Neural Fuzzy Systems

This Lecture Notes containes the material of the course on Neural Fuzzy Systems delivered by the author at Turku Center for Computer Science in 1995.Fuzzy sets were introduced by Zadeh (1965) as a means of representing and manipulating data that was not precise, but rather fuzzy. Fuzzy logic provides an inference morphology that enables approximate human reasoning capabilities to be applied to knowledge-based systems. The theory of fuzzy logic provides a mathematical strength to capture the uncertainties associated with human cognitive processes, such as thinking and reasoning. The conventional approaches to knowledge representation lack the means for representating the meaning of fuzzy concepts. As a consequence, the approaches based on-rst order logic and classical probablity theory do not provide an appropriate conceptual framework for dealing with the representation of commonsense knowledge, since such knowledge is by its nature both lexically imprecise and noncategorical.

The developement of fuzzy logic was motivated in large measure by the need for a conceptual

framework which can address the issue of uncertainty and lexical imprecision.

Some of the essential characteristics of fuzzy logic relate to the following.

· In fuzzy logic, exact reasoning is viewed as a limiting case of approximate reasoning.

· In fuzzy logic, everything is a matter of degree.

· In fuzzy logic, knowledge is interpreted a collection of elastic or, equivalently, fuzzy constraint on a collection of variables.

· Inference is viewed as a process of propagation of elastic constraints.

· Any logical system can be fuzzied.

There are two main characteristics of fuzzy systems that give them better performance

for specic applications.

· Fuzzy systems are suitable for uncertain or approximate reasoning, especially for the system with a mathematical model that is difficult to derive.

· Fuzzy logic allows decision making with estimated values under incomplete or uncertain information.

Artificial neural systems can be considered as simplified mathematical models of brainlike systems and they function as parallel distributed computing networks. However,in contrast to conventional computers, which are programmed to perform specific task, most neural networks must be taught, or trained. They can learn new associations, new functional dependencies and new patterns.

The study of brain-style computation has its roots over 50 years ago in the work of Mc- Culloch and Pitts (1943) and slightly later in Hebb's famous Organization of Behavior (1949). The early work in artificial intelligence was torn between those who believed that intelligent systems could best be built on computers modeled after brains, and those like Minsky and Papert who believed that intelligence was fundamentally symbol processing

Kata kunci : Neural Fuzzy Systems, logika fuzzy

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