# Download PDF by Ned Gulley: Fuzzy Logic Toolbox For Use with MATLAB

By Ned Gulley

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Extra info for Fuzzy Logic Toolbox For Use with MATLAB

Example text

But such a distinction is clearly absurd. It may make sense to consider the set of all real numbers greater than six because numbers belong on an abstract plane, but when we want to talk about real people, it is unreasonable to call one person short and another one tall when they differ in height by the width of a hair. excellent! You must be taller than this line to be considered TALL But if the kind of distinction shown above is unworkable, then what is the right way to define the set of tall people?

2-118 2 Tutorial The Big Picture We’ll start with a little motivation for where we are headed in this chapter. The point of fuzzy logic is to map an input space to an output space, and the primary mechanism for doing this is a list of if-then statements called rules. All rules are evaluated in parallel, and the order of the rules is unimportant. The rules themselves are useful because they refer to variables and the adjectives that describe those variables. Before we can build a system that interprets rules, we have to define all the terms we plan on using and the adjectives that describe them.

Finally, the fourth requirement allows us to take the intersection of any number of sets in any order of pairwise groupings. Like fuzzy intersection, the fuzzy union operator is specified in general by a binary mapping S: µA∪B(x) = S(µA(x), µB(x)) For example, the binary operator S can represent the addition of µ A ( x ) and µ B ( x ). These fuzzy union operators, which are often referred to as T-conorm (or S-norm) operators, must satisfy the following basic requirements. A T-conorm (or S-norm) operator is a binary mapping S( .