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Additional ExamplesAbsoluteDifference

Fuzzy Logic Index

A

AbsoluteDifference, Aggregation Operations

absorption by empty set, Standard Operations

addition, Fuzzy Arithmetic

aggregators, user-defined, Aggregation Operations

alpha cuts, New Features

AlphaLevelSet, New Features, Fuzzy Operations

associativity, Standard Operations

averaging

    formula, Appendix

    operations, Aggregation Operations

B

bell shaped fuzzy sets, New Features

binary fuzzy relation, Fuzzy Relations

     antisymmetry, Fuzzy Relations

binary fuzzy relations,

    reflexivity, Fuzzy Relations

    symmetry, Fuzzy Relations

    transivity, Fuzzy Relations

BisectorOfArea, New Features, Fuzzy Operations

    options, Fuzzy Operations

BuildModel, Fuzzy Inferencing

C

cardinality, New Features

    fuzzy, Fuzzy Operations

    relative, Fuzzy Operations

Cardinality, Fuzzy Operations

CenterOfArea, Fuzzy Operations

    options, Fuzzy Operations

characteristic function, Sets Versus Fuzzy Sets

ChopValue, New Features

clustering, New Features

    algorithm, Fuzzy Clustering

    functions, Fuzzy Clustering

commutativity, Standard Operations

comparability, Standard Operations

complement, Appendix, Fuzzy Relations

complement, CapitalLSlashukasiewicz sets, CapitalLSlashukasiewicz Sets and Logic

Complement, Fuzzy Operations

    Ln sets, CapitalLSlashukasiewicz Sets and Logic

    CapitalLSlashukasiewicz sets, CapitalLSlashukasiewicz Sets and Logic

    options, Fuzzy Operations

complementation, Standard Operations

composition, Compositions

    fuzzy relations, Fuzzy Relations

    fuzzy relations, max-min, Fuzzy Relations

    fuzzy relations, max-star, Fuzzy Relations

Composition, Fuzzy Compositions, Fuzzy Relations

    options, Compositions

CompositionBasedInference, Fuzzy Inferencing

concentrate, Appendix

Concentrate, Fuzzy Operations, Additional Examples

contradiction, law of, Standard Operations

contrast, intensify, Appendix

contrast, intensifying, Fuzzy Operations

control surface, Fuzzy Logic Control

core, New Features

Core, New Features, Fuzzy Operations

CreateFuzzyRelation, Creating Fuzzy Relations

CreateFuzzySet, Creating Fuzzy Sets

    options, Creating Fuzzy Sets

CreateFuzzySets, Creating Fuzzy Sets

creating,

    digital fuzzy sets, Digital Fuzzy Sets and Multivalued Logic

    fuzzy numbers, Fuzzy Numbers

    fuzzy relations, Creating Fuzzy Relations

    fuzzy sets, Creating Fuzzy Sets

    Ln sets, CapitalLSlashukasiewicz Sets and Logic

    CapitalLSlashukasiewicz sets, CapitalLSlashukasiewicz Sets and Logic

Crisp, Fuzzy Set Visualization

crisp sets, Sets Versus Fuzzy Sets

D

defuzzification, New Features, Fuzzy Operations

    bisector of area, New Features, Fuzzy Operations

    center of area, Fuzzy Operations

    largest of maximum, Fuzzy Operations

    mean of maximum, Fuzzy Operations

    smallest of maximum, New Features, Fuzzy Operations

difference, Fuzzy Arithmetic

    of fuzzy sets, Standard Operations

    of fuzzy sets, properties, Standard Operations

    operations, Aggregation Operations

Difference, Aggregation Operations

digital fuzzy sets, creating, Digital Fuzzy Sets and Multivalued Logic

DigitalSet, CapitalLSlashukasiewicz Sets and Logic

dilate, Appendix

Dilate, Fuzzy Operations, Additional Examples

dilation of membership grades, Fuzzy Operations

discrete fuzzy arithmetic, Fuzzy Numbers

DiscreteFuzzyImage, Discrete Fuzzy Arithmetic, Fuzzy Numbers

DiscreteFuzzyMinus, Discrete Fuzzy Arithmetic, Fuzzy Numbers

DiscreteFuzzyMultiply, Discrete Fuzzy Arithmetic, Fuzzy Numbers

DiscreteFuzzyPlus, Discrete Fuzzy Arithmetic, Fuzzy Numbers

distributivity, Standard Operations

division, Fuzzy Arithmetic

Dombi, Aggregation Operations

double-sided Gaussian fuzzy set, New Features

DuboisPrade, Aggregation Operations

E

empty set, Sets Versus Fuzzy Sets

equality, Standard Operations

Equality, Fuzzy Operations

EquilibriumSet, Fuzzy Operations

excluded middle, law of, Standard Operations

F

FCMCluster, Fuzzy Clustering

FCM (fuzzy C-means clustering), Fuzzy Clustering

FirstProjection, Fuzzy Operations, Fuzzy Relations

first projection of fuzzy relation, Fuzzy Relations

Frank, Aggregation Operations

FromMembershipMatrix, Creating Fuzzy Relations, Fuzzy Relations

fuzzy arithmetic, Fuzzy Numbers

fuzzy arithmetic operations,

    addition, Fuzzy Arithmetic

    division, Fuzzy Arithmetic

    multiplication, Fuzzy Arithmetic

    multiplication by a constant, Fuzzy Arithmetic

    subtraction, Fuzzy Arithmetic

    using infix form, Fuzzy Numbers

FuzzyArithmeticMean, Aggregation Operations

FuzzyBell, Creating Fuzzy Sets, New Features, Creating Fuzzy Sets

fuzzy cardinality, New Features, Fuzzy Operations

FuzzyCardinality, New Features, Fuzzy Operations

fuzzy clustering, New Features

fuzzy clusters, Fuzzy Clustering

fuzzy C-means clustering, Fuzzy Clustering

