Conventional and fuzzy regression : theory and engineering applications / Vlassios Hrissanthou, Mike Spiliotis, editors.

Format:

Book

Contributor:

Hrissanthou, Vlassios, editor.

Spiliotis, Mike, editor.

Series:

Environmental science, engineering and technology series.

Environmental science, engineering and technology

Language:

English

Subjects (All):

Fuzzy statistics.

Regression analysis.

Physical Description:

1 online resource (344 pages).

Edition:

1st ed.

Place of Publication:

New York : Nova Science Publishers, [2018]

Summary:

"Aims to present both conventional and fuzzy regression analyses from theoretical aspects followed by application examples. The present book contains chapters originating from different scientific fields. The first 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. 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. Third describes the crisp linear, multiple linear, nonlinear and Gaussian process regressions. The fourth