## Foundations of Fuzzy Logic and Soft Computing: 12th International Fuzzy Systems Association World Congress, IFSA 2007, Cancun, Mexico, Junw 18-21, 2007, ProceedingsPatricia Melin, Oscar Castillo, Luis T. Aguilar, Witold Pedrycz This book comprises a selection of papers from IFSA 2007 on new methods and theories that contribute to the foundations of fuzzy logic and soft computing. These papers were selected from over 400 submissions and constitute an imp- tant contribution to the theory and applications of fuzzy logic and soft c- puting methodologies. Soft computing consists of several computing paradigms, including fuzzy logic, neural networks, genetic algorithms, and other techniques, which can be used to produce powerful intelligent systems for solving real-world problems. The papers of IFSA 2007 also make a contribution to this goal. This book is intended to be a major reference for scientists and engineers interested in applying new computational and mathematical tools to achieve intelligent solutions to complex problems. We consider that this book can also be used to get novel ideas for new lines of research, or to continue the lines of research proposed by the authors of the papers contained in the book. The book is divided into 14 main parts.Eachpart contains a set of papers on a common subject, so that the reader can ?nd similar papers grouped together. Some of these parts comprise the papers of organized sessions of IFSA 2007 and we thank the session organizers for their incredible job in forming these sessions with invited and regular paper submissions. |

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### Contents

Case of Hierarchical Estimation | 3 |

Testing Stochastic Arithmetic and CESTACMethod Via Polynomial Computation | 13 |

Friction Model by Using Fuzzy DifferentialEquations | 23 |

TowardsFaster Estimation of Statistics and ODEs UnderInterval pBox and Fuzzy Uncertainty | 33 |

Noncommutative System of Fuzzy IntervalLogic Generated by the Checklist ParadigmMeasure m3 Containing Early Zadeh Implication | 43 |

Points with Type2 Operations | 56 |

II Intuitionistic Fuzzy Sets and Their Applications | 67 |

Atanassovs Intuitionistic Fuzzy Sets as aClassification Model | 68 |

X Fuzzy Logic Theory | 417 |

SemiBoolean and HyperArchimedeanBLAlgebras | 419 |

A Fuzzy HahnBanach Theorem | 427 |

The Algebraic Properties of Linguistic ValueTruth and Its Reasoning | 436 |

Fuzzy Subgroups with Meet Operation in theConnection of Mobius Transformations | 445 |

A Method for Automatic Membership FunctionEstimation Based on Fuzzy Measures | 451 |

Counting Finite Residuated Lattices | 461 |

On Proofs and Rule of Multiplication in FuzzyAttribute Logic | 471 |

Classification with Nominal Data UsingIntuitionistic Fuzzy Sets | 76 |

Intuitionistic Fuzzy Histograms of an Image | 86 |

Image Threshold Using AIFSs Based onBounded Histograms | 96 |

The Role of Entropy inIntuitionistic Fuzzy Contrast Enhancement | 104 |

Representation of Rough Sets Based onIntuitionistic Fuzzy Special Sets | 114 |

III The Application of Fuzzy Logic and Soft Computing in Flexible Querying | 123 |

Towards Vague Query Answering in LogicProgramming for LogicBased InformationRetrieval | 125 |

On Browsing Domain Ontologies for InformationBase Content | 135 |

Go Soft on Your Nodes | 145 |

SurfaceArea | 155 |

Qualification of Fuzzy Statements Under FuzzyCertainty | 162 |

Weighted Conjunctive and DisjunctiveAggregation of Possibilistic Truth Values | 171 |

Bipolar Queries Using Various Interpretations ofLogical Connectives | 181 |

A Hierarchical Approach to Object Comparison | 191 |

Using Fuzzy Logic an IR Featuresto Approximately Query XML Documents | 199 |

IV Philosophical and HumanScientific Aspects of Soft Computing | 209 |

Designing Representative Bodies When theVoter Preferences Are Fuzzy | 210 |

Possibility Based Modal Semantics for GradedModifiers | 220 |

New Perspective for Structural LearningMethod of Neural Networks | 231 |

V Search Engine and Information Processing and Retrieval | 241 |

Web Usage Mining Via Fuzzy Logic Techniques | 243 |

Deduction Engine Design for PNLBasedQuestion Answering System | 253 |

Granular Computing and Modeling the HumanThoughts in Web Documents | 263 |

VI Perception Based Data Mining and Decision Making | 271 |

Extracting Fuzzy Linguistic Summaries Basedon Including Degree Theory and FCA | 272 |

