This book focuses on the fields of fuzzy logic and metaheuristic algorithms, particularly the harmony search algorithm and fuzzy control. There are currently several types of metaheuristics used to solve a range of real-world of problems, and these metaheuristics contain parameters that are usually fixed throughout the iterations. However, a number of techniques are also available that dynamically adjust the parameters of an algorithm, such as probabilistic fuzzy logic. This book proposes a method of addressing the problem of parameter adaptation in the original harmony search algorithm using type-1, interval type-2 and generalized type-2 fuzzy logic. The authors applied this methodology to the resolution of problems of classical benchmark mathematical functions, CEC 2015, CEC2017 functions and to the optimization of various fuzzy logic control cases, and tested the method using six benchmark control problems - four of the Mamdani type: the problem of filling a water tank, the problem of controlling the temperature of a shower, the problem of controlling the trajectory of an autonomous mobile robot and the problem of controlling the speed of an engine; and two of the Sugeno type: the problem of controlling the balance of a bar and ball, and the problem of controlling control the balance of an inverted pendulum. When the interval type-2 fuzzy logic system is used to model the behavior of the systems, the results show better stabilization because the uncertainty analysis is better. As such, the authors conclude that the proposed method, based on fuzzy systems, fuzzy controllers and the harmony search optimization algorithm, improves the behavior of complex control plants.

This book presents a new meta-heuristic algorithm, inspired by the self-defense mechanisms of plants in nature. Numerous published works have demonstrated the various self-defense mechanisms (survival strategies) plants use to protect themselves against predatory organisms, such as herbivorous insects. The proposed algorithm is based on the predator-prey mathematical model originally proposed by Lotka and Volterra, consisting of two nonlinear first-order differential equations, which allow the growth of two interacting populations (prey and predator) to be modeled. The proposed meta-heuristic is able to produce excellent results in several sets of benchmark optimization problems. Further, fuzzy logic is used for dynamic parameter adaptation in the algorithm.

In this book, a methodology for parameter adaptation in meta-heuristic op-timization methods is proposed. This methodology is based on using met-rics about the population of the meta-heuristic methods, to decide through a fuzzy inference system the best parameter values that were carefully se-lected to be adjusted. With this modification of parameters we want to find a better model of the behavior of the optimization method, because with the modification of parameters, these will affect directly the way in which the global or local search are performed.Three different optimization methods were used to verify the improve-ment of the proposed methodology. In this case the optimization methods are: PSO (Particle Swarm Optimization), ACO (Ant Colony Optimization) and GSA (Gravitational Search Algorithm), where some parameters are se-lected to be dynamically adjusted, and these parameters have the most im-pact in the behavior of each optimization method.Simulation results show that the proposed methodology helps to each optimization method in obtaining better results than the results obtained by the original method without parameter adjustment.

In this book a neural network learning method with type-2 fuzzy weight adjustment is proposed. The mathematical analysis of the proposed learning method architecture and the adaptation of type-2 fuzzy weights are presented. The proposed method is based on research of recent methods that handle weight adaptation and especially fuzzy weights.The internal operation of the neuron is changed to work with two internal calculations for the activation function to obtain two results as outputs of the proposed method. Simulation results and a comparative study among monolithic neural networks, neural network with type-1 fuzzy weights and neural network with type-2 fuzzy weights are presented to illustrate the advantages of the proposed method.The proposed approach is based on recent methods that handle adaptation of weights using fuzzy logic of type-1 and type-2. The proposed approach is applied to a cases of prediction for the Mackey-Glass (for o=17) and Dow-Jones time series, and recognition of person with iris biometric measure. In some experiments, noise was applied in different levels to the test data of the Mackey-Glass time series for showing that the type-2 fuzzy backpropagation approach obtains better behavior and tolerance to noise than the other methods.The optimization algorithms that were used are the genetic algorithm and the particle swarm optimization algorithm and the purpose of applying these methods was to find the optimal type-2 fuzzy inference systems for the neural network with type-2 fuzzy weights that permit to obtain the lowest prediction error.