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2000 | Buch

Classical sets and fuzzy sets Basic definitions and terminology Kapitel lesen Erstes Kapitel lesen

Fuzzy and Neuro-Fuzzy Intelligent Systems

verfasst von: Professor Ernest Czogała, Ph.D., D.Sc., Professor Jacek Łęski, Ph.D., D.Sc.

Verlag: Physica-Verlag HD

Buchreihe : Studies in Fuzziness and Soft Computing

Enthalten in: Professional Book Archive

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Über dieses Buch

Intelligence systems. We perfonn routine tasks on a daily basis, as for example: • recognition of faces of persons (also faces not seen for many years), • identification of dangerous situations during car driving, • deciding to buy or sell stock, • reading hand-written symbols, • discriminating between vines made from Sauvignon Blanc, Syrah or Merlot grapes, and others. Human experts carry out the following: • diagnosing diseases, • localizing faults in electronic circuits, • optimal moves in chess games. It is possible to design artificial systems to replace or "duplicate" the human expert. There are many possible definitions of intelligence systems. One of them is that: an intelligence system is a system able to make decisions that would be regarded as intelligent ifthey were observed in humans. Intelligence systems adapt themselves using some example situations (inputs of a system) and their correct decisions (system's output). The system after this learning phase can make decisions automatically for future situations. This system can also perfonn tasks difficult or impossible to do for humans, as for example: compression of signals and digital channel equalization.

Inhaltsverzeichnis

Frontmatter
1. Classical sets and fuzzy sets Basic definitions and terminology
Abstract
Classical sets are sets with crisp boundaries. Usually an ordinary set (a classical or crisp set) is called a collection of objects which have some properties distinguishing them from other objects which do not possess these properties.
Ernest Czogała, Jacek Łęski
2. Approximate reasoning
Abstract
A fuzzy conditional statement (or conditional rule, or fuzzy if-then rule) assumes the form:
$$IF X is A THEN y is B,$$
(2.1)
where A and B are linguistic values of linguistic variables X and Y, defined by fuzzy sets A and B, respectively. Proposition “X is A” is called the premise or antecedent, and “Y is B” is called conclusion or consequence. In classical logic the statement “if P then Q” is written with implication P ⇒ Q. Implication is a connective defined by Table 2.1.
Ernest Czogała, Jacek Łęski
3. Artificial neural networks
Abstract
Artificial neural networks are systems whose structure is inspired by the action of the nervous system and the human brain. A neuron is the basic unit of a biological neural network. This neuron is shown in Fig. 3.1.a. The neuron consists of inputs called dendrites and output (to other neurons) called axon. The transmission of a signal from an axon to dendrites of other neurons goes through synaptic contacts. The signals transmitted from the synapse to dendrites are modified according to the synaptic strength of connection (synaptic weight).
Ernest Czogała, Jacek Łęski
4. Unsupervised learning Clustering methods
Abstract
In the learning method described in the previous chapter we assume that we have target (desired) output of network for inputs from training data set. In contrast to that, in this chapter we use data set without the desired output of network. Such an approach to network learning without a teacher or supervisor is called an unsupervised method. The effect of that learning are features, regularities and structure of data extraction, and sometimes it is called a method that search for structures of data. For example in biology and medicine, where sets of physical and biochemical measurements define species and diseases, respectively, unsupervised methods are very useful. In this book unsupervised methods will be used to search fuzzy if-then rules. Grouping found by unsupervised methods is frequently referred to as clusters. The cluster is a natural and homogeneous subset of data. The data in each cluster are as similar as possible to each other, and as different (dissimilar) as possible from other cluster’s data.
Ernest Czogała, Jacek Łęski
5. Fuzzy systems
Abstract
Fuzzy systems meant here as rule-based or knowledge-based systems. These systems consist of a knowledge base and a reasoning mechanism called fuzzy inference engine. A fuzzy rule base consists of a collection of fuzzy if-then rules. A fuzzy inference engine combines these rules into a mapping from the inputs of the system into its output, using fuzzy reasoning methods (see Chapter 2). The fuzzy systems can take either fuzzy sets or crisp values as inputs. In the latter case, we use a fuzzifier at the system input. Fuzzy systems produce a fuzzy set as output. In some applications we need real-valued output. To extract crisp value from the output fuzzy set defuzzification methods are used (see Section 2.9).
Ernest Czogała, Jacek Łęski
6. Neuro-fuzzy systems
Abstract
There are generally three approaches to building mathematical models:
  • white box modeling, where everything is considered to be known from physical laws,
  • black box modeling (system identification), where all knowledge derives from measurements,
  • gray box modeling, where both physical laws and observed measurements are used to design a model.
Ernest Czogała, Jacek Łęski
7. Applications of artificial neural network based fuzzy inference system
Abstract
In previous chapters we introduced the artificial neural network based fuzzy inference system (ANNBFIS) network structure. The learning methods, clustering of input space, use of different fuzzy implications in inference process and other related topics are shown. In this chapter we will show several applications of ANNBFIS to solving many practical problems, as: time series prediction, signal compression, classifications of patterns, system identifications, control and equalization of digital communication channel. All above applications will be tested on benchmark data sets. These data can be easily obtained via Internet. This approach ensures easy comparison of the proposed system to systems known from literature, and the readers can compare their own systems to the system presented in this book.
Ernest Czogała, Jacek Łęski
Backmatter
Metadaten
Titel
Fuzzy and Neuro-Fuzzy Intelligent Systems
verfasst von
Professor Ernest Czogała, Ph.D., D.Sc.
Professor Jacek Łęski, Ph.D., D.Sc.
Copyright-Jahr
2000
Verlag
Physica-Verlag HD
Electronic ISBN
978-3-7908-1853-6
Print ISBN
978-3-662-00389-3
DOI
https://doi.org/10.1007/978-3-7908-1853-6