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Adaptive Neuro-Fuzzy Inference System

(ANFIS) A technique for automatically tuning Sugeno-type inference systems based on training data.


The combination of the consequents of each rule in a Mamdani fuzzy inference system in preparation for defuzzification.


The initial (or “if”) part of a fuzzy rule.


The final (or “then”) part of a fuzzy rule.


The process of transforming a fuzzy output of a fuzzy inference system into a crisp output.

degree of fulfillment

See firing strength

degree of membership

The output of a membership function, this value is always limited to between 0 and 1. Also known as a membership value or membership grade.

firing strength

The degree to which the antecedent part of a fuzzy rule is satisfied. The firing strength may be the result of an AND or an OR operation, and it shapes the output function for the rule. Also known as degree of fulfillment.


The process of generating membership values for a fuzzy variable using membership functions.

fuzzy c-means clustering

A data clustering technique wherein each data point belongs to a cluster to a degree specified by a membership grade.

fuzzy inference system (FIS)

The overall name for a system that uses fuzzy reasoning to map an input space to an output space.

fuzzy operators

AND, OR, and NOT operators. These are also known as logical connectives.

fuzzy set

A set that can contain elements with only a partial degree of membership.

fuzzy singleton

A fuzzy set with a membership function that is unity at a one particular point and zero everywhere else.


The process of shaping the fuzzy set in the consequent based on the results of the antecedent in a Mamdani-type FIS.

Mamdani-type inference

A type of fuzzy inference in which the fuzzy sets from the consequent of each rule are combined through the aggregation operator and the resulting fuzzy set is defuzzified to yield the output of the system.

membership function (MF)

A function that specifies the degree to which a given input belongs to a set or is related to a concept.

singleton output function

An output function that is given by a spike at a single number rather than a continuous curve. In the Fuzzy Logic Toolbox™ software, it is only supported as part of a zero-order Sugeno model.

subtractive clustering

A technique for automatically generating fuzzy inference systems by detecting clusters in input-output training data.

Sugeno-type inference

A type of fuzzy inference in which the consequent of each rule is a linear combination of the inputs. The output is a weighted linear combination of the consequents.


A two-input function that describes a superset of fuzzy union (OR) operators, including maximum, algebraic sum, and any of several parameterized T-conorms Also known as S-norm.


A two-input function that describes a superset of fuzzy intersection (AND) operators, including minimum, algebraic product, and any of several parameterized T-norms.

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