Genetic Fuzzy Systems Applied to Ports and Coasts Engineering

Genetic Fuzzy Systems Applied to Ports and Coasts Engineering

Óscar Ibáñez (University of A Coruña, Spain) and Alberte Castro (University of Santiago de Compostela, Spain)
Copyright: © 2009 |Pages: 8
DOI: 10.4018/978-1-59904-849-9.ch113
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Abstract

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.
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Introduction

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 19731973) 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.

Figure 1.

A typical GA cycle

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.

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Background

Many works have been done in the area of artificial intelligence applied to Coastal Engineering. It can be said that Artificial Intelligence methods have a wide acceptance among Coastal & Ports Engineers. Artificial Neural Network has been applied for years with very good results. The big drawback is their inability to explain their results, how have reached them, because they work as a black box and it can not be known what happen inside them. Over the last few years, a lot of works about fuzzy systems with engineering applications have been developed (Mercan, Yagci & Kabdasli, 2003; Dingerson, 2005; Gezer, 2004; Ross, 2004; Oliveira, Souza & Mandorino, 2006; Ergin, Williams & Micallef, 2006; Yagci, Mercan, Cigizoglu & Kabdasli, 2005). These systems have the advantage of being easy to understand (their solutions) and the capacity to handle uncertainty. However, most of these found a problem with knowledge extraction; when they try to define their RB and DB, in many cases for the difficulty of the problem and more often for the difficulty of represent all the expert knowledge in some rules and membership function.

Key Terms in this Chapter

Fuzzy System (FS): Any FL-based system, which either uses FL as the basis for the representation of different forms of knowledge, or to model the interactions and relationships among the system variables.

Genetic Fuzzy System: A fuzzy system that is augmented with an evolutionary learning process.

Mamdani Inference System: Derives the fuzzy outputs from the inputs fuzzy sets according to the relation defined through fuzzy rules. Establishes a mapping between fuzzy sets U = U1 x U2 x . . . x Un in the input domain of X1…, Xn and fuzzy sets V in the output domain of Y. The fuzzy inference scheme employs the generalized modus ponens, an extension to the classical modus ponens (Zadeh, 1973).

Takagi-Sugeno-Kang Fuzzy Rule-Based System: A rule based system whose antecedent is composed of linguistic variables and the consequent is represented by a function of the input variables.

Genetic Algorithm: General-purpose search algorithms that use principles by natural population genetics to evolve solutions to problems

Mamdani Fuzzy Rule-Based System: A rule based system where fuzzy logic (FL) is used as a tool for representing different forms of knowledge about the problem at hand, as well as for modelling the interactions and relationships that exist between its variables.

Fuzzification: Establishes a mapping from crisp input values to fuzzy set defined in the universe of discourse of that input.

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