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Book Categories |
1 | Introduction | 1 |
2 | Basic notions | 9 |
2.1 | Fuzzy sets | 9 |
2.2 | Set-theoretic operations | 13 |
2.3 | Special fuzzy sets | 19 |
2.4 | Extension principle and applications | 24 |
2.5 | Fuzzy relations | 33 |
2.6 | Fuzzy functions | 40 |
2.7 | Measuring the uncertainty | 44 |
3 | Basic notions of data analysis | 61 |
3.1 | Data | 61 |
3.2 | Grouping and transformations | 63 |
3.3 | Similarity and distances | 64 |
3.4 | Cluster analysis | 73 |
3.5 | Evaluation of functional relationships | 79 |
3.6 | Projection techniques | 82 |
4 | Fuzzy data | 89 |
4.1 | Simple fuzzy data | 89 |
4.2 | Complex fuzzy data | 98 |
4.3 | Simple operations and transformations | 108 |
5 | Qualitative analysis | 121 |
5.1 | Fuzzy clustering | 122 |
5.2 | Similarity of fuzzy data | 127 |
5.3 | Fuzzy similarity of fuzzy data | 145 |
5.4 | Shape similarity | 160 |
6 | Quantitative analysis | 185 |
6.1 | Preliminary operations | 185 |
6.2 | Local functional approximation | 188 |
6.3 | Global evaluation | 191 |
6.4 | Global approximation of fuzzy data | 207 |
6.5 | Some fuzzy counterparts | 215 |
6.6 | Minimization of fuzzy functions | 230 |
7 | Evaluation of methods | 241 |
7.1 | Towards a normative theory | 242 |
7.2 | Truth evaluation | 251 |
7.3 | Possibility evaluation | 263 |
7.4 | Probability evaluation | 273 |
7.5 | Fuzzy measure evaluation | 300 |
Bibliography | 307 | |
Subject Index | 327 | |
List of Symbols | 339 |
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