Contents -- Preface -- List of Tables -- List of Figures -- Chapter 1: Introduction -- Chapter 2: Basic Knowledge on Classical Sets -- 2.1 Classical Sets and Set Inclusion -- 2.2 Set Operations -- 2.3 Set Sequences and Set Classes -- 2.4 Set Classes Closed Under Set Operations -- 2.5 Relations, Posets, and Lattices -- 2.6 The Supremum and Infimum of Real Number Sets -- Exercises -- Chapter 3: Fuzzy Sets -- 3.1 The Membership Functions of Fuzzy Sets -- 3.2 Inclusion and Operations of Fuzzy Sets -- 3.3 a-Cuts -- 3.4 Convex Fuzzy Sets -- 3.5 Decomposition Theorems -- 3.6 The Extension Principle -- 3.7 Interval Numbers -- 3.8 Fuzzy Numbers and Linguistic Attribute -- 3.9 Binary Operations for Fuzzy Numbers -- 3.10 Fuzzy Integers -- Exercises -- Chapter 4: Set Functions -- 4.1 Weights and Classical Measures -- 4.2 Extension of Measures -- 4.3 Monotone Measures -- 4.4 -Measures -- 4.5 Quasi-Measures -- 4.6 M bius and Zeta Transformations -- 4.7 Belief Measures and Plausibility Measures -- 4.8 Necessity Measures and Possibility Measures -- 4.9 k-Interactive Measures -- 4.10 Efficiency Measures and Signed Efficiency Measures -- Exercises -- Chapter 5: Integrations -- 5.1 Measurable Functions -- 5.2 The Riemann Integral -- 5.3 The Lebesgue-Like Integral -- 5.4 The Choquet Integral -- 5.5 Upper and Lower Integrals -- 5.6 r-Integrals on Finite Spaces -- Exercises -- Chapter 6: Information Fusion -- 6.1 Information Sources and Observations -- 6.2 Integrals Used as Aggregation Tools -- 6.3 Uncertainty Associated with Set Functions -- 6.4 The Inverse Problem of Information Fusion -- Chapter 7: Optimization and Soft Computing -- 7.1 Basic Concepts of Optimization -- 7.2 Genetic Algorithms -- 7.3 Pseudo Gradient Search -- 7.4 A Hybrid Search Method -- Chapter 8: Identification of Set Functions -- 8.1 Identification of l-Measures.

8.2 Identification of Belief Measures -- 8.3 Identification of Monotone Measures -- 8.3.1 Main algorithm -- 8.3.2 Reordering algorithm -- 8.4 Identification of Signed Efficiency Measures by a Genetic Algorithm -- 8.5 Identification of Signed Efficiency Measures by the Pseudo Gradient Search -- 8.6 Identification of Signed Efficiency Measures Based on the Choquet Integral by an Algebraic Method -- 8.7 Identification of Monotone Measures Based on r-Integrals by a Genetic Algorithm -- Chapter 9: Multiregression Based on Nonlinear Integrals -- 9.1 Linear Multiregression -- 9.2 Nonlinear Multiregression Based on the Choquet Integral -- 9.3 A Nonlinear Multiregression Model Accommodating Both Categorical and Numerical Predictive Attributes -- 9.4 Advanced Consideration on the Multiregression Involving Nonlinear Integrals -- 9.4.1 Nonlinear multiregressions based on the Choquet integral with quadratic core -- 9.4.2 Nonlinear multiregressions based on the Choquet integral involving unknown periodic variation -- 9.4.3 Nonlinear multiregressions based on upper and lower integrals -- Chapter 10: Classifications Based on Nonlinear Integrals -- 10.1 Classification by an Integral Projection -- 10.2 Nonlinear Classification by Weighted Choquet Integrals -- 10.3 An Example of Nonlinear Classification in a Three-Dimensional Sample Space -- 10.4 The Uniqueness Problem of the Classification by the Choquet Integral with a Linear Core -- 10.5 Advanced Consideration on the Nonlinear Classification Involving the Choquet Integral -- 10.5.1 Classification by the Choquet integral with the widest gap between classes -- 10.5.2 Classification by cross-oriented projection pursuit -- 10.5.3 Classification by the Choquet integral with quadratic core -- Chapter 11: Data Mining with Fuzzy Data -- 11.1 Defuzzified Choquet Integral with Fuzzy-Valued Integrand (DCIFI).

11.1.1 The a-level set of a fuzzy-valued function -- 11.1.2 The Choquet extension of µ -- 11.1.3 Calculation of DCIFI -- 11.2 Classification Model Based on the DCIFI -- 11.2.1 Fuzzy data classification by the DCIFI -- 11.2.2 GA-based adaptive classifier-learning algorithm via DCIFI projection pursuit -- 11.2.3 Examples of the classification problems solved by the DCIFI projection classifier -- 11.3 Fuzzified Choquet Integral with Fuzzy-Valued Integrand (FCIFI) -- 11.3.1 Definition of the FCIFI -- 11.3.2 The FCIFI with respect to monotone measures -- 11.3.3 The FCIFI with respect to signed efficiency measures -- 11.3.4 GA-based optimization algorithm for the FCIFI with respect to signed efficiency measures -- 11.4 Regression Model Based on the CIII -- 11.4.1 CIII regression model -- 11.4.2 Double-GA optimization algorithm -- 11.4.3 Explanatory examples -- Bibliography -- Index.