FuzzyConstantTimes, Fuzzy Arithmetic

fuzzy control, Fuzzy Logic Control

    control surface, Fuzzy Logic Control

    defining control rules, Fuzzy Logic Control

    defining input membership functions, Fuzzy Logic Control

    defining output membership functions, Fuzzy Logic Control

    simulation functions, Fuzzy Logic Control

FuzzyDivide, New Features, Fuzzy Arithmetic

FuzzyGaussian, Creating Fuzzy Sets

FuzzyGeometricMean, Aggregation Operations

FuzzyGraph, Fuzzy Set Visualization

FuzzyHarmonicMean, Aggregation Operations

FuzzyImage, Fuzzy Arithmetic

fuzzy logic control, Fuzzy Logic Control

FuzzyMinus, Fuzzy Arithmetic

fuzzy modeling,

    building the model, Fuzzy Modeling

    creating linguistic control rules, Fuzzy Modeling

    evaluating the model, Fuzzy Modeling

    representing the model input, Fuzzy Modeling

    representing the model output, Fuzzy Modeling

    using the model, Fuzzy Modeling

FuzzyModify, Fuzzy Operations

FuzzyMultiply, New Features, Fuzzy Arithmetic

fuzzy numbers, Fuzzy Numbers

    addition, Fuzzy Arithmetic

    division, New Features, Fuzzy Arithmetic

    image, Fuzzy Arithmetic

    multiplication, New Features, Fuzzy Arithmetic

    multiplication by a constant, Fuzzy Arithmetic

    subtraction, Fuzzy Arithmetic

fuzzy operations, Standard Operations

    relations, Fuzzy Relations

fuzzy operator formulas, Appendix

fuzzy operators,

    complement, Appendix

    dilate, Appendix

    intensify contrast, Appendix

    normalize, Appendix

FuzzyPlot, Fuzzy Set Visualization

    options, Fuzzy Set Visualization

FuzzyPlot3D, Fuzzy Relation Visualization

    options, Fuzzy Relation Visualization

FuzzyPlus, Fuzzy Arithmetic

fuzzy relation, Fuzzy Relations

    binary, Fuzzy Relations

    complement, Fuzzy Relations

    envelope, Fuzzy Relations

    equations, New Features

    first projection, Fuzzy Relations

    normalized, Fuzzy Operations

    operations, Fuzzy Operations

    projections, Fuzzy Relations

    random, New Features

    second projection, Fuzzy Relations

FuzzyRelation, Creating Fuzzy Relations, Fuzzy Relations

    options, Creating Fuzzy Relations

fuzzy relations, Fuzzy Relations

    absolute difference, Aggregation Operations

    algebraic product, Fuzzy Relations

    basic objects, Creating Fuzzy Relations

    composition, Fuzzy Relations

    compositions, Compositions

    creating, Creating Fuzzy Relations

    difference, Aggregation Operations

    disjunctive sum, Additional Examples

    distinctions, Fuzzy Operations

    general aggregator, Aggregation Operations

    Hamming distance, New Features, Fuzzy Operations

    HammingDistance, New Features, Fuzzy Operations

    intersection, Fuzzy Relations

    operations, Fuzzy Operations

    subsethood, New Features

    symmetric difference, Aggregation Operations

    union, Fuzzy Relations

    universal space, Fuzzy Relations

    visualization, Fuzzy Relation Visualization

fuzzy set,

    cardinality, Fuzzy Operations

    core, Fuzzy Operations

    equilibrium, Fuzzy Operations

    modifying, Fuzzy Operations

    normalized, Fuzzy Operations

    operations, Fuzzy Operations

    random, New Features

    sigmoidal, New Features

    support, Fuzzy Operations

FuzzySet, Creating Fuzzy Sets

    definition, Creating Fuzzy Sets

    options, Creating Fuzzy Sets

fuzzy sets,

    absolute difference, Aggregation Operations

    basic objects, Creating Fuzzy Sets

    bell-shaped, New Features

    complementation, Standard Operations

    difference, Aggregation Operations, Standard Operations

    distinctions, Fuzzy Operations

    double-sided Gaussian, New Features

    equality, Standard Operations

    general aggregator, Aggregation Operations

    Hamming distance, New Features, Fuzzy Operations

    Hamming distance, New Features, Fuzzy Operations

    intersection, Aggregation Operations

    operations, Standard Operations

    subsethood, New Features

    symmetric difference, Aggregation Operations

    union, Aggregation Operations, Standard Operations

    visualization, Fuzzy Set Visualization

FuzzySigmoid, New Features, Creating Fuzzy Sets

FuzzySurfacePlot, Fuzzy Relation Visualization

FuzzyTrapezoid, Creating Fuzzy Relations, Creating Fuzzy Sets, Creating Fuzzy Relations

FuzzyTwoGaussian, New Features, Creating Fuzzy Sets

G

Gaussian fuzzy numbers, image, Discrete Fuzzy Arithmetic

GeneralAggregator, Aggregation Operations

GlobalProjection, Fuzzy Operations

H

Hamacher, Aggregation Operations

Hamming Distance, New Features, Fuzzy Operations

HammingDistance, New Features, Fuzzy Operations

Height, Fuzzy Operations

I

idempotence, Standard Operations

identity, Standard Operations

image of a fuzzy number, Fuzzy Arithmetic

Implication, Ln sets, CapitalLSlashukasiewicz Sets and Logic

implication, CapitalLSlashukasiewicz sets, CapitalLSlashukasiewicz Sets and Logic

