fuzzy sets in artificial intelligence

fuzzy sets in artificial intelligence

Fuzzy Set Theory

Problems in the real world quite often turn out to be complex owing to an element of uncertainty either in the parameters which define the problem or in the situations in which the problem occurs.

Although probability theory has been an age-old and effective tool to handle uncertainty, it can be applied only to situations whose characteristics are based on random processes, that is, processes in which the occurrence of events is strictly determined by chance. However, in reality, there turn out to be problems, a large class of them whose uncertainty is characterized by a nonrandom process. Here, the uncertainty may arise due to partial information about the problem, or due to information which is not fully reliable, or due to inherent imprecision in the language with which the problem is defined, or due to receipt of information from more than one source about the problem which is conflicting.

It is in such situations that fuzzy set theory exhibits immense potential for effective solving of. the uncertainty in the problem. Fuzziness means 'vagueness'. Fuzzy set theory is an excellent mathematical tool to handle the uncertainty arising due to vagueness. Understanding human speech and recognizing handwritten characters are some common instances where fuzziness manifests.

It was Lotfi A. Zadeh who propounded the fuzzy set theory in his seminal paper (Zadeh, 1965). Since then, a lot of theoretical developments have taken place in this field. It is, however, the Japanese who seem to have fully exploited the potential of fuzzy sets by commercializing the technology.

More than 2000 patents have been acquired by the Japanese in the application of the technique and the area spans a wide spectrum, from consumer products and electronic instruments to automobile and traffic monitoring systems.

fuzzy versus crisp

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Consider the query, "Is water colorless?" The answer to this is a definite Yes/True, or No/False, as warranted by the situation. If "yes"/"true" is accorded a value of 1 and "no"/"false" is accorded a value of O, this statement results in a 0/1 type of situation. Such a logic which demands a binary (0/1) type of handling is termed crisp in the domain of fuzzy set theory. Thus, statements such as "Temperature is 32°C", "The running time of the program is 4 seconds" are examples of crisp situations. On the other hand, consider the statement, "Is Ram honest?" The answer to this query need not be a definite "yes"

or "no". Considering the degree to which one knows Ram, a variety of the artificial intelligancey