The book under the title “Conventional and Fuzzy Regression: Theory
and Engineering Applications” aims at the presentation of both
conventional and fuzzy regression analysis from theoretical aspects
followed by application examples. It addresses the need of young or
concerned researchers and postgraduate students for advanced regression
techniques.
Traditionally, crisp (conventional) linear regression could be seen as a
statistic tool applied to different scientific fields in order to find a linear
relationship between a dependent variable and one or more independent
variables. However, in fact, the crisp regression is based on an
unconstrained optimization process, whilst the statistics can be used in
order to check and extend the regression results.
Author(s): Vlassios Hrissanthou, Mike Spiliotis
Publisher: Nova Science Publishers
Year: 2018
Language: English
Pages: 343
Contents......Page 6
Preface......Page 8
Abstract......Page 12
CRISP Conventional Regression......Page 13
CRISP, No Conventional Regression......Page 18
Fuzzy Regression......Page 21
Case Studies......Page 30
Κimmeria Torrent Basin......Page 32
Kosynthos River Basin......Page 40
Conclusion......Page 46
Fuzzy Numbers and Fuzzy Sets......Page 47
L-fuzzy Numbers......Page 48
Extension Principle......Page 49
Appendix III......Page 51
References......Page 52
Biographical Sketches......Page 55
Abstract......Page 62
Introduction......Page 63
Materials and Methods......Page 64
Models Considered for Simple Regression Analysis......Page 67
Model I: BCF Values or Correlation Analysis......Page 75
Models II, III, IV, V and VI......Page 80
References......Page 82
About the Author......Page 84
Abstract......Page 86
1. Introduction......Page 87
2.1. Simple Linear Regression......Page 93
2.1.1. Example 1: Simple Linear Regression......Page 94
2.2. Multiple Linear Regression......Page 99
2.2.1. Example 2: Multiple Linear Regression with One Dependent Variable and Two Independent Variables......Page 100
2.3. Logistic Regression......Page 103
2.3.1. Example 4: Logistic Regression......Page 105
2.4. Polynomial Regression......Page 106
2.4.1. Example 5: Polynomial Regression (Quadratic Model)......Page 107
2.4.2. Example 6. Polynomial Regression (Cubic Model)......Page 108
2.5. Gaussian Process Regression......Page 109
2.5.1. Example 7: Gaussian Process Regression......Page 110
3.1. Prediction in Wireless Systems......Page 112
3.2. Predictive Analytics in Internet of Things (IoT) Based Systems......Page 115
3.3. Coding Theory: Extrinsic Information Scaling in Turbo Codes......Page 118
Conclusion......Page 120
References......Page 121
About the Authors......Page 127
Abstract......Page 130
Introduction......Page 131
Spatial Dependence and Spatial Autocorrelation......Page 132
Spatial Heterogeneity/Spatial Non-Stationarity......Page 134
Spatial Expansion Method and Local Weighted Regression......Page 135
Geographically Weighted Regression (GWR)......Page 136
GWR Equation, Kernel and Bandwidth Choice......Page 138
Multicollinearity in GWR......Page 140
Example......Page 141
Data......Page 143
Methodology......Page 145
Results......Page 146
References......Page 157
Biographical Sketches......Page 166
Abstract......Page 174
Introduction......Page 175
Symmetric Triangular Fuzzy Numbers......Page 177
Principles of Fuzzy Linear Regression......Page 178
An Application of Fuzzy Linear Regression Based on Symmetric Triangular Fuzzy Numbers......Page 184
Forecast with the Method of Fuzzy Linear Regression......Page 192
Comparison of the Forecasting Accuracy and Ability of the Fuzzy and the Classical Linear Regression......Page 194
Similarities in Fuzzy Regression Models......Page 195
Fuzzy Classification Using Similarity Ratios......Page 199
An Application of Similarity Ratios and Fuzzy Classification......Page 205
References......Page 213
Biographical Sketches......Page 217
Abstract......Page 220
1. Introduction......Page 221
2.1.1. Generalities......Page 226
2.1.2.2. Constraints......Page 230
2.1.3. Tendency Problem......Page 232
2.2.1. Generalities......Page 234
2.2.2.1. Optimization Criterion......Page 236
2.2.2.2. Constraints......Page 237
2.2.3. Modified Model......Page 239
2.3.2. Step 1......Page 240
2.3.2. Step 2......Page 241
3.1.1. Bisserier Shift Model......Page 242
3.1.2. Fung et al. Model (initial)......Page 244
3.1.3. Fung et al. Model (modified)......Page 245
3.1.4. Tzimopoulos et al. Model......Page 246
3.2.1. Step 1......Page 247
3.2.2. Step 2......Page 248
Conclusion......Page 249
References......Page 250
Biographical Sketches......Page 253
Abstract......Page 260
Introduction......Page 261
Experimental Measurements......Page 265
Multivariable Ordinary (Conventional) Linear Regression Method......Page 270
Fuzzy Linear Regression Method......Page 273
Determination of Model Credibility......Page 275
Development of Models......Page 276
Efficiency and Comparison of Models......Page 278
Conclusion......Page 284
References......Page 285
Biographical Sketches......Page 290
Abstract......Page 296
1. Introduction......Page 297
2.1. Study Area and Data Base......Page 298
2.2. Description of the Fuzzy Model......Page 300
2.2.1. Min Problem......Page 301
2.2.3. The Least Squares Model......Page 303
3. Results-Discussion......Page 304
Conclusion......Page 308
An Application in Engineering Using the Methods of Min, Max and Least Squares......Page 310
Appendix II......Page 313
References......Page 315
Biographical Sketches......Page 317
About the Editors......Page 334
Index......Page 336
Blank Page......Page 0
