Antonio Rodríguez-Díaz

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.

Simulation of the bird age-structured population growth based on an interval type-2 fuzzy cellular structure

In this paper an age-structured population growth model, based on a fuzzy cellular structure, is proposed. An age-structured population growth model enables a better description of population dynamics. In this paper, the dynamics of a particular bird species is considered. The dynamics is governed by the variation of natality, mortality and emigration rates, which in this work are evaluated using an interval type-2 fuzzy logic system. The use of type-2 fuzzy logic enables handling the effects caused by environment heterogeneity on the population. A set of fuzzy rules, about population growth, are derived from the interpretation of the ecological laws and the bird life cycle. The proposed model is formulated using discrete mathematics within the framework of a fuzzy cellular structure. The fuzzy cellular structure allows us to visualize the evolution of the populations spatial dynamics. The spatial distribution of the population has a deep effect on its dynamics. Moreover, the model enables not only to estimate the percentage of occupation on the cellular space when the species reaches its stable equilibrium level, but also to observe the occupation patterns.

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.

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.

A Hybrid Learning Algorithm for Interval Type-2 Fuzzy Neural Networks: The Case of Time Series Prediction

In this work, a class of Interval Type-2 Fuzzy Neural Networks (IT2FNN) is proposed, which is functionally equivalent to interval type-2 fuzzy inference systems. The computational process envisioned for fuzzy neural systems is as follows: it starts with the development of an ”Interval Type-2 Fuzzy Neuron”, which is based on biological neural morphologies, followed by the learning mechanisms. We describe how to decompose the parameter set such that the hybrid learning rule of adaptive networks can be applied to the IT2FNN architecture for the Takagi-Sugeno-Kang reasoning.

Universal approximation of a class of interval type-2 fuzzy neural networks in nonlinear identification

Neural networks (NNs), type-1 fuzzy logic systems (T1FLSs), and interval type-2 fuzzy logic systems (IT2FLSs) have been shown to be universal approximators, which means that they can approximate any nonlinear continuous function. Recent research shows that embedding an IT2FLS on an NN can be very effective for a wide number of nonlinear complex systems, especially when handling imperfect or incomplete information. In this paper we show, based on the Stone-Weierstrass theorem, that an interval type-2 fuzzy neural network (IT2FNN) is a universal approximator, which uses a set of rules and interval type-2membership functions (IT2MFs) for this purpose. Simulation results of nonlinear function identification using the IT2FNN for one and three variables and for the Mackey-Glass chaotic time series prediction are presented to illustrate the concept of universal approximation.

Big five patterns for software engineering roles using an ANFIS learning approach with RAMSET

This paper proposes an ANFIS (Adaptive Network Based Fuzzy Inference System) Learning Approach where we have found patterns of personality types using Big Five Personality Tests for Software Engineering Roles in Software Development Project Teams as part of RAMSET (Role Assignment Methodology for Software Engineering Teams) methodology. An ANFIS model is applied to a set of role traits resulting from Big Five personality tests in our case studies obtaining a Takagi-Sugeno-Kang (TSK) Fuzzy Inference System (FIS) type model with rules that helps us recommend best suited roles for performing in software engineering teams.

Fuzzy Sets in Dynamic Adaptation of Parameters of a Bee Colony Optimization for Controlling the Trajectory of an Autonomous Mobile Robot

A hybrid approach composed by different types of fuzzy systems, such as the Type-1 Fuzzy Logic System (T1FLS), Interval Type-2 Fuzzy Logic System (IT2FLS) and Generalized Type-2 Fuzzy Logic System (GT2FLS) for the dynamic adaptation of the alpha and beta parameters of a Bee Colony Optimization (BCO) algorithm is presented. The objective of the work is to focus on the BCO technique to find the optimal distribution of the membership functions in the design of fuzzy controllers. We use BCO specifically for tuning membership functions of the fuzzy controller for trajectory stability in an autonomous mobile robot. We add two types of perturbations in the model for the Generalized Type-2 Fuzzy Logic System to better analyze its behavior under uncertainty and this shows better results when compared to the original BCO. We implemented various performance indices; ITAE, IAE, ISE, ITSE, RMSE and MSE to measure the performance of the controller. The experimental results show better performances using GT2FLS then by IT2FLS and T1FLS in the dynamic adaptation the parameters for the BCO algorithm.

Handling Uncertainty in Controllers Using Type-2 Fuzzy Logic

In this paper, we show the advantages of using type-2 fuzzy logic in the design of controllers for real-world applications because of their inherent uncertainty. We support this statement with experimental results, qualitative observations, and quantitative measures of errors. For quantifying the errors, we utilized three widely accepted performance criteria, namely: Integral of Square Error (ISE), Integral of the Absolute value of the Error (IAE), and Integral of the Time multiplied by the Absolute value of the Error (ITAE).