What is Takagi-Sugeno-Kang Fuzzy Rule-Based System

Fuzzy Logic (FL) and fuzzy sets in a wide interpretation of FL (in terms in which fuzzy logic is coextensive with the theory of fuzzy sets, that is, classes of objects in which the transition from membership to non membership is gradual rather than abrupt) have placed modelling into a new and broader perspective by providing innovative tools to cope with complex and ill-defined systems. The area of fuzzy sets has emerged following some pioneering works of Zadeh (Zadeh, 1965 and 1973) where the first fundamentals of fuzzy systems were established. Rule based systems have been successfully used to model human problem-solving activity and adaptive behaviour. The conventional approaches to knowledge representation are based on bivalent logic. A serious shortcoming of such approaches is their inability to come to grips with the issue of uncertainty and imprecision. As a consequence, the conventional approaches do not provide an adequate model for modes of reasoning. Unfortunately, all commonsense reasoning falls into this category. The application of FL to rule based systems leads us to fuzzy systems. The main role of fuzzy sets is representing Knowledge about the problem or to model the interactions and relationships among the system variables. There are two essential advantages for the design of rule-based systems with fuzzy sets and logic: • The key features of knowledge captured by fuzzy sets involve handling uncertainty. • Inference methods become more robust and flexible with approximate reasoning methods of fuzzy logic. Genetic Algorithms (GAS) are a stochastic optimization technique that mimics natural selection (Holland, 1975). GAs are intrinsically robust and capable of determining a near global optimal solution. The use of GAS is usually recommended for optimization in high-dimensional, multimodal complex search spaces where deterministic methods normally fail. GAs explore a population of solutions in parallel. The GA is a searching process based on the laws of natural selections and genetics. Generally, a simple GA contains three basic operations: selection, genetic operations and replacement. A typical GA cycle is shown in Fig. 1. In this paper it is shown how a genetic algorithm can be used in order to optimize a fuzzy system which is used in wave reflection analysis at submerged breakwaters.