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 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, 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, 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 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 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 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     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 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 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, 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     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, 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 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 Support, Fuzzy Operations SymmetricDifference, Aggregation Operations T t-norm, Aggregation Operations     operations, Aggregation Operations ToDigital, ukasiewicz 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     formulas, Appendix     ukasiewicz sets, ukasiewicz Sets and Logic     operations, Aggregation Operations     properties, Standard Operations     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     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 Z