Fuzzy Logic Essay

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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…show more content…
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. The degree of truth of the statement is the second element of the ordered pair. To understand this graphically, lets use a Zadeh example that measures tallness. In this case the set S (the universe of discourse) is the set of people. We define a fuzzy subset TALL, which will answer the question "to what degree is person x tall?" Zadeh describes TALL as a linguistic variable, which represents our cognitive category of "tallness". To each person in the universe of discourse, we have to assign a degree of membership in the fuzzy subset TALL. The easiest way to do this is with a membership function based on the person's height. The following figure is how to define this using a graph. Fig. 1 tall(x) = { 0, if height(x) * 5 ft., (height(x)-5ft.)/2ft., if 5 ft. *= height (x) *= 7 ft., 1, if height(x) * 7 ft. } A graph of this looks like: 1.0 + +------------------- | / | / 0.5 + / | / | / 0.0 +-------------+-----+------------------- | | 5.0 7.0 height, ft. -* Person Height degree of tallness
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