In contrast, defining a universe and then randomly selecting and interviewing a probability sample from a large population can be time-consuming and expensive (often disproportionately so).
To generalize the toy-network to real metabolic networks we would need to define a suitable universe of possible enzymatic reactions.
For each enrichment test, we first defined a reference "universe" of blocks from which the "target" annotation group is drawn.
An intuitionistic fuzzy set
Definition 3. A fuzzy set (FS) ( tilde{A} ) is defined
On this universe, we define a fuzzy success state S, ( S = left{ {(S_{text{i}},, mu_{text{s}} left( {S_{text{i}} } right);, i {kern 1pt} = {kern 1pt} 1,2,3, ldots,n} right}, ) and a fuzzy failure state F, F = left{ {(S{text{i}},, mu_{text{F}} left( {S_{text{i}} } right);, i = 1,2,3, ldots,n} right}, where µ s (S i) and µ F (S i) are trapezoidal fuzzy numbers, respectively.
The final set of attributes and levels defines a universe of 4096 profiles (2*2*2*4*2*4*4*4).
Once the universe has been defined, a sample of the universe must be chosen.
In a first step we define the universe of metabolic reactions [ 14, 15] as a large set of possible metabolic reactions that can be used to convert all available nutrients into biomass.
A fuzzy set A defined on the universe X is characterized by a membership function such that μ A ( x ) : x → [ 0, 1 ].