Included, Fuzzy Operations

inclusion, Standard Operations

inference, Fuzzy Inferencing

    composition based, building model, Fuzzy Inferencing

    composition based, defining inputs, Fuzzy Inferencing

    composition based, defining outputs, Fuzzy Inferencing

    composition based, defining rules, Fuzzy Inferencing

    composition based, inferencing, Fuzzy Inferencing

    functions, Fuzzy Inferencing

    rule based, New Features

    rule based, defining inputs, Fuzzy Inferencing

    rule based, defining outputs, Fuzzy Inferencing

    rule based, defining rules, Fuzzy Inferencing

    rule based, inferencing, Fuzzy Inferencing

InitializeU, Fuzzy Clustering

intensify contrast, Appendix

IntensifyContrast, Fuzzy Operations, Fuzzy Operations

intersection, New Features, Aggregation Operations

    formulas, Appendix

    CapitalLSlashukasiewicz sets, CapitalLSlashukasiewicz Sets and Logic

    operations, Aggregation Operations

    properties, Standard Operations

Intersection, New Features, Aggregation Operations, Fuzzy Relations

    Ln sets, CapitalLSlashukasiewicz Sets and Logic

    CapitalLSlashukasiewicz sets, CapitalLSlashukasiewicz Sets and Logic

    options, Aggregation Operations

intersection, Standard Operations

J

K

L

LargestOfMax, Fuzzy Operations

    options, Fuzzy Operations

LevelSet, New Features, Fuzzy Operations

Ln sets,

    creating, CapitalLSlashukasiewicz Sets and Logic

    operations on, CapitalLSlashukasiewicz Sets and Logic

logic,

    CapitalLSlashukasiewicz , Digital Fuzzy Sets and Multivalued Logic

    multivalued, Digital Fuzzy Sets and Multivalued Logic

CapitalLSlashukasiewicz logic, Digital Fuzzy Sets and Multivalued Logic

CapitalLSlashukasiewicz sets,

    creating, CapitalLSlashukasiewicz Sets and Logic

    operations on, CapitalLSlashukasiewicz Sets and Logic

M

Mamdani, Fuzzy Inferencing

MAX, Discrete Fuzzy Arithmetic

MaxMin, Compositions

MaxProduct, Compositions

MaxStar, Compositions

mean,

    arithmetic, Aggregation Operations

    geometric, Aggregation Operations

    harmonic, Aggregation Operations

MeanOfMax, Fuzzy Operations

    options, Fuzzy Operations

membership,

    function, Sets Versus Fuzzy Sets

    matrix, Fuzzy Relation Visualization

MIN, Discrete Fuzzy Arithmetic

multiplication, Fuzzy Arithmetic

    by a constant, Fuzzy Arithmetic

multivalued logic, Digital Fuzzy Sets and Multivalued Logic

N

normalize, Appendix

Normalize, Fuzzy Operations

n-valued logic, CapitalLSlashukasiewicz Sets and Logic

O

operations,

    averaging, Aggregation Operations

    difference, Aggregation Operations

    intersection, Aggregation Operations

    on Ln sets, CapitalLSlashukasiewicz Sets and Logic

    on CapitalLSlashukasiewicz sets, CapitalLSlashukasiewicz Sets and Logic

    s-norm, Aggregation Operations

    t-norm, Aggregation Operations

    union, Aggregation Operations

operations on Gaussian fuzzy numbers,

    addition, Discrete Fuzzy Arithmetic

    multiplication, Discrete Fuzzy Arithmetic

    subtraction, Discrete Fuzzy Arithmetic

operations on triangular fuzzy numbers,

    addition, Discrete Fuzzy Arithmetic

