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Membership functions

A membership function is a function that allows to calculate the membership degree of a random element of the universal set to a fuzzy set. Consequently, the domain of a membership function should be within the range [0, 1].

In most cases, the membership function is continuous and monotonic.

Classes of membership functions

Description

CConstantMembershipFunction

Class for implementing a membership function as a straight line in parallel with the coordinate axis

CCompositeMembershipFunction

Class for implementing a composition of membership functions

CDifferencTwoSigmoidalMembershipFunction

Class for implementing the membership function in the form of a difference between two sigmoid functions with the А1, А2, С1 and С2 parameters

CGeneralizedBellShapedMembershipFunction

Class for implementing a generalized bell-shaped membership function with А, B and С parameters

CNormalCombinationMembershipFunction

Class for implementing a two-sided Gaussian membership function with the B1, B2, Sigma1 and Sigma2 parameters

CNormalMembershipFunction

Class for implementing a symmetrical Gaussian membership function with the B and Sigma parameters

CP_ShapedMembershipFunction

Class for implementing a pi-shaped membership function with the А, B, С and D parameters

CProductTwoSigmoidalMembershipFunction

Class for implementing the membership function in the form of a product of two sigmoid functions with the А1, А2, С1 and С2 parameters

CS_ShapedMembershipFunction

Class for implementing an S-like membership function with the А and B parameters

CTrapezoidMembershipFunction

Class for implementing a trapezoidal membership function with the X1, X2, X3 and X4 parameters

CTriangularMembershipFunction

Class for implementing a triangle membership function with the X1, X2 and X3 parameters

CSigmoidalMembershipFunction

Class for implementing a sigmoid membership function with the A and C parameters

CZ_ShapedMembershipFunction

Class for implementing a z-like membership function with the А and B parameters.

IMembershipFunction

Basic class for all membership function classes.


Updated: 2017.03.07