What is Fuzzy Logic?

Rule based logic has been used to capture human expertise in classification, assessment, diagnostic and planning tasks. Probability has traditionally been used to capture decision making under uncertain conditions. For example, consider the rule:

IF symptom-A is present THEN diagnosis is illness-X

There will be situations in which we are uncertain about the presence of symptom-A. In such cases we can enter the probability of symptom-A being present which will result in a confidence factor in our diagnosis of illness-X. A number of methods have been used to propagate probabilities during rule based inference. Many of these techniques are based on the probabilistic inference techniques used in Mycin and Prospector. The weakness of such techniques is that they do not reflect the way human experts reason under uncertainty. XpertRule allows an alternative methodology to the probabilistic reasoning approach. This involves defining symptom-A and illness-X as logical attribute with values likely, unsure, unlikely. This allows the expert to dictate the relationship between the symptoms and diagnosis, instead of relying on the mathematical propagation of probabilities.

Some people confuse the above example of uncertain reasoning with fuzzy reasoning. Probabilistic reasoning is concerned with the uncertain reasoning about well defined events or concepts such as symptom-A and illness-X. On the other hand, Fuzzy Logic is concerned with the reasoning about 'Fuzzy' events or concepts. Examples of fuzzy concepts are 'temperature is high' and 'person is tall'. When is a person tall, at 170cm, 180cm or 190cm? If we define the threshold of tallness at 180cm, then the implication is that a person of 179.9cm is not tall. When humans reason with terms such as 'tall' they do not normally have a fixed threshold in mind, but a smooth fuzzy definition. Humans can reason very effectively with such fuzzy definitions, therefore, in order to capture human fuzzy reasoning we need fuzzy logic. An example of a fuzzy rule which involves a fuzzy condition and a fuzzy conclusion is:

IF salary is high THEN credit risk is low

Fuzzy reasoning involves three steps:

1. Fuzzification of the terms that appear in the conditions of rules

2. Inference from fuzzy rules

3. Defuzzification of the fuzzy terms that appear in the conclusions of rules.