I must admit, I was a rather bit confused by one of the diagrams that I came across in my readings.
This diagram was intended to demonstrate the Complement of a Fuzzy set (Figure 4.7, pg. 101, Negnevitsky)
As Negnevitsky presents it, a triangular set A, in a domain of 0 to X and the standard memberships of 0 to 1, the complement (as he shows) is the inverted set A on the domain. This is incorrect. The complement requires that when x has a membership of 1 in A then its membership in NOT A is 0, and when its membership in A is 0 then its membership in A is 1. The complement, then, is everything NOT in the triangle that Negnevitsky has labeled “Not A“
So for anyone looking at that diagram going “huh?” I’m not surprised! In fact, his diagram of the complement completely equates to the diagram of A. Though the triangle is upside down, the percentage of membership would still be the same, though it seems like it should be quite different graphically.
Negnevitsky, M., (2005) Artificial Intelligence – A Guide to Intelligent Systems (Second Edition), Pearson Education Limited, Edinburgh Gate, Harlow