Linguistic Summarization of Time Series byUsing the Choquet Integral | 284 |

Visualization of Possibilistic Potentials | 295 |

The Fuzzy Logic Approach | 305 |

Applied to Market Segmentation | 307 |

Fuzzy Backpropagation Neural Networks forNonstationary Data Prediction | 318 |

Fuzzy Model Based Iterative Learning Controlfor Phenol Biodegradation | 328 |

Fuzzy Modelling Methodologies for LargeDatabase | 338 |

VIII Fuzzy Possibilistic Optimization | 349 |

On PossibilisticFuzzy Optimization | 350 |

The Use of IntervalValued Probability Measuresin Optimization Under Uncertainty for ProblemsContaining a Mixture of Fuzzy Possibilisiticand Inter... | 361 |

On Selecting an Algorithm for FuzzyOptimization | 371 |

A RiskMinimizing Model Under Uncertainty inPortfolio | 381 |

IX Fuzzy Trees | 393 |

A Case Study withCustomer Satisfaction Dataset | 395 |

An Empirical Studywith Linguistic Decision Trees | 407 |

Graded Fuzzy Rules | 481 |

On External Measures for Validation of FuzzyPartitions | 491 |

Coherence Index of Radial Conjunctive FuzzySystems | 502 |

Basic Notions | 513 |

Features of Mathematical Theoriesin Formal Fuzzy Logic | 523 |

A New Method to Compare Dynamical Systems | 533 |

Advances in the Geometrical Study ofRotationInvariant TNorms | 543 |

Fuzzy Reversed Posynomial GeometricProgramming and Its Dual Form | 553 |

Posynomial Fuzzy Relation GeometricProgramming | 563 |

XI Type2 Fuzzy Logic | 573 |

A Vector Similarity Measurefor Type1 Fuzzy Sets | 575 |

On Approximate Representation of Type2Fuzzy Sets Using Triangulated Irregular Network | 584 |

Hybrid Control for an Autonomous WheeledMobile Robot Under Perturbed Torques | 594 |

Type2 Fuzzy Logic for Improving Training Dataand Response Integration in Modular NeuralNetworks for Image Recognition | 604 |

XII Fuzzy Logic Applications | 613 |

A Fuzzy Model for Olive Oil Sensory Evaluation | 615 |

An IntervalBased Index Structure for StructureElucidation in Chemical Databases | 625 |

Fuzzy Cognitive Layer in RoboCupSoccer | 635 |

An Approach to Theory of Fuzzy DiscreteSignals | 646 |

Using Gradual Numbers for SolvingFuzzyValued Combinatorial OptimizationProblems | 656 |

Fuzzy Classifier with Probabilistic IFTHENRules | 666 |

Fuzzy Adaptive Search Method for ParallelGenetic Algorithm Tuned by Evolution DegreeBased on Diversity Measure | 677 |

Fuzzy Controller for Robot Manipulators | 688 |

Collaboration Between Hyperheuristics to SolveStripPacking Problems | 698 |

XIII Neural Networks and Control | 709 |

DiscreteTime Recurrent High Order NeuralObserver for Induction Motors | 710 |

Strict Generalization in Multilayered PerceptronNetworks | 722 |

Fault Tolerant Control of a Three TankBenchmark Using Weighted Predictive Control | 732 |

Synchronization in Arrays of Chaotic NeuralNetworks | 743 |

XIV Intelligent Agents and Knowledge Ant Colony | 755 |

On Fuzzy ProjectionBased UtilityDecomposition in Compound MultiagentNegotiations | 757 |

Conditional DempsterShafer Theory forUncertain Knowledge Updating | 767 |

Ant Colony Optimization Applied to FeatureSelection in Fuzzy Classifiers | 778 |

Artificial Bee Colony ABC OptimizationAlgorithm for Solving Constrained OptimizationProblems | 789 |

BeamACO Distributed Optimization Applied toSupplyChain Management | 799 |

A Cultural Algorithm with Operator ParametersControl for Solving Timetabling Problems | 810 |

On Control for Agents Formation | 820 |

829 | |

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### Common terms and phrases

aggregation algebra algorithm ant colony optimization application approach attribute Berlin Heidelberg 2007 classification clustering computing concept consider constraints crisp Data Mining data set database decision trees deﬁned Deﬁnition degree denote elements entropy evaluation example formula fuzzy logic fuzzy measure fuzzy model fuzzy number fuzzy relation fuzzy rule Fuzzy Systems Genetic Algorithms geometric programming given graded heuristic IEEE IFSA input interval intuitionistic fuzzy sets Kacprzyk linear LNAI mathematics matrix Melin membership function method neural network nodes objective function obtained operator optimal solution output paper parameters pattern trees possibilistic possible posynomial problem programming Prolog properties proposed query Rand index represented residuated lattices robot semantics Sets and Systems simulation Springer-Verlag Berlin Heidelberg structure subset t-norm Table Theorem theory transformations truth value tuples type-2 fuzzy sets uncertainty variable vector weight Zadeh