.Open Theories of Fuzzy Sets An object is either in or out of a standard set. Membership is a sharp concept with only two values: true and false. We can model standard sets via a membership function maping objects into either 1(true) or 0 (false). In Lofteh Zadeh's Fuzzy Set theory membership can be any value from 0 to 1. A person can be only partly a member of the fuzzy set of tall people. There has been a lot written about what can be done by applying fuzzy logic. .Hole At first glance such thinking would lead to a probability theory. But Zadeh created a new way of thinking by interpreting union and intersection in a different way. FUZZY::=following, .Net Set::Sets= given. fuzzy_set(Set) ::= Set>->[0..1], .See http://www.csci.csusb.edu/dick/maths/math_21_Order.html#Interval Notation For A:fuzzy_set(Set), not A ::= x+>(1-A(x)). For A,B:fuzzy_set(Set), A and B ::= x+>\$min(A(x), B(y)). For A,B:fuzzy_set(Set), A or B ::= x+>\$max(A(x), B(y)). ()|-\$LATTICE(fuzzy_set(Set), min, max) and Net{ complete}. Here For a,b:Real, min(x) ::= if(xy , x , y). The properties of min and max in general are formulated in .See http://www.csci.csusb.edu/dick/maths/math_21_Order.html#MINMAX and more on lattices is in LATTICE::=http://www.csci.csusb.edu/dick/maths/math_41_Two_Operators.html#Lattice. .Close.Net FUZZY .Hole .Close Theories of Fuzzy Sets . Also See .See http://www/dick/maths/math_81_Probabillity.html .See http://www/dick/maths/math_82_MultiSets_and_Bags.html .See http://www/dick/maths/math_83_Fuzzy_Sets.html .See http://www/dick/maths/math_84_Spectra.html