| Preface | p. vii |
| List of Tables | p. xv |
| List of Figures | p. xvi |
| Introduction | p. 1 |
| Basic Knowledge on Classical Sets | p. 4 |
| Classical Sets and Set Inclusion | p. 4 |
| Set Operations | p. 7 |
| Set Sequences and Set Classes | p. 10 |
| Set Classes Closed Under Set Operations | p. 13 |
| Relations, Posets, and Lattices | p. 17 |
| The Supremum and Infimum of Real Number Sets | p. 20 |
| Exercises | p. 22 |
| Fuzzy Sets | p. 24 |
| The Membership Functions of Fuzzy Sets | p. 24 |
| Inclusion and Operations of Fuzzy Sets | p. 27 |
| ¿-Cuts | p. 33 |
| Convex Fuzzy Sets | p. 36 |
| Decomposition Theorems | p. 37 |
| The Extension Principle | p. 40 |
| Interval Numbers | p. 42 |
| Fuzzy Numbers and Linguistic Attribute | p. 45 |
| Binary Operations for Fuzzy Numbers | p. 51 |
| Fuzzy Integers | p. 58 |
| Exercises | p. 59 |
| Set Functions | p. 62 |
| Weights and Classical Measures | p. 63 |
| Extension of Measures | p. 66 |
| Monotone Measures | p. 69 |
| ¿-Measures | p. 74 |
| Quasi-Measures | p. 82 |
| Möbius and Zeta Transformations | p. 87 |
| Belief Measures and Plausibility Measures | p. 91 |
| Necessity Measures and Possibility Measures | p. 102 |
| ¿-Interactive Measures | p. 107 |
| Efficiency Measures and Signed Efficiency Measures | p. 108 |
| Exercises | p. 112 |
| Integrations | p. 115 |
| Measurable Functions | p. 115 |
| The Riemann Integral | p. 123 |
| The Lebesgue-Like Integral | p. 128 |
| The Choquet Integral | p. 133 |
| Upper and Lower Integrals | p. 153 |
| r-Integrals on Finite Spaces | p. 162 |
| Exercises | p. 174 |
| Information Fusion | p. 177 |
| Information Sources and Observations | p. 177 |
| Integrals Used as Aggregation Tools | p. 181 |
| Uncertainty Associated with Set Functions | p. 186 |
| The Inverse Problem of Information Fusion | p. 190 |
| Optimization and Soft Computing | p. 193 |
| Basic Concepts of Optimization | p. 193 |
| Genetic Algorithms | p. 195 |
| Pseudo Gradient Search | p. 199 |
| A Hybrid Search Method | p. 202 |
| Identification of Set Functions | p. 204 |
| Identification of ¿-Measures | p. 204 |
| Identification of Belief Measures | p. 206 |
| Identification of Monotone Measures | p. 207 |
| Main algorithm | p. 210 |
| Reordering algorithm | p. 211 |
| Identification of Signed Efficiency Measures by a Genetic Algorithm | p. 213 |
| Identification of Signed Efficiency Measures by the Pseudo Gradient Search | p. 215 |
| Identification of Signed Efficiency Measures Based on the Choquet Integral by an Algebraic Method | p. 217 |
| Identification of Monotone Measures Based on r-Integrals by a Genetic Algorithm | p. 219 |
| Multiregression Based on Nonlinear Integrals | p. 221 |
| Linear Multiregression | p. 221 |
| Nonlinear Multiregression Based on the Choquet Integral | p. 226 |
| A Nonlinear Multiregression Model Accommodating Both Categorical and Numerical Predictive Attributes | p. 232 |
| Advanced Consideration on the Multiregression Involving Nonlinear Integrals | p. 234 |
| Nonlinear multiregressions based on the Choquet integral with quadratic core | p. 234 |
| Nonlinear multiregressions based on the Choquet integral involving unknown periodic variation | p. 235 |
| Nonlinear multiregressions based on upper and lower integrals | p. 236 |
| Classifications Based on Nonlinear Integrals | p. 238 |
| Classification by an Integral Projection | p. 238 |
| Nonlinear Classification by Weighted Choquet Integrals | p. 242 |
| An Example of Nonlinear Classification in a Three-Dimensional Sample Space | p. 250 |
| The Uniqueness Problem of the Classification by the Choquet Integral with a Linear Core | p. 263 |
| Advanced Consideration on the Nonlinear Classification Involving the Choquet Integral | p. 267 |
| Classification by the Choquet integral with the widest gap between classes | p. 267 |
| Classification by cross-oriented projection pursuit | p. 268 |
| Classification by the Choquet integral with quadratic core | p. 270 |
| Data Mining with Fuzzy Data | p. 272 |
| Defuzzified Choquet Integral with Fuzzy-Valued Integrand (DCIFI) | p. 273 |
| The ¿-level set of a fuzzy-valued function | p. 274 |
| The Choquet extension of ¿ | p. 275 |
| Calculation of DCIFI | p. 277 |
| Classification Model Based on the DCIFI | p. 282 |
| Fuzzy data classification by the DCIFI | p. 283 |
| GA-based adaptive classifier-learning algorithm via DCIFI projection pursuit | p. 286 |
| Examples of the classification problems solved by the DCIFI projection classifier | p. 290 |
| Fuzzified Choquet Integral with Fuzzy-Valued Integrand (FCIFI) | p. 300 |
| Definition of the FCIFI | p. 300 |
| The FCIFI with respect to monotone measures | p. 303 |
| The FCIFI with respect to signed efficiency measures | p. 306 |
| GA-based optimization algorithm for the FCIFI with respect to signed efficiency measures | p. 309 |
| Regression Model Based on the CIII | p. 319 |
| CIII regression model | p. 319 |
| Double-GA optimization algorithm | p. 321 |
| Explanatory examples | p. 324 |
| Bibliography | p. 329 |
| Index | p. 337 |
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