3 Pattern Classification Based on New Interpretation of MFI 43 3.1 Introduction 3.2 Statement of the problem 3.3 Design of the Multidimensional Classifier Based on Fuzzy Relational Calculus(FRC) 46 3.4 Effectiveness of the Proposed Method 3.4.1 Classification of First Synthetic Data 3.4.2 Classification of Second Synthetic Data 3.5 Applications 3.5.1 Experiment on the Classification of the Telugu Vowels 3.5.2 Experiment on the Classification of Bengali Vowels 3.6 Conclusion References 4 Pattern Classification Based on New Interpretation of MFT and Floating Point Genetic algorithm 61 4.1 Introduction 4.2 Solution of Fuzzy Relational Equation by GA 63 4.2.1 Computational Details to Solve Eq(4. 4) Using Floating Point ga 4.2.2 Algorithm for the Estimation of 4.3 Designing of the Classifier Based on the Fuzzy Relational Calculus and genetic algorithms 4.4 Effectiveness of the Proposed Method 4.4.1 Classification of First Synthetic Data 68 4. 4.2 Classification of Second Synthetic Data 4.5 Application of the Proposed Method for Vowel Classification problem 4.5.1 Experiment on the Classification of the Telugu Vowels 7 .6 Comparative Study 4.7 Benchmark stud 73 5 Neuro-Genetic Approach to Pattern Classification Based on the New Interpretation of MFI 5.1 Introduction 77 5.2 Implementation of the New Interpretation of MFI on MLP Type Neural Network 5.3 Genetic-Algorithm-Based Learning Environment 5.3.1 Genetic Algorithm for Global Optimizatio 5.3.2 Backpropagation Versus GA3 Pattern Classification Based on New Interpretation of MFI. . . . . . 43 3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44 3.2 Statement of the Problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44 3.3 Design of the Multidimensional Classifier Based on Fuzzy Relational Calculus (FRC) . . . . . . . . . . . . . . . . . . . . . . . . . . . 46 3.4 Effectiveness of the Proposed Method . . . . . . . . . . . . . . . . . . . 48 3.4.1 Classification of First Synthetic Data. . . . . . . . . . . . . . . 49 3.4.2 Classification of Second Synthetic Data. . . . . . . . . . . . . 49 3.5 Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51 3.5.1 Experiment on the Classification of the Telugu Vowels . . . . . . . . . . . . . . . . . . . . . . . . . 51 3.5.2 Experiment on the Classification of Bengali Vowels . . . . 57 3.6 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59 4 Pattern Classification Based on New Interpretation of MFI and Floating Point Genetic Algorithm . . . . . . . . . . . . . . . . . . . . . 61 4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62 4.2 Solution of Fuzzy Relational Equation by GA . . . . . . . . . . . . . 63 4.2.1 Computational Details to Solve Eq. (4.4) Using Floating Point GA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64 4.2.2 Algorithm for the Estimation of < . . . . . . . . . . . . . . . . 66 4.3 Designing of the Classifier Based on the Fuzzy Relational Calculus and Genetic Algorithms . . . . . . . . . . . . . . . . . . . . . . 67 4.4 Effectiveness of the Proposed Method . . . . . . . . . . . . . . . . . . . 68 4.4.1 Classification of First Synthetic Data. . . . . . . . . . . . . . . 68 4.4.2 Classification of Second Synthetic Data. . . . . . . . . . . . . 68 4.5 Application of the Proposed Method for Vowel Classification Problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71 4.5.1 Experiment on the Classification of the Telugu Vowels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71 4.6 Comparative Study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71 4.7 Benchmark Study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73 4.8 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76 5 Neuro-Genetic Approach to Pattern Classification Based on the New Interpretation of MFI . . . . . . . . . . . . . . . . . . . . . . . . 77 5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77 5.2 Implementation of the New Interpretation of MFI on MLP Type Neural Network . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78 5.3 Genetic-Algorithm-Based Learning Environment. . . . . . . . . . . . 79 5.3.1 Genetic Algorithm for Global Optimization . . . . . . . . . . 79 5.3.2 Backpropagation Versus GA . . . . . . . . . . . . . . . . . . . . 80 x Contents