Conventional and Fuzzy Regression : Theory and Applications

Conventional and Fuzzy Regression: Theory and Applications aims to present both conventional and fuzzy regression analyses from theoretical aspects followed by application examples. The present book contains eight chapters originating from different scientific fields: River Engineering, Ecohydraulics, Telecommunications, Urban Planning, Transportation Planning, Hydrology, Soil Mechanics and Ecology. The first chapter deals with both crisp (conventional) linear or nonlinear regression and fuzzy linear or nonlinear regression. The application example refers to the relationship between sediment transport rates on the one hand and stream discharge and rainfall intensity on the other hand. In the examined case, the data of both categories are insufficient, and furthermore, the phenomenon is characterized by high complexity and uncertainties. The second chapter refers to the crisp linear or nonlinear regression of six heavy metals between different soft tissues and shells of Telescopium telescopium and its habitat surface sediments. The third chapter describes the crisp linear, multiple linear, nonlinear and Gaussian process regressions. The main application paradigms include the prediction in wireless systems, the predictive analytics in Internet of Things (IoT) based systems, and coding theory focused on extrinsic information scaling in turbo codes. The fourth chapter is confronted with a classic regression model, named Geographically Weighted Regression (GWR), which constitutes a spatial statistics method. The application example of this chapter concerns the housing value, i.e., a spatial phenomenon that is expressed as a function of housing characteristics. The fifth chapter regards fuzzy linear regression based on symmetric triangular fuzzy numbers. The main application of this regression consists of the analysis and forecast of rail passenger demand between two nearby cities. The dependent variable concerns the rail passengers and the independent variables are the Gross Domestic Product (GDP) per capita, the cost of transport by rail and the road transport fuel prices. The sixth chapter treats fuzzy linear regression based on trapezoidal membership functions. In concrete terms, three possible models with trapezoidal fuzzy parameters are described. The main application of this chapter concerns the dependence of rainfall records between neighboring rainfall stations for a small sample of data. The seventh chapter refers to the multivariable crisp and fuzzy linear regression. In the application paradigm, the dependent variable is the strength of fiber reinforced soils, while the independent variables are pertinent to soil, fiber and laboratory tests. The eighth chapter deals with the fuzzy linear regression, with crisp input data and fuzzy output data. In the application example, a relation between the levels of chlorophyll-a in an artificial lake and water temperature, nitrate, total phosphorus and Secchi depth is established. All the above chapters offer a proper foundation of either widely used or new techniques upon regression. Among the new techniques, several innovated fuzzy regression based methodologies are developed for real problems, and useful conclusions are drawn.