Fuzzy Logic1. General
Fuzzy logic is an extension of conventional (Boolean) logic working with the two values {0,1} to a logic extending over the closed interval [0,1]. Founder of fuzzy logic is
Lotfi Zadeh. Let R = { x | x Ï x }. Then R Î R iff R Ï R. In words: Let R be the set of all sets that are not members of themselves. Then R is a member of itself if and only if R is not a member of itself. This ofcourse is a paradox.The solution that fuzzy logic offers is that the truth value of this statement is 0.5. In fuzzy logic paradoxes of selfreference are half-truths.
2. ExplanationA paradox is of the type: A = not-A.In other words: the truthvalue of A = the truthvalue of not-A. In short: t(A) = t(not-A). In binary logic you only have the choice between 0 and 1. So if t(A) = 1, then t(not-A) = 0
But: t(not-A) can also be written as 1 - t(A) This example has been taken from Bart Kosko's book Fuzzy Thinking. More information about fuzzy sets and fuzzy logic. |
Next: Fuzzy Sets
Home: Homepage
Last edited: