International Journal of Computer Applications (0975 – 8887) Volume 58– No.6, November 2012 1 Fuzzy Model Identification: A Firefly Optimization Approach Shakti Kumar Computational Intelligence Laboratory, IST Klawad, Haryana, INDIA Parvinder Kaur Department of Electronics & Communications, SLIET, Longowal, Punjab, INDIA Amarpartap Singh Department of Electronics & Communications, SLIET, Longowal, Punjab, INDIA ABSTRACT Nature-inspired methodologies are currently among the most powerful algorithms for optimization problems. This paper presents a recent nature-inspired algorithm named Firefly algorithm (FA) for automatically evolving a fuzzy model from numerical data. FA is a meta-heuristic inspired by the flashing behavior of fireflies. The rate and the rhythmic flash, and the amount of time form part of the signal system to attract other fireflies. The paper discusses fuzzy modeling for zero-order Takagi-Sugeno-Kang (TSK) type fuzzy systems. Simulations on two well known problems, one battery charger that is a fuzzy control problem and another Iris data classification problem are conducted to verify the performance of above approach. The results indicate that the FA is a very promising optimizing algorithm for evolving fuzzy logic based Systems as compared to some of the existing approaches. General Terms Soft Computing, Fuzzy Model Identification. Keywords Fuzzy logic, Firefly algorithm, Rule Base, Nature-inspired optimization, Fuzzy Modeling. 1. INTRODUCTION Developing models of complex real-systems is an important topic in many fields of science and engineering. Models are generally used for simulation, identifying the system’s behavior and design of controllers etc. The principles of fuzzy modeling were outlined by Zadeh when he gave the concept of grade of membership and published his seminal paper on fuzzy sets that lead to the birth of fuzzy logic technology [1]. Fuzzy systems provide a scheme to represent the knowledge in a way that resembles human communication and reasoning. Design of fuzzy model or fuzzy model identification is the task of finding the parameters of fuzzy model so as to get the desired behavior. Two different approaches are used for the design of fuzzy models: Knowledge driven and Data driven models. In the first approach, the design is constructed from the knowledge acquired from the expert, while in the second; the input-output data is used for building model. In the first approach there were many problems and shortcomings; the interviews are generally long, inefficient and frustrating for both the domain experts and knowledge engineers, especially so in domains where experts make decisions based on incomplete or imprecise information. This knowledge acquisition phase is often the main bottleneck within the knowledge engineering process and therefore considerable effort has been expended in designing algorithms that automatically induce fuzzy rules from data [3]. Tagaki, Sugeno and Kang [4][5] developed the first approach for building and tuning fuzzy rules from the training data that laid the foundation for an important sub-area in fuzzy logic, referred to as fuzzy modeling or fuzzy model identification. Many intelligent optimization techniques such as neural networks, genetic algorithms, swarm intelligence, ant colony optimization, biogeography based optimization etc. have been proposed to automatically generate fuzzy rules from numerical data [6]-[52]. This paper discusses a new approach to fuzzy model identification problem making use of Firefly algorithm. The paper is set up as follows. In Section 2 a brief introduction to fuzzy system modeling is presented. Section 3 provides a brief account of FA optimization algorithm and the framework for fuzzy model identification through FA is presented in Section 4. Section 5 represents simulation results considering two examples, one control problem and other Iris data classification problem. Finally, conclusions are drawn in Section 6. 2. FUZZY SYSTEMS MODELING Fuzzy modeling is the task of identifying the parameters of fuzzy inference system so as to achieve a desired behaviour. The fuzzy model identification process involves the question of providing a methodology for development i.e. a set of techniques for obtaining the fuzzy model from information and knowledge about the system. The problem of fuzzy model identification includes the following issues [2]:  Selecting the type of fuzzy model.  Selecting input and output variables for the model.  Choosing the structure of membership functions.  Determining the number of fuzzy rules.  Identifying the parameters of antecedent and consequent membership functions.  Identifying the consequent parameters of rules.  Defining some performance criteria for evaluating fuzzy models. These issues can be grouped into three subproblems: structure identification, parameter estimation and model validation as shown in Figure 1. If the performance of the model obtained is not satisfactory, the model structure is modified and the parameters are re-estimated till the performance is satisfactory. Figure 1: Fuzzy Model Identification Process 3. FIREFLY ALGORITHM The Firefly Algorithm (FA) is a meta-heuristic, nature- inspired, optimization algorithm which is based on the social Numerical Information Satisfied Not Satisfied Structure Identification Parameter Estimation Model Validation Linguistic Information