## Documentation |

You can implement two types of fuzzy inference systems in the toolbox:

Mamdani

Sugeno

These two types of inference systems vary somewhat in the way outputs are determined.

Mamdani's fuzzy inference method is the most commonly seen fuzzy methodology. Mamdani's method was among the first control systems built using fuzzy set theory. It was proposed in 1975 by Ebrahim Mamdani [4] as an attempt to control a steam engine and boiler combination by synthesizing a set of linguistic control rules obtained from experienced human operators. Mamdani's effort was based on Lotfi Zadeh's 1973 paper on fuzzy algorithms for complex systems and decision processes [13]. Although the inference process described in the next few sections differs somewhat from the methods described in the original paper, the basic idea is much the same.

*Mamdani-type inference*, as defined for
the toolbox, expects the output membership functions to be fuzzy sets.
After the aggregation
process, there is a fuzzy set for each output variable that needs
defuzzification. It is possible, and in many cases much more efficient,
to use a single spike as the output membership function rather than
a distributed fuzzy set. This type of output is sometimes known as
a *singleton* output
membership function, and it can be thought of as a pre-defuzzified
fuzzy set. It enhances the efficiency of the defuzzification process
because it greatly simplifies the computation required by the more
general Mamdani method, which finds the centroid of a two-dimensional
function. Rather than integrating across the two-dimensional function
to find the centroid, you use the weighted average of a few data points.
Sugeno-type systems support this type of model. In general, Sugeno-type systems
can be used to model any inference system in which the output membership
functions are either linear or constant.

See the Bibliography for references to descriptions of these two types of fuzzy inference systems, [5], [4], [9].

Fuzzy inference systems have been successfully applied in fields such as automatic control, data classification, decision analysis, expert systems, and computer vision. Because of its multidisciplinary nature, fuzzy inference systems are associated with a number of names, such as fuzzy-rule-based systems, fuzzy expert systems, fuzzy modeling, fuzzy associative memory, fuzzy logic controllers, and simply (and ambiguously) fuzzy systems.

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