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Fuzzy Inference System Modeling

Build Mamdani and Sugeno fuzzy inference systems

Fuzzy inference is the process of formulating input/output mappings using fuzzy logic. Fuzzy Logic Toolbox™ software provides command-line functions and an app for creating Mamdani and Sugeno fuzzy systems. For more information on fuzzy logic, see What Is Fuzzy Logic?. For more information on fuzzy inference, see Fuzzy Inference Process.


Fuzzy Logic DesignerDesign and test fuzzy inference systems


newfisCreate new fuzzy inference system
genfisGenerate fuzzy inference system structure from data
genfisOptionsOption set for genfis command
addvarAdd variable to fuzzy inference system
rmvarRemove variables from fuzzy inference system
mam2sugTransform Mamdani Fuzzy Inference System into Sugeno Fuzzy Inference System
getfisGet fuzzy system properties
setfisSet fuzzy system properties
mfeditOpen Membership Function Editor
addmfAdd membership function to fuzzy inference system
rmmfRemove membership function from fuzzy inference system
ruleeditOpen Rule Editor
ruleviewOpen Rule Viewer
addruleAdd rule to fuzzy inference system
showruleDisplay fuzzy inference system rules
parsruleParse fuzzy rules
evalfisPerform fuzzy inference calculations
plotfisPlot Fuzzy Inference System
surfviewOpen Surface Viewer
gensurfGenerate fuzzy inference system output surface
gensurfOptionsOption set for gensurf command
showfisDisplay annotated Fuzzy Inference System
readfisLoad Fuzzy Inference System from file
writefisSave fuzzy inference system to file
gaussmfGaussian curve membership function
gbellmfGeneralized bell-shaped membership function
trimfTriangular-shaped membership function
dsigmfDifference between two sigmoidal membership functions
gauss2mfGaussian combination membership function
pimfΠ-shaped membership function
psigmfProduct of two sigmoidal membership functions
sigmfSigmoidal membership function
smfS-shaped membership function
trapmfTrapezoidal-shaped membership function
zmfZ-shaped membership function
plotmfPlot all membership functions for given variable
evalmfGeneric membership function evaluation
mf2mfTranslate parameters between membership functions
defuzzDefuzzify membership function
proborProbabilistic OR
fuzarithPerform fuzzy arithmetic


Fuzzy Logic Basics

What Is Fuzzy Logic?

Fuzzy logic uses linguistic variables, defined as fuzzy sets, to approximate human reasoning.

Foundations of Fuzzy Logic

A fuzzy logic system is a collection fuzzy if-then rules that perform logical operations on fuzzy sets.

Fuzzy Inference

Fuzzy Inference Process

Fuzzy inference maps an input space to an output space using a series of fuzzy if-then rules.

What Is Mamdani-Type Fuzzy Inference?

In Mamdani systems, the output of each if-then rule is a fuzzy set. To determine a crisp output value, these fuzzy sets are aggregated and defuzzified.

What Is Sugeno-Type Fuzzy Inference?

In Sugeno systems, the output of each if-then rule is either constant or a linear function of the input variables. The final output value is the weighted average of all rule outputs.

Comparison of Sugeno and Mamdani Systems

Both Mamdani and Sugeno systems have several advantages depending on your specific application.

Build Fuzzy Inference Systems

Build Mamdani Systems Using Fuzzy Logic Designer

Interactively construct a Mamdani fuzzy inference system using the Fuzzy Logic Designer app.

Build Mamdani Systems at the Command Line

Construct a Mamdani fuzzy inference system at the MATLAB® command line.

Build Fuzzy Systems Using Custom Functions

You can replace the built-in membership functions and fuzzy inference functions with your own custom functions.

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