The interaction between Fuzzy Set theory and Neural Network theory is multi-faceted and occurs at many different levels. The connection between these two concepts occurs both in the framework of real and artificial neural systems.
The brain is not just a collection of neurons grouped together at some part of the animal’s body, but it requires the neurons to interact among themselves and agglutinate into a higher order system. Because of this, while some of the properties of the brain are directly inherited from neurons, new emergent properties arise which are not possessed by any of these neurons themselves but which are derived from the association among them [1-4]. The theories of Neural Networks (NN) and Fuzzy Logic (FL) provide two complementary ways of modeling this dual and complex organization of the human brain. At one level, NN provides a means for modeling the lower level processes of human reasoning, that is the physiology of the brain. At the other extreme, FL provides a means of capturing the higher level human thought processes as well as emergent properties, that is it can be seen as a psychologic modeling of the mind. In this sense, neural networks are related to the hardware of the brain, while fuzzy logic is involved with the software of the brain , however, they are strongly associated to provide a full description of the human mind. In addition to providing a mechanism for representing the higher order reasoning process in the brain the language of fuzzy logic helps in the description and understanding of the basic behavior of the nerve cell. One purpose of this chapter is to explore this association.
Any neuron or cell is a partially closed system because its membrane is selective in separating chemicals which are used by the cell to synthesize its constituents and to maintain its physiology. For example, the cellular membrane is selective to sodium (Na) and potassium (K), the first being maintained predominantly outside the cell and in small quantities inside the cell, whereas the second has an opposite distribution. This ionic selection is the main mechanism involved in the electrical activity of the neuron, and it is described by the fuzzy assertion that Na is mainly an extracellular ion and K is predominantly an intracellular ion. The fuzziness of this assertion is not a lack of knowledge or information about the system because the laws governing such distribution are precisely known (e.g. ). (As a matter of fact their discovery resulted in a Nobel Prize.) The fuzziness in this case is associated with the basic structure of the cell as a partially opened system for getting its constituents from the outside world, and as a partially closed system for maintaining its identity.