Fuzzy Logic Index
A
AbsoluteDifference, Aggregation Operations
absorption by empty set, Standard Operations
addition, Fuzzy Arithmetic
aggregators, userdefined, 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, ukasiewicz sets, ukasiewicz Sets and Logic
Complement, Fuzzy Operations
Ln sets, ukasiewicz Sets and Logic
ukasiewicz sets, ukasiewicz Sets and Logic
options, Fuzzy Operations
complementation, Standard Operations
composition, Compositions
fuzzy relations, Fuzzy Relations
fuzzy relations, maxmin, Fuzzy Relations
fuzzy relations, maxstar, 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, ukasiewicz Sets and Logic
ukasiewicz sets, ukasiewicz 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, ukasiewicz 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
doublesided 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 Cmeans 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 Cmeans 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
bellshaped, New Features
complementation, Standard Operations
difference, Aggregation Operations, Standard Operations
distinctions, Fuzzy Operations
doublesided 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, ukasiewicz Sets and Logic
implication, ukasiewicz sets, ukasiewicz 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
ukasiewicz sets, ukasiewicz Sets and Logic
operations, Aggregation Operations
properties, Standard Operations
Intersection, New Features, Aggregation Operations, Fuzzy Relations
Ln sets, ukasiewicz Sets and Logic
ukasiewicz sets, ukasiewicz 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, ukasiewicz Sets and Logic
operations on, ukasiewicz Sets and Logic
logic,
ukasiewicz , Digital Fuzzy Sets and Multivalued Logic
multivalued, Digital Fuzzy Sets and Multivalued Logic
ukasiewicz logic, Digital Fuzzy Sets and Multivalued Logic
ukasiewicz sets,
creating, ukasiewicz Sets and Logic
operations on, ukasiewicz 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
nvalued logic, ukasiewicz Sets and Logic
O
operations,
averaging, Aggregation Operations
difference, Aggregation Operations
intersection, Aggregation Operations
on Ln sets, ukasiewicz Sets and Logic
on ukasiewicz sets, ukasiewicz Sets and Logic
snorm, Aggregation Operations
tnorm, 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, ukasiewicz 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
snorm 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
tnorm, Aggregation Operations
operations, Aggregation Operations
ToDigital, ukasiewicz Sets and Logic
ToMembershipMatrix, Fuzzy Relation Visualization, Fuzzy Relations
triangular fuzzy numbers, discrete arithmetic, Discrete Fuzzy Arithmetic
twosided Gaussian fuzzy set, New Features
U
union, New Features, Aggregation Operations
formulas, Appendix
ukasiewicz sets, ukasiewicz Sets and Logic
operations, Aggregation Operations
properties, Standard Operations
Union, New Features, Aggregation Operations
Ln sets, ukasiewicz Sets and Logic, ukasiewicz Sets and Logic
ukasiewicz sets, ukasiewicz 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
userdefined aggregators, Aggregation Operations
V
visualization,
fuzzy relations, Fuzzy Relation Visualization
fuzzy sets, Fuzzy Set Visualization
W
X
Yager, Fuzzy Operations, Aggregation Operations
Z
