Juan R. Castro

A hybrid learning algorithm for a class of interval type-2 fuzzy neural networks

In real life, information about the world is uncertain and imprecise. The cause of this uncertainty is due to: deficiencies on given information, the fuzzy nature of our perception of events and objects, and on the limitations of the models we use to explain the world. The development of new methods for dealing with information with uncertainty is crucial for solving real life problems. In this paper three interval type-2 fuzzy neural network (IT2FNN) architectures are proposed, with hybrid learning algorithm techniques (gradient descent backpropagation and gradient descent with adaptive learning rate backpropagation). At the antecedents layer, a interval type-2 fuzzy neuron (IT2FN) model is used, and in case of the consequents layer an interval type-1 fuzzy neuron model (IT1FN), in order to fuzzify the rules antecedents and consequents of an interval type-2 Takagi-Sugeno-Kang fuzzy inference system (IT2-TSK-FIS). IT2-TSK-FIS is integrated in an adaptive neural network, in order to take advantage the best of both models. This provides a high order intuitive mechanism for representing imperfect information by means of use of fuzzy If-Then rules, in addition to handling uncertainty and imprecision. On the other hand, neural networks are highly adaptable, with learning and generalization capabilities. Experimental results are divided in two kinds: in the first one a non-linear identification problem for control systems is simulated, here a comparative analysis of learning architectures IT2FNN and ANFIS is done. For the second kind, a non-linear Mackey-Glass chaotic time series prediction problem with uncertainty sources is studied. Finally, IT2FNN proved to be more efficient mechanism for modeling real-world problems.

An Interval Type-2 Fuzzy Logic Toolbox for Control Applications

This paper presents the development and design of a graphical user interface and a command line programming toolbox for construction, edition and observation of interval type-2 fuzzy inference systems. The interval type-2 fuzzy logic system toolbox (IT2FLS), is an environment for interval type-2 fuzzy logic inference system development. Tools that cover the different phases of the fuzzy system design process, from the initial description phase, to the final implementation phase, build the toolbox. The toolboxs best qualities are the capacity to develop complex systems and the flexibility that permits the user to extend the availability of functions for working with the use of type-2 fuzzy operators, linguistic variables, interval type-2 membership functions, defuzzification methods and the evaluation of interval type-2 fuzzy inference systems.

Edge-Detection Method for Image Processing Based on Generalized Type-2 Fuzzy Logic

This paper presents an edge-detection method that is based on the morphological gradient technique and generalized type-2 fuzzy logic. The theory of alpha planes is used to implement generalized type-2 fuzzy logic for edge detection. For the defuzzification process, the heights and approximation methods are used. Simulation results with a type-1 fuzzy inference system, an interval type-2 fuzzy inference system, and with a generalized type-2 fuzzy inference system for edge detection are presented. The proposed generalized type-2 fuzzy edge-detection method was tested with benchmark images and synthetic images. We used the merit of Pratt measure to illustrate the advantages of using generalized type-2 fuzzy logic.

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.

Building fuzzy inference systems with a new interval type-2 fuzzy logic toolbox

This paper presents the development and design of a graphical user interface and a command line programming Toolbox for construction, edition and simulation of Interval Type-2 Fuzzy Inference Systems. The Interval Type- 2 Fuzzy Logic System (IT2FLS) Toolbox, is an environment for interval type-2 fuzzy logic inference system development. Tools that cover the different phases of the fuzzy system design process, from the initial description phase, to the final implementation phase, constitute the Toolbox. The Toolboxs best qualities are the capacity to develop complex systems and the flexibility that allows the user to extend the availability of functions for working with the use of type-2 fuzzy operators, linguistic variables, interval type-2 membership functions, defuzzification methods and the evaluation of Interval Type-2 Fuzzy Inference Systems.

A comparative study of type-1 fuzzy logic systems, interval type-2 fuzzy logic systems and generalized type-2 fuzzy logic systems in control problems

This paper presents a comparative study of type-2 fuzzy logic systems with respect to interval type-2 and type-1 fuzzy logic systems to show the efficiency and performance of a generalized type-2 fuzzy logic controller (GT2FLC). We used different types of fuzzy logic systems for designing the fuzzy controllers of complex non-linear plants. The theory of alpha planes is used for approximating generalized type-2 fuzzy logic in fuzzy controllers. In the defuzzification process, the Karnik and Mendel Algorithm is used. Simulation results with a type-1 fuzzy logic controller (T1FLC), an interval type-2 fuzzy logic controller (IT2FLC) and with a generalized type-2 fuzzy logic controller (GT2FLC) for benchmark plants are presented. The advantage of using generalized type-2 fuzzy logic in fuzzy controllers is verified with four benchmark problems. We considered different levels of noise, number of alpha planes and four types of membership functions in the simulations for comparison and to analyze the approach of generalized type-2 fuzzy logic systems when applied in fuzzy control.

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.

Application of interval type-2 fuzzy neural networks in non-linear identification and time series prediction

Neural networks (NNs), type-1 fuzzy logic systems and interval type-2 fuzzy logic systems (IT2FLSs) have been shown to be important methods in real world applications, which range from pattern recognition, time series prediction, to intelligent control. Recent research shows that embedding an IT2FLS on an NN can be very effective for a wide number of non-linear complex systems, especially when handling imperfect or incomplete information. In this paper we are presenting several models of interval type-2 fuzzy neural networks (IT2FNNs) that use a set of rules and interval type-2 membership functions for that purpose. Simulation results of non-linear function identification using the IT2FNN for one and three variables and for the Mackey–Glass chaotic time series prediction are presented to illustrate that the proposed models have potential for real world applications.

An Interval Type-2 Fuzzy Neural Network for Chaotic Time Series Prediction with Cross-Validation and Akaike Test

A novel homogeneous integration strategy of an interval type-2 fuzzy inference system (IT2FIS) with Takagi-Sugeno-Kang reasoning (TSK IT2FIS) is presented. This TSK IT2FIS is represented as an adaptive neural network (NN) with hybrid learning (IT2FNN:BP+RLS) in order to automatically generate an interval type-2 fuzzy logic system (TSK IT2FLS). Consequent parameters are updated with recursive least-square (RLS) algorithm; antecedent parameters with back-propagation (BP) algorithm. Mackey-Glass chaotic time series forecasting results are presented ((=17, 30, 100) with different signal noise ratio (SNR). Soundness for uncertainty, adaptability and learning and generalization capabilities is shown using 10-fold Cross Validation, Akaike Information Criteria (AIC) and F-Test.

Building Fuzzy Inference Systems with the Interval Type-2 Fuzzy Logic Toolbox

This paper presents the development and design of a graphical user interface and a command line programming Toolbox for construction, edition and simulation of Interval Type-2 Fuzzy Inference Systems. The Interval Type-2 Fuzzy Logic System Toolbox (IT2FLS), is an environment for interval type-2 fuzzy logic inference system development. Tools that cover the different phases of the fuzzy system design process, from the initial description phase, to the final implementation phase, constitute the Toolbox. The Toolbox’s best qualities are the capacity to develop complex systems and the flexibility that allows the user to extend the availability of functions for working with the use of type-2 fuzzy operators, linguistic variables, interval type-2 membership functions, defuzzification methods and the evaluation of Interval Type-2 Fuzzy Inference Systems.