Artificial intelligence and Expert system

Soft Computing MethodsJ.A. Johnson

Dept. of Math and Computer Science Seminar SeriesFebruary 8, 2013

OutlineFuzzy Sets

Neural Nets Rough Sets

Bayesian Nets

Genetic AlgorithmsFuzzy sets

Fuzzy set theory is a means of specifying how well an object satisfies a vague description.

A fuzzy set can be defined as a set with fuzzy boundaries

Fuzzy sets were first introduced by Zadeh (1965).

First, the membership function must be determined.How do we represent a fuzzy set in a computer?

ExampleConsider the proposition "Nate is tall."

Is the proposition true if Nate is 5' 10"?

The linguistic term "tall" does not refer to a sharp demarcation of objects into two classesthere are degrees of tallness. Fuzzy set theory treats Tall as a fuzzy predicate and says that the truth value of Tall(Nate) is a number between 0 and 1, rather than being either true or false.

Let A denote the fuzzy set of all tall employees and x be a member of the universe X of all employees. What would the function A(x) look like

A(x) = 1 if x is definitely tall

A(x) = 0 if x is definitely not tall

0