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.

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.