1. Why do the controllers, when using the Sugeno form of fuzzy rules, take a specific value instead of a fuzzy set as a right-hand side of each rule?
This was done for efficiency reasons. As the right-hand side is usually a fixed fuzzy set, it is left to the user to defuzzify the set before it is passed to the controller. In most cases, it is unnecessary to even go to the fuzzy set form for the right-hand side, and instead just give a value.
2. Where did you get the names Gamma, L, Lambda, and PI from? These aren't standard.
While I tried as much as possible to use what is commonly used in the literature, the idea of using L and Gamma (Γ) to define fuzzy sets with decreasing and increasing membership functions comes from the Handbook of Mathematics and Computational Science text by Hosrt Stocker and John W. Harris. I thought it's a nice idea, and Lambda and PI (Λ and Π) are obvious generalizations. So far, there have been no requests for a PseudoTrapezoid constructor, but it is possible to write such a function.
3. I don't see your name on any fuzzy publications. Why are you doing this?
I learned about fuzzy sets in a course on soft computing while I was at the University of Guelph as an undergraduate. I saw them again as a graduate student at the University of Waterloo during my masters (in relation to iterated functions on fuzzy sets). Since then, I have kept up my interest in fuzzy sets and I have tried to write such a package ever since I joined Waterloo Maple Inc. in 1997. After many false starts, the MapleConnect program finally convinced me to finish the product. Also, it was fun, which is probably the most important.