ABSTRACT
In Chapter 1, we discussed modeling fuzzy concepts such as uncertainty with fuzzy sets. Applications demand combining these fuzzy sets in various ways. This means that we must understand the set F(U) of all fuzzy subsets of a set U as a mathematical object. The basic mathematical structure of F(U) comes from the fact that the unit interval [0, 1] is ordered. This ordering on [0, 1] induces a partial order on F(U), which in turn, gives F(U) the algebraic structure of a lattice. So we need some background material about partially ordered sets, lattices, and related mathematical notions. These notions are fundamental, and are absolutely essential in understanding the mathematics of fuzzy sets.