    maximum, Discrete Fuzzy Arithmetic

    minimum, Discrete Fuzzy Arithmetic

    multiplication, Discrete Fuzzy Arithmetic

    subtraction, Discrete Fuzzy Arithmetic

P

PlotJoined, Fuzzy Set Visualization

PrimitiveMatrix, CapitalLSlashukasiewicz Sets and Logic

product, Fuzzy Arithmetic

product type, Aggregation Operations

projections of fuzzy relation, Fuzzy Relations

Q

R

RandomFuzzyRelation, Creating Fuzzy Relations

    options, Creating Fuzzy Relations

RandomFuzzySet, Creating Fuzzy Sets

    options, Creating Fuzzy Sets

RelativeCardinality, Fuzzy Operations

RuleBasedInference, Fuzzy Inferencing

    options, Fuzzy Inferencing

S

SecondProjection, Fuzzy Operations, Fuzzy Relations

second projection of fuzzy relation, Fuzzy Relations

set,

    complement, Standard Operations

sets,

    comparable, Standard Operations

    equal, Standard Operations

    graphic representation, Sets Versus Fuzzy Sets

    inclusion, Standard Operations

SetsToRelation, Creating Fuzzy Relations

ShowCenterProgression, Fuzzy Clustering

ShowCenters, Fuzzy Clustering

ShowDots, Fuzzy Set Visualization, Fuzzy Relation Visualization

ShowGraph, Fuzzy Operations

sigmoidal fuzzy sets, New Features

SmallestOfMax, New Features, Fuzzy Operations

    options, Fuzzy Operations

s-norm operations, Aggregation Operations

StrongAlphaLevel, Fuzzy Operations

StrongAlphaLevelSet, Fuzzy Operations

subsethood, New Features

Subsethood, New Features, Fuzzy Operations

subtraction, Fuzzy Arithmetic

Sugeno, Fuzzy Operations

sum, Fuzzy Arithmetic

    drastic, Aggregation Operations

    type, Aggregation Operations

Support, Fuzzy Operations

SymmetricDifference, Aggregation Operations

T

t-norm, Aggregation Operations

    operations, Aggregation Operations

ToDigital, CapitalLSlashukasiewicz Sets and Logic

ToMembershipMatrix, Fuzzy Relation Visualization, Fuzzy Relations

triangular fuzzy numbers, discrete arithmetic, Discrete Fuzzy Arithmetic

two-sided Gaussian fuzzy set, New Features

U

union, New Features, Aggregation Operations

    formulas, Appendix

    CapitalLSlashukasiewicz sets, CapitalLSlashukasiewicz Sets and Logic

    operations, Aggregation Operations

    properties, Standard Operations

Union, New Features, Aggregation Operations

    Ln sets, CapitalLSlashukasiewicz Sets and Logic, CapitalLSlashukasiewicz Sets and Logic

    CapitalLSlashukasiewicz sets, CapitalLSlashukasiewicz Sets and Logic

    options, Aggregation Operations

universal set, Sets Versus Fuzzy Sets

universal space, Creating Fuzzy Sets, Creating Fuzzy Relations, Sets Versus Fuzzy Sets

    continuous, Digital Fuzzy Sets and Multivalued Logic

    discrete, Digital Fuzzy Sets and Multivalued Logic

    graphical representation, Sets Versus Fuzzy Sets

UniversalSpace, Creating Fuzzy Sets, Creating Fuzzy Relations

user-defined aggregators, Aggregation Operations

V

visualization,

    fuzzy relations, Fuzzy Relation Visualization

    fuzzy sets, Fuzzy Set Visualization

W

X

Yager, Fuzzy Operations, Aggregation Operations

Z

Additional ExamplesAbsoluteDifference


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