired by the principle of justifiable granularity, and by obtaining a meaningful granule of information, general type-2 Gaussian membership functions are created which better represent a piece of information. Some examples are given, a synthetic example to show the general behavior, as well as an example taken from the iris dataset.

Fuzzy granular gravitational clustering algorithm

Given the nature of clustering algorithms of finding automatically, or semi-automatically, an unspecified number of clusters, much work has been done in this area. This paper will introduce a proposed gravitational model for finding clusters, the algorithm is based on the gravitational forces from Newtons law of universal gravitation and the output clusters are then fuzzified. Two examples of datasets are compared, one synthetic and one of the Iris, are benchmarked against the fuzzy subtractive algorithm.

A hybrid method for IT2 TSK formation based on the principle of justifiable granularity and PSO for spread optimization

In this paper, a new hybrid method for forming interval type 2 fuzzy inference systems (IT2 FIS) is shown. This methodology builds upon an existing type 1 fuzzy inference system (T1 FIS) or from the output centers from any clustering algorithm, calculating the footprint of uncertainty (FOU) based on the implementation of the principle of justifiable granularity, and finally a particle swarm optimization algorithm (PSO) optimizes the spreads from First Order Takagi-Sugeno-Kang (TSK) type consequents to improve the coverage of the FOU. Focusing mainly in the coverage of the FOU, two datasets are used to demonstrate the effectiveness of FOU coverage in environments with noise, especially when the noise is on the outputs. These two datasets are a simple Fifth Order curve, and the iris benchmark dataset.

Review of Recent Type-2 Fuzzy Image Processing Applications

This paper presents a literature review of applications using type-2 fuzzy systems in the area of image processing. Over the last years, there has been a significant increase in research on higher-order forms of fuzzy logic; in particular, the use of interval type-2 fuzzy sets and general type-2 fuzzy sets. The idea of making use of higher orders, or types, of fuzzy logic is to capture and represent uncertainty that is more complex. This paper is focused on image processing systems, which includes image segmentation, image filtering, image classification and edge detection. Various applications are presented where general type-2 fuzzy sets, interval type-2 fuzzy sets, and interval-value fuzzy sets are used; some are compared with the traditional type-1 fuzzy sets and others methodologies that exist in the literature for these areas in image processing. In all accounts, it is shown that type-2 fuzzy sets outperform both traditional image processing techniques as well as techniques using type-1 fuzzy sets, and provide the ability to handle uncertainty when the image is corrupted by noise.

An Analysis on the Intrinsic Implementation of the Principle of Justifiable Granularity in Clustering Algorithms

The initial process for the granulation of information is the clustering of data, once the relationships between this data have been found these become clusters, each cluster represents a coarse granule, whereas each data point represents a fine granule. All clustering algorithms find these relationships by different means, yet the notion of the principle of justifiable granularity is not considered by any of them, since it is a recent idea in the area of Granular Computing. This paper describes a first approach in the analysis of the relationship between the size of the clusters found and their intrinsic implementation of the principle of justifiable granularity. An analysis is done with two datasets, simplefit and iris, and two clustering algorithms, subtractive and granular gravitational.

Uncertainty-Based Information Granule Formation

A new technique for forming information granules is shown in this chapter. Based on the theory of uncertainty-based information, an approach is proposed which forms Interval Type-2 Fuzzy information granules. This approach captures multiple evaluations of uncertainty from taken samples and uses these models to measure the uncertainty from the difference in these. The proposed approach is tested through multiple benchmark datasets: iris, wine, glass, and a 5th order curve identification.