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2003 | Buch

Fuzzy Sets and Fuzzy Systems Kapitel lesen Erstes Kapitel lesen

Advanced Fuzzy Systems Design and Applications

verfasst von: Dr. Yaochu Jin

Verlag: Physica-Verlag HD

Buchreihe : Studies in Fuzziness and Soft Computing

Enthalten in: Professional Book Archive

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Über dieses Buch

Fuzzy rule systems have found a wide range of applications in many fields of science and technology. Traditionally, fuzzy rules are generated from human expert knowledge or human heuristics for relatively simple systems. In the last few years, data-driven fuzzy rule generation has been very active. Compared to heuristic fuzzy rules, fuzzy rules generated from data are able to extract more profound knowledge for more complex systems. This book presents a number of approaches to the generation of fuzzy rules from data, ranging from the direct fuzzy inference based to neural net­ works and evolutionary algorithms based fuzzy rule generation. Besides the approximation accuracy, special attention has been paid to the interpretabil­ ity of the extracted fuzzy rules. In other words, the fuzzy rules generated from data are supposed to be as comprehensible to human beings as those generated from human heuristics. To this end, many aspects of interpretabil­ ity of fuzzy systems have been discussed, which must be taken into account in the data-driven fuzzy rule generation. In this way, fuzzy rules generated from data are intelligible to human users and therefore, knowledge about unknown systems can be extracted.

Inhaltsverzeichnis

Frontmatter
1. Fuzzy Sets and Fuzzy Systems
Abstract
A set is a collection of finite or infinite number of objects, which are called elements or members of the set. In the classical set theory, an object either belongs to a set or does not. If x is an element of set A, we notate x ∈ A; if not, we notate x ∉ A.
Yaochu Jin
2. Evolutionary Algorithms
Abstract
The basic idea behind evolutionary algorithm is to simulate the natural process of evolution to achieve systems that are able to improve themselves by applying three main genetic operations called recombination, mutation and selection. Through these conceptually simple operations, evolutionary algorithms are able to exhibit very attractive properties such as self-organization, adaptation, optimization and creation. Due to these properties, evolutionary algorithms have been widely applied in the fields ranging from the basic research on biological intelligence such as artificial life [151] to real word applications such as design optimization [181].
Yaochu Jin
3. Artificial Neural Networks
Abstract
Artificial neural networks are historically simplified models for simulating the functions of human brains. From the cognition point of view, neural networks are able to acquire Knowledge through a process of learning and the acquired knowledge is stored in distribution among nodes and weights. Mathematically, most feed-forward neural networks are linear or non-linear function mapping systems that can perform function approximation (regression) and classification.
Yaochu Jin
4. Conventional Data-driven Fuzzy Systems Design
Abstract
The central point in designing a fuzzy system for modeling and control is the generation of a set of efficient and effective fuzzy rules. Generally, fuzzy rules can be generated either from heuristics or from experimental data. Heuristic fuzzy rule generation, as discussed in Chapter 1, consists of the following main steps:
  • Determination of the structure of the fuzzy systems. This includes mainly the selection of the inputs and outputs. Usually, a multi-input multi-output fuzzy systems can be decomposed into a number of multi-input single-output fuzzy systems.
  • Definition of linguistic terms and their fuzzy membership function for each fuzzy variables. If a Mamdani fuzzy system is designed, each input and output can be seen as a linguistic variable. Therefore, it is necessary to define the linguistic terms (e.g., Small, Medium, Large etc.) and their fuzzy membership function. Details about the definition of a linguistic variable is presented in Section 1.2.1.
  • Determination of fuzzy inference method. For example, for fuzzy mapping rules, the fuzzy Cartesian product can be used to define the fuzzy relation. Refer to Section 1.2.2.
  • Defuzzification. If the Mamdani type fuzzy rules are used, the fuzzy output derived from the fuzzy rule base should be defuzzified. Refer also to Section 1.2.2 for different defuzzification methods. If the Takagi-Sugeno fuzzy rules are used, the defuzzification is included in the fuzzy inference and a crisp output is obtained directly.
Yaochu Jin
5. Neural Network Based Fuzzy Systems Design
Abstract
Fuzzy rules are able to represent knowledge that is understandable to human beings. Traditional fuzzy rules are usually generated from expert knowledge and human heuristics. This gives rise to two main drawbacks of traditional fuzzy systems for modeling and control. First, the fuzzy rules are very simple and the performance of the fuzzy system is low. In most cases, fuzzy memberships are determined heuristically and therefore, the knowledge represented by the fuzzy rules may be shallow. Second, it is difficult to efficiently extract fuzzy rules for high-dimensional systems due to the limitation of human thinking. In particular, traditional fuzzy systems are lack of learning capability, whereas learning is one of the most important features of intelligent systems.
Yaochu Jin
6. Evolutionary Design of Fuzzy Systems
Abstract
Neurofuzzy systems are adaptive fuzzy systems that are able to learn using learning methods developed in the field of neural networks. Besides, neurofuzzy systems are assumed to have all important features of fuzzy systems, i.e., the knowledge represented by a neurofuzzy system should be transparent to human users.
Yaochu Jin
7. Knowledge Discovery by Extracting Interpretable Fuzzy Rules
Abstract
Data, information and knowledge are three closely related but different concepts cepts. The following are the definitions abstracted from Webster’s dictionary:
  • Data: 1. factual information (as measurements or statistics) used as a basis for reasoning, discussion, or calculation 2. information output by a sensing device or organ that includes both useful and irrelevant or redundant information and must be processed to be meaningful 3. information in numerical form that can be digitally transmitted or processed.
  • Information: 1. the communication or reception of knowledge or intelligence 2. knowledge obtained from investigation, study, or instruction.
  • Knowledge: 1. the fact or condition of knowing something with familiarity gained through experience or association 2. acquaintance with or understanding of a science, art, or technique 3. the fact or condition of being aware of something.
Yaochu Jin
8. Fuzzy Knowledge Incorporation into Neural Networks
Abstract
Conventional neural network learning algorithms use data as the only source of knowledge, no matter whether the supervised, the unsupervised or the reinforcement learning is employed. This is due to the fact that the conventional learning algorithms are derived from statistics or probability theory, both of which are strongly dependent on data samples.
Yaochu Jin
9. Fuzzy Preferences Incorporation into Multi-objective Optimization
Abstract
To facilitate the discussions on multi-objective optimization (MOO), we first give a short review on the definitions related to multiobjective optimization.
Yaochu Jin
Backmatter
Metadaten
Titel
Advanced Fuzzy Systems Design and Applications
verfasst von
Dr. Yaochu Jin
Copyright-Jahr
2003
Verlag
Physica-Verlag HD
Electronic ISBN
978-3-7908-1771-3
Print ISBN
978-3-7908-2520-6
DOI
https://doi.org/10.1007/978-3-7908-1771-3