Fuzzy Logic
Fuzzy logic is a subset of a traditional type of logic called Boolean logic. Boolean logic is quantitative, distinguishing between truth and non-truth. Fuzzy logic, however, is a qualitative type of logic that is able to distinguish more than simple true and false values. It was introduced by Lotfi Zadeh of the University of California at Berkeley in the 1960's as a way to model the uncertainty of natural language.
Zadeh pursued a model that was imposing in program development, but was germane to everyday life. Vagueness and ambiguity are a part of everyday life. For example, the question, "Is it hot outside?" generates a variety of responses, based on the responder's experiences and knowledge. The question and the responses are both subjective. Abstract, subjective thought is a complex human thought process, and fuzzy logic has thus been compared to the human thought process.
Fuzzy logic was developed on two premises: that for many tasks, precise, numerical information is not required, and that people can process diverse pieces of information to formulate a decision or conclusion. If computers could be made similarly capable of accepting nonprecise input, computerized decision making could be easier.
Fuzzy logic utilizes what has been termed fuzzy set theory—the grouping of data using criteria that is not sharply defined. For example, fuzzy logic can incorporate evaluative parameters such as large, medium, and small. In practice, fuzzy logic uses a rule-based approach that can be expressed simply as "IF X AND Y THEN Z." A quantitative approach attempts to reach a conclusion through mathematical means. The operator's experience is given more weight, rather than the level of technical expertise. In another illustrative analogy, temperature control, a fuzzy logic approach could read as follows: "IF (process is too hot) AND (process is heating rapidly) THEN (cool the process quickly)." A traditional programming approach would consider temperature using language such as: "SP = 500F," "T < 1000F," of "210C <TEMP <220C." Other aspects of fuzzy logic, besides fuzzy set theory, are fuzzy arithmetic, fuzzy mathematical programming, fuzzy topology, fuzzy graph theory, and fuzzy data analysis.
Fuzzy logic must still be responsive to numerical data in order to function. Precision, however, is not critical for most tasks. Rather, fuzzy logic incorporates mathematical concepts such as significant error and significant rate of change error. The value zero is used to represent a complete exclusion of a data element with a subset of data, and the value one represents a complete association of the data element with the subset. These associations also hold in Boolean logic. In fuzzy logic, the values in between zero and one are also considered, as they represent degrees of membership, a measure of the strength of the association between the data element and the subset.
A hierarchy of processes operates in fuzzy logic. First, the objectives and criteria of the task need to be established. Typical considerations would be the nature of what is to be controlled, how the control is achieved, and what response is required to formulate a decision. Next, the relationships between the incoming and ongoing data are established in order to set the variables used to screen the incoming data, such as error and rate of change error. Third, the control problem is broken down into a series of the "IF X AND Y THEN Z" rules, to define the desired result based on the incoming information. The number and complexity of these rules will depend on the amount of incoming data and the nature of the problem. Subsequent steps involve setting and testing the language used to query the data, testing the system and modifying and re-testing until satisfactory results are obtained.
The power of fuzzy logic began to be recognized in the late 1980's and early 1990's. Since then, it has had a significant influence on the development of computerized technology. Control problems, such as the monitoring of a manufacturing process, are suited to fuzzy logic technology. Currently, fuzzy logic is found in a myriad of control applications, including:
- automated control of dam gates for hydroelectric power plants
- aiming of cameras at sporting events
- control of automobile engines
- automobile cruise control
- quality control inspection of products during manufacture
- recognition of hand-written symbols with hand-held computers
- computer voice recognition
- automatic adjustment of vacuum cleaners to changing surface conditions and soiling
- anti-vibration control in camcorders.
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