# Fuzzy Logic

Fuzzy Logic is a term used to identify a new trend of quantifying partial truths. One disadvantage of most rule sets that they cannot process inconsistent data. Fuzzy logic is a superset of conventional logic that has been extended to handle the concept of partial truth, being values that lie between "completely true" and "completely untrue". Dr. Lotfi Zadeth of UC/Berkley first introduced it in the 1960s as a means of modeling the uncertainty of natural language. All this works by using expanding on Boolean logic and the concept of subsets. In classical set theory, a subset X of a set Y can be defined as a mapping from the elements of Y to the elements of the set (0,1), X: Y --* (0,1). This mapping can be represented by a set of ordered pairs, with one ordered pair present for each element of the set X, and the second element is an element of the set (0,1). The value 0 represents non-membership, and the value 1 is used to represent membership. This approach is limited to only two opposing possible outcomes. If a variable z is in X, then the statement is true if z=1 and false if z=0. Fuzzy logic takes this process a few steps further and quantifies the degree of membership instead of stopping at a positive or negative correlation. A fuzzy subset F of a set Y can be defined as a set of ordered pairs, each with the first element from S, and the second element from the interval [0,1], with exactly one ordered pair present for each element of S. This defines a mapping between elements of the set S and values in the interval [0,1]. The value zero is still used to represent complete non-membership, the value one is used to represent complete membership, and values in between are used to represent intermediate degrees of membership. The set S is referred to as the universe of discourse for the fuzzy subset F. Frequently, the mapping is described as a function, the membership function of F. The degree to which the statement x is in F is true is determined by finding the ordered pair whose first element is x.

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