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| Introduction | |
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| Application of Mathematics | |
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| The Quality of the Mathematical Treatment | |
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| The Quality of the Model | |
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| The Quality of the Solving Procedure | |
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| The Quality of the Data | |
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| On Model Harmony | |
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| On Information Balance | |
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| Mathematical Representation of Simple Data and Connections | |
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| Some Elementary Procedures of Data Analysis | |
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| Data and Their Representation | |
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| Simple Procedures of Data Analysis | |
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| Representation of Functional Relationships Basing on Data | |
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| Relationships and Data | |
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| Interpolation | |
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| Local Approximation | |
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| Approximation | |
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| Other Approximation Principles | |
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| Empirical Smoothing | |
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| Global Approximation | |
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| Approximating Functional Relationships | |
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| Approximation with Locally Variable Setups | |
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| Approximation in Differential and Integral Equations | |
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| Approximate Optimization of Empirical Functions | |
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| Specification and Use of Observation Fuzziness | |
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| Specification by Intervals | |
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| Simple Error Propagation | |
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| Basic Ideas of Interval Mathematics | |
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| Specification by Fuzzy Sets | |
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| The Idea of a Fuzzy Set | |
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| Specification of Fuzzy Sets | |
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| Operations with Fuzzy Sets | |
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| Connections Via Functions and of Fuzzy Numbers | |
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| Fuzzy Relations | |
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| Specification and Use of Uncertain Variability | |
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| Chance and Probability | |
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| Model Ideas for the Notion Chance | |
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| Probability | |
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| Random Variables and Their Distributions | |
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| Asymptotic Statements | |
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| Probabilistic Inference | |
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| Samples | |
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| Parameter Estimation | |
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| Testing of Hypotheses | |
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| Problems with Imprecise Data | |
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| Bayesian Theory | |
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| Bayesian Inference | |
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| Hierarchical Inference and Robustness | |
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| Numerical Problems | |
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| Specification of Vagueness of Statements on Sets | |
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| Fuzzy Measures | |
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| The Idea of a Fuzzy Measure | |
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| Forms and Properties of Fuzzy Measures | |
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| Simple Inference with Fuzzy Measures | |
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| Specification of Partial Ignorance | |
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| Possibilistic Inference | |
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| Probability and Fuzziness | |
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| Probability of Fuzzy Events | |
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| Random Fuzzy Sets | |
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| Methods from Qualitative Data Analysis | |
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| Crisp Classification of Crisp Data | |
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| The Problem of Cluster Analysis | |
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| Mathematical Formulation of the Problem | |
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| Some Procedures for Crisp Cluster Partition | |
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| Clustering with a Mathematical-Statistical Background | |
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| Basic Ideas of Neural Networks | |
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| Fuzzy Classification of Crisp Data | |
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| Fuzzy Cluster | |
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| Procedures of Fuzzy Cluster Analysis | |
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| Fuzzy Classification of Fuzzy Data | |
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| Fuzzy Similarity of Fuzzy Data | |
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| The Use of The Concept for Classification | |
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| Evaluation of Functional Relationships | |
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| Statistical Regression Analysis | |
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| Model Assumptions with Random Dependent Variables | |
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| The Problem of Estimation | |
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| Discussion of the Model Assumptions | |
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| Further A-Priori Knowledge and Assumptions | |
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| Random Influence in All Variables | |
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| Local Regression in a Random Field | |
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| Fuzzy Evaluation of Functional Relationships | |
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| Crisp Data Analysis as a Starting Point | |
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| Explorative Evaluation of Functional Relationships | |
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| Evaluation with Additional Assumptions | |
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| Inference with Fuzzy Parameter Values | |
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| Outlook and Conclusions | |
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| References | |
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| Index | |