Fuzzy Inference System Modeling

Build fuzzy inference systems and fuzzy trees

Fuzzy inference is the process of formulating input/output mappings using fuzzy logic. Fuzzy Logic Toolbox™ software provides tools for creating:

For more information on fuzzy logic, see What Is Fuzzy Logic? For more information on fuzzy inference, see Fuzzy Inference Process.

Apps

Design, test, and tune fuzzy inference systems

`mamfis`	Mamdani fuzzy inference system
`sugfis`	Sugeno fuzzy inference system
`genfis`	Generate fuzzy inference system object from data
`genfisOptions`	Option set for `genfis` function

`mamfistype2`	Interval type-2 Mamdani fuzzy inference system
`sugfistype2`	Interval type-2 Sugeno fuzzy inference system

fistree Network of connected fuzzy inference systems

`convertToSugeno`	Convert Mamdani fuzzy inference system into Sugeno fuzzy inference system
`convertToType1`	Convert type-2 fuzzy inference system into type-1 fuzzy inference system
`convertToType2`	Convert type-1 fuzzy inference system into type-2 fuzzy inference system
`convertToStruct`	Convert fuzzy inference system object into a structure
`convertfis`	Convert previous versions of fuzzy inference data in current format

`addInput`	Add input variable to fuzzy inference system
`addOutput`	Add output variable to fuzzy inference system
`removeInput`	Remove input variable from fuzzy inference system
`removeOutput`	Remove output variable from fuzzy inference system
`fisvar`	Fuzzy variable

`addMF`	Add membership function to fuzzy variable
`removeMF`	Remove membership function from fuzzy variable
`fismf`	Fuzzy membership function
`fismftype2`	Interval type-2 fuzzy membership function

`addRule`	Add rule to fuzzy inference system
`showrule`	Display fuzzy inference system rules
`fisrule`	Fuzzy rule
`update`	Update fuzzy rule using fuzzy inference system

`evalfis`	Evaluate fuzzy inference system
`evalfisOptions`	Option set for `evalfis` function
`plotfis`	Display fuzzy inference system
`plotmf`	Plot membership functions for input or output variable
`comparefis`	Plot simulated output of fuzzy systems for comparison (Since R2024b)
`plotrule`	Visualize rule inference process for fuzzy inference system (Since R2024b)
`plotfiserr`	Plot simulation error for fuzzy system compared to reference outputs (Since R2024b)
`gensurf`	Generate fuzzy inference system output surface
`gensurfOptions`	Option set for `gensurf` function

`readfis`	Load fuzzy inference system from file
`writeFIS`	Save fuzzy inference system to file

`evalmf`	Evaluate fuzzy membership function
`gaussmf`	Gaussian membership function
`gbellmf`	Generalized bell-shaped membership function
`trimf`	Triangular membership function
`dsigmf`	Difference between two sigmoidal membership functions
`gauss2mf`	Gaussian combination membership function
`linsmf`	Linear s-shaped saturation membership function (Since R2022a)
`linzmf`	Linear z-shaped saturation membership function (Since R2022a)
`pimf`	Pi-shaped membership function
`psigmf`	Product of two sigmoidal membership functions
`sigmf`	Sigmoidal membership function
`smf`	S-shaped membership function
`trapmf`	Trapezoidal membership function
`zmf`	Z-shaped membership function
`defuzz`	Defuzzify membership function
`probor`	Probabilistic OR
`fuzarith`	Perform fuzzy arithmetic

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 of fuzzy if-then rules that perform logical operations on fuzzy sets.
Fuzzy Inference Process
Fuzzy inference maps an input space to an output space using a series of fuzzy if-then rules.

Mamdani and Sugeno Fuzzy Inference Systems
You can implement either Mamdani or Sugeno fuzzy inference systems using Fuzzy Logic Toolbox software.
Type-2 Fuzzy Inference Systems
You can create and evaluate interval type-2 fuzzy inference systems with additional membership function uncertainty.
FIS Trees
You can implement a complex fuzzy system as a collection of smaller interconnected fuzzy inference systems.

Build Fuzzy Systems Using Fuzzy Logic Designer

Interactively construct a fuzzy inference system using the Fuzzy Logic Designer app. (Since R2022b)
Build FIS Tree Using Fuzzy Logic Designer
Interactively construct a tree of interconnected fuzzy inference systems using the Fuzzy Logic Designer app. (Since R2023b)
Build Fuzzy Systems at the Command Line
Construct a 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.
Generate MATLAB Code for Building Fuzzy Systems
Once you interactively build a fuzzy system using Fuzzy Logic Designer, you can generate MATLAB code to programmatically build that system. (Since R2024a)
Generate MATLAB Code for Simulating Fuzzy Systems
Once you interactively build a fuzzy system using Fuzzy Logic Designer, you can generate MATLAB code to programmatically simulate that system. (Since R2024b)

You can use fuzzy logic for image processing tasks, such as edge detection.

Create a type-2 fuzzy logic PID controller and compare its performance with a type-1 fuzzy PID controller and a conventional PID controller.

Model medical treatment events using fuzzy state-transition matrices and compute expected patient outcomes.