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. 1tall(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--------------------------------------Billy 3' 2" 0.00 Yoke 5' 5" 0.21Drew 5' 9" 0.38Erik 5' 10" 0.42Mark 6' 1" 0.54Kareem 7' 2" 1.00 The application of fuzzy logic allows us to go beyond the simple categories of "tall" and "not tall" and apply a real world understanding of other outside variables that are always included when considering humanistic characteristics. If someone were to ask "how tall is Shaq?", you probably wouldn't say "tall", you would probably add a descriptive variable like "really tall". Fuzzy logic is a way of measuring more discrete variables for further understanding.Fuzzy logic i...
