Tuesday, April 24, 2007

Self-Generated Fuzzy Rules [Fuzzification Techniques in Fuzzy Logic].




Fuzzy Logic is the use of Fuzzy Sets to give what its proponents believe is a truer representation of most real world situations. In the real world, things are often not strictly black or white but shades of grey. Unlike computers, humans think in shades of gray also not just Yes/No, Black/White or One/Zero but everything in-between. For example, what does it mean to say the temperature is cool or hot? The areas falling into cool and hot, overlap. Fuzzy Logic applications is widely used in modern consumer appliances with the Japanese engineers as early-adopters and pioneers of Fuzzy Logic controllers for airconditioners, washing machines, rice cookers, cameras, elevators etc. It is only in the last decade that Europe and America have caught up with Fuzzy controllers for automotive, aircraft and machinery components such as for engine performance, brakes and driving control.
The first step in the creation of a Fuzzy controller is to draw up the Fuzzy sets. {see middle picture}. This designates the area [patch ] of fuzziness, where each Fuzzy Rule is applied. Thus a Rule is generated with reference to this area. This is called 'Fuzzification'. The shape used for the Fuzzy operator determines the area that will be affected by each rule. [see the shapes of typical fuzzy operators in top picture]. In an airconditioner, Fuzzy sets may be labeled Cool or Hot. In washing machines Sets for Heavy Load, Clean, Dirty, Rinse, Wash etc etc may be used. Fuzzification sets have numerical values, and a sensor that senses the properties of the set concerned will then translate the raw sensor values to data point position on the Fuzzy set.
The weakness of a fuzzy system is its rules. Almost all the fuzzy consumer products now on the market rely on rules supplied by an expert. Engineers then engage in a lengthy process of tuning those rules and the fuzzy sets. To automate this process, some engineers are building adaptive fuzzy systems that use neural networks or other statistical tools to refine or even able to generate the initial rules.
Supervised networks do have drawbacks. Tuning such systems can take hours or days of computer time because networks may converge on an inappropriate solution or rule or may fail to converge at all. Researchers have proposed hundreds of schemes to alleviate this problem, but none has removed it. Even after a lengthy tuning session, the final rules may not be much better than the first set. Rather than relying on an expert to supply a training set of data and correct a network in the process of learning, unsupervised neural networks learn simply by observing an expert's decisions. In this way, an adaptive fuzzy system can learn to spot rule patterns in the incoming data. Broad rule patches form quickly, based on a few inputs. Those patches are refined over time based on data, the mapping of input to output and learning and adaptation by the neural-network.
Unsupervised neural networks cluster data into groups, the members of which resemble one another. Unsupervised learning is thus much faster than supervised learning. With numerical inputs and outputs supplied by an expert or a physical process or even an algorithm, an unsupervised neural network can find the first set of rules for a fuzzy system. The quality of the rules depends on the quality of the data and therefore on the skills of the expert who generates the data. Because unsupervised networks are best used to create rules and supervised networks are better at refining them, hybrid adaptive fuzzy systems include both.
So far the use of Fuzzy Logic is mainly for engineering and closed physical systems such as the consumer appliances. It would be very challenging but of great benefit if Fuzzy Logic could be used for classification, forecasting and general pattern recognition in economics and financial markets. The basis of this would be: an initial unsupervised clustering algorithm to generate the fuzzy sets. [2] a module that then continuously refines the fuzzy rules based on the learning from data that is generated by the user. [3] the System then becomes adaptive and is always relevant.

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