C++ Neural Networks and Fuzzy Logic by Valluru B. Rao M&T Books, IDG Books Worldwide, Inc. ISBN: 1558515526   Pub Date: 06/01/95

Fuzziness in Neural Networks

Fuzziness can enter neural networks to define the weights from fuzzy sets. A comparison between expert systems and fuzzy systems is important to understand in the context of neural networks. Expert systems are based on crisp rules. Such crisp rules may not always be available. Expert systems have to consider an exhaustive set of possibilities. Such sets may not be known beforehand. When crisp rules are not possible, and when it is not known if the possibilities are exhaustive, the expert systems approach is not a good one.

Some neural networks, through the features of training and learning, can function in the presence of unexpected situations. Therein neural networks have an advantage over expert systems, and they can manage with far less information than expert systems need.

One form of fuzziness in neural networks is called a fuzzy cognitive map. A fuzzy cognitive map is like a dynamic state machine with fuzzy states. A traditional state machine is a machine with defined states and outputs associated with each state. Transitions from state to state take place according to input events or stimuli. A fuzzy cognitive map looks like a state machine but has fuzzy states (not just 1 or 0). You have a set of weights along each transition path, and these weights can be learned from a set of training data.

Our treatment of fuzziness in neural networks is with the discussion of the fuzzy associative memory, abbreviated as FAM, which, like the fuzzy cognitive map, was developed by Bart Kosko. The FAM and the C++ implementation are discussed in Chapter 9.

Neural-Trained Fuzzy Systems

So far we have considered how fuzzy logic plays a role in neural networks. The converse relationship, neural networks in fuzzy systems, is also an active area of research. In order to build a fuzzy system, you must have a set of membership rules for fuzzy categories. It is sometimes difficult to deduce these membership rules with a given set of complex data. Why not use a neural network to define the fuzzy rules for you? A neural network is good at discovering relationships and patterns in data and can be used to preprocess data in a fuzzy system. Further, a neural network that can learn new relationships with new input data can be used to refine fuzzy rules to create a fuzzy adaptive system. Neural trained fuzzy systems are being used in many commercial applications, especially in Japan:

•  The Laboratory for International Fuzzy Engineering Research (LIFE) in Yokohama, Japan has a backpropagation neural network that derives fuzzy rules and membership functions. The LIFE system has been successfully applied to a foreign-exchange trade support system with approximately 5000 fuzzy rules.

•  Ford Motor Company has developed trainable fuzzy systems for automobile idle-speed control.

•  National Semiconductor Corporation has a software product called NeuFuz that supports the generation of fuzzy rules with a neural network for control applications.

•  A number of Japanese consumer and industrial products use neural networks with fuzzy systems, including vacuum cleaners, rice cookers, washing machines, and photocopying machines.

•  AEG Corporation of Germany uses a neural-network-trained fuzzy control system for its water- and energy-conserving washing machine. After the machine is loaded with laundry, it measures the water level with a pressure sensor and infers the amount of laundry in the machine by the speed and volume of water. A total of 157 rules were generated by a neural network that was trained on data correlating the amount of laundry with the measurement of water level on the sensor.

Summary

In this chapter, you read about fuzzy logic, fuzzy sets, and simple operations on fuzzy sets. Fuzzy logic, unlike Boolean logic, has more than two on or off categories to describe behavior of systems. You use membership values for data in fuzzy categories, which may overlap. In this chapter, you also developed a fuzzifier program in C++ that takes crisp values and converts them to fuzzy values, based on categories and memberships that you define. For use with neural networks, fuzzy logic can serve as a post-processing or pre-processing filter. Kosko developed neural networks that use fuzziness and called them fuzzy associative memories, which will be discussed in later chapters. You also read about how neural networks can be used in fuzzy systems to define membership functions and fuzzy rules.