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Defuzzification methods

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Type-1 defuzzifiers

# FuzzyLogic.BisectorDefuzzifier — Type

struct BisectorDefuzzifier <: FuzzyLogic.AbstractDefuzzifier

Bisector defuzzifier. Given the aggregated output function and the output variable domain ] the defuzzified output is the value ] that divides the area under into two equal parts. That is

Parameters

  • N::Int64: number of subintervals for integration, default 100.

Algorithm

The domain is partitioned into N equal subintervals. For each subinterval endpoint, the left and right area are approximated using the trapezoidal rule. The end point leading to the best approximation is the final result.

# FuzzyLogic.CentroidDefuzzifier — Type

struct CentroidDefuzzifier <: FuzzyLogic.AbstractDefuzzifier

Centroid defuzzifier. Given the aggregated output function and the output variable domain ] the defuzzified output is the centroid computed as

Parameters

  • N::Int64: number of subintervals for integration, default 100.

Algorithm

The integrals are computed numerically using the trapezoidal rule.

# FuzzyLogic.LeftMaximumDefuzzifier — Type

struct LeftMaximumDefuzzifier <: FuzzyLogic.AbstractDefuzzifier

Left maximum defuzzifier. Returns the smallest value in the domain for which the membership function reaches its maximum.

Parameters

  • N::Int64: number of subintervals, default 100.

  • tol::Float64: absolute tolerance to determine if a value is maximum, default eps(Float64).

# FuzzyLogic.MeanOfMaximaDefuzzifier — Type

struct MeanOfMaximaDefuzzifier <: FuzzyLogic.AbstractDefuzzifier

Mean of maxima defuzzifier. Returns the mean of the values in the domain for which the membership function reaches its maximum.

Parameters

  • N::Int64: number of subintervals, default 100.

  • tol::Float64: absolute tolerance to determine if a value is maximum, default eps(Float64).

# FuzzyLogic.RightMaximumDefuzzifier — Type

struct RightMaximumDefuzzifier <: FuzzyLogic.AbstractDefuzzifier

Right maximum defuzzifier. Returns the largest value in the domain for which the membership function reaches its maximum.

Parameters

  • N::Int64: number of subintervals, default 100.

  • tol::Float64: absolute tolerance to determine if a value is maximum, default eps(Float64).

Type-2 defuzzifiers

# FuzzyLogic.EIASCDefuzzifier — Type

struct EIASCDefuzzifier <: FuzzyLogic.Type2Defuzzifier

Defuzzifier for type-2 inference systems using Iterative Algorithm with Stopping Condition (IASC).

PARAMETERS

  • N::Int64: number of subintervals for integration, default 100.

Extended help

The algorithm was introduced in

  • Wu, D. and M. Nie, "Comparison and practical implementations of type-reduction algorithms for type-2 fuzzy sets and systems," Proceedings of FUZZ-IEEE, pp. 2131-2138 (2011)

# FuzzyLogic.EKMDefuzzifier — Type

struct EKMDefuzzifier <: FuzzyLogic.Type2Defuzzifier

Enhanced Karnik-Mendel type-reduction/defuzzification algorithm for Type-2 fuzzy systems.

Parameters

  • N::Int64: number of subintervals for integration, default 100.

  • maxiter::Int64: maximum number of iterations, default 100.

Extended help

The algorithm was introduced in

  • Wu, D. and J.M. Mendel, "Enhanced Karnik-Mendel algorithms," IEEE Transactions on Fuzzy Systems, vol. 17, pp. 923-934. (2009)

# FuzzyLogic.IASCDefuzzifier — Type

struct IASCDefuzzifier <: FuzzyLogic.Type2Defuzzifier

Defuzzifier for type-2 inference systems using Iterative Algorithm with Stopping Condition (IASC).

PARAMETERS

  • N::Int64: number of subintervals for integration, default 100.

Extended help

The algorithm was introduced in

  • Duran, K., H. Bernal, and M. Melgarejo, "Improved iterative algorithm for computing the generalized centroid of an interval type-2 fuzzy set," Annual Meeting of the North American Fuzzy Information Processing Society, pp. 190-194. (2008)

# FuzzyLogic.KarnikMendelDefuzzifier — Type

struct KarnikMendelDefuzzifier <: FuzzyLogic.Type2Defuzzifier

Karnik-Mendel type-reduction/defuzzification algorithm for Type-2 fuzzy systems.

Parameters

  • N::Int64: number of subintervals for integration, default 100.

  • maxiter::Int64: maximum number of iterations, default 100.

  • atol::Float64: absolute tolerance for stopping iterations

Extended help

The algorithm was introduced in

  • Karnik, Nilesh N., and Jerry M. Mendel. ‘Centroid of a Type-2 Fuzzy Set’. Information Sciences 132, no. 1—​4 (February 2001): 195—​220