There are many concepts that are used in fuzzy logic that sometimes become useful when studying fuzzy control. The following problems introduce some of the more popular fuzzy logic oncepts that were not treated earlier in the chapter or were treated only briefly (a)The complement(\not )of a fuzzy set with a membership function has a membership function given by A(x)=1-u(x). Sketch the complement of the fuzzy set shown in Figure 2.6 on page 30 (b)There are other ways to def ine the\triangular norm\for representing
Definition A tree is a collection of nodes. The collection can be empty: otherwise, a tree consists of (1) a distinguished node r, called the root; (2)and zero or more nonempty(sub)trees T1,., Tk, each of whose roots are connected by a directed edge from r Note:
The location of the dehydration factory must be considered very carefully, because, whereas at one time proximity to the source of raw materials was of paramount importance, availability of an adequate labour force and the provision for effluent disposal will, perhaps, constitute a more pressing requirement. A rural environment is obviously better than a location in a highly industrialised area, because the operation involves the utilisation of a considerable amount
1 Graphs and Trees The following two definitions of a tree are equivalent Definition 1: A tree is an acyclic graph of n vertices that has n-1 edges Definition 2: A tree is a connected graph such that Vu, v E V, there is a unique path connecting u to u. In general, when we want to show the equivalence of two definitions, we must show
1 Unstacking Here is another wildly fun 6.042 game that's surely about to sweep the nation! You begin with a stack of n boxes. Then you make a sequence of moves. In each move, you divide one stack of boxes into two nonempty stacks. The game ends when you have n stacks, each containing a single box You earn points for each move; in particular, if you divide one stack of height a b into two stacks with heights a and b, then you score
