Logical connectives

Conjuction methods

DrasticAnd

FuzzyLogic.DrasticAndType
struct DrasticAnd <: FuzzyLogic.AbstractAnd

Drastic T-norm defining conjuction as $A ∧ B = \min(A, B)$ is $A = 1$ or $B = 1$ and $A ∧ B = 0$ otherwise.

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Example block output

EinsteinAnd

FuzzyLogic.EinsteinAndType
struct EinsteinAnd <: FuzzyLogic.AbstractAnd

Einstein T-norm defining conjuction as $A ∧ B = \frac{AB}{2 - A - B + AB}$.

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Example block output

HamacherAnd

FuzzyLogic.HamacherAndType
struct HamacherAnd <: FuzzyLogic.AbstractAnd

Hamacher T-norm defining conjuction as $A ∧ B = \frac{AB}{A + B - AB}$ if $A \neq 0 \neq B$ and $A ∧ B = 0$ otherwise.

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Example block output

LukasiewiczAnd

FuzzyLogic.LukasiewiczAndType
struct LukasiewiczAnd <: FuzzyLogic.AbstractAnd

Lukasiewicz T-norm defining conjuction as $A ∧ B = \max(0, A + B - 1)$.

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Example block output

MinAnd

FuzzyLogic.MinAndType
struct MinAnd <: FuzzyLogic.AbstractAnd

Minimum T-norm defining conjuction as $A ∧ B = \min(A, B)$.

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Example block output

NilpotentAnd

FuzzyLogic.NilpotentAndType
struct NilpotentAnd <: FuzzyLogic.AbstractAnd

Nilpotent T-norm defining conjuction as $A ∧ B = \min(A, B)$ when $A + B > 1$ and $A ∧ B = 0$ otherwise.

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Example block output

ProdAnd

FuzzyLogic.ProdAndType
struct ProdAnd <: FuzzyLogic.AbstractAnd

Product T-norm defining conjuction as $A ∧ B = AB$.

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Example block output

Disjunction methods

BoundedSumOr

FuzzyLogic.BoundedSumOrType
struct BoundedSumOr <: FuzzyLogic.AbstractOr

Bounded sum S-norm defining disjunction as $A ∨ B = \min(1, A + B)$.

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Example block output

DrasticOr

FuzzyLogic.DrasticOrType
struct DrasticOr <: FuzzyLogic.AbstractOr

Drastic S-norm defining disjunction as $A ∨ B = \min(1, A + B)$.

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Example block output

EinsteinOr

FuzzyLogic.EinsteinOrType
struct EinsteinOr <: FuzzyLogic.AbstractOr

Einstein S-norm defining disjunction as $A ∨ B = \frac{A + B}{1 + AB}$.

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Example block output

HamacherOr

FuzzyLogic.HamacherOrType
struct HamacherOr <: FuzzyLogic.AbstractOr

Hamacher S-norm defining conjuction as $A ∨ B = \frac{A + B - AB}{1 - AB}$ if $A \neq 1 \neq B$ and $A ∨ B = 1$ otherwise.

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Example block output

MaxOr

FuzzyLogic.MaxOrType
struct MaxOr <: FuzzyLogic.AbstractOr

Maximum S-norm defining disjunction as $A ∨ B = \max(A, B)$.

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Example block output

NilpotentOr

FuzzyLogic.NilpotentOrType
struct NilpotentOr <: FuzzyLogic.AbstractOr

Nilpotent S-norm defining disjunction as $A ∨ B = \max(A, B)$ when $A + B < 1$ and $A ∧ B = 1$ otherwise.

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Example block output

ProbSumOr

FuzzyLogic.ProbSumOrType
struct ProbSumOr <: FuzzyLogic.AbstractOr

Probabilistic sum S-norm defining disjunction as $A ∨ B = A + B - AB$.

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Example block output

Implication methods

MinImplication

Example block output

ProdImplication

Example block output