Environmental Engineering Reference
In-Depth Information
5.3.1 Fuzzy Logic
Fuzzy Logic was developed by Lotfi Zadeh for use in control systems that are
not easily converted into mathematical models. He wrote a paper in the 1960s
called “Fuzzy Logic,” which described this new technology. Acceptance in the
United States was initially slow and may have been hindered by the word
“fuzzy” in its name. Despite its slow start, it is now being used in a wide
range of control systems.
Fuzzy Logic works well in domains that are complex and where knowledge
is contained in engineering experience and rules of thumb, rather than math-
ematical models. Fuzzy Logic allows the creation of set-membership functions
that support reasoning about a particular value's degree of membership in
that set. Figure 5.7 shows three fuzzy sets that define Cold, Warm, and Hot.
A specific temperature, say 100 , has different membership in each of these
sets. Combiners are used to connect fuzzy expressions together to generate
compound expressions. Rules can be constructed that reason on these mem-
berships and perform some action. For example, “if EngineTemp is Hot and
the DeltaV is NecessaryDeltaV then Stop Burn” would reason on the current
engine temperature in relationship to the necessary delta V and determine
whether it should terminate burn. Other rules could deal with a hot engine
and an insucient delta V, or could stop the engine when the delta V is
optimal.
Despite their name, Fuzzy Logic systems are time invariant, determinis-
tic, and nonlinear. They are computationally ecient. Once rules have been
developed, they can be “compiled” to run in limited computational environ-
ments. Unfortunately, how and when to use fuzzy combination rules are not
well understood or systematic.
Engineers might be drawn to this technique because it is easy to get an
initial prototype running and incrementally add features. If the domain is
primarily engineering rules of thumb, the use of this technique is defensi-
ble. If, however, good mathematical or other models of the domain can be
100%
75%
50%
25%
100
°
200
°
300
°
400
°
Cold
Warm
Hot
Fig. 5.7. Fuzzy sets
 
 
Search WWH ::




Custom Search