Fuzzy System Analysis

From the Paper:

"Traditional sorts of mathematical analysis generally yield hard yes or no answers. A number is, say, greater than 7 or it is not. There is another type of commonly asked question, however, which cannot readily be answered in this way. Suppose, for example, we wish to ask whether a given number is "a lot" less than 7, or "a lot" more, or is "rather close" to 7" Such questions cannot be properly answered by a simple yes or no. Suppose that we say that 6 and 8 are close to 7. Does that mean, however, that 5.9 and 8.1 are no longer "close" to 7? Intuitively, we may sense that this is not what we intend, but the conventional mathematics of set theory, and computer programs applying such mathematics, compel us to set such artificial boundaries.

Yet in a great many practical situations, however, we are..."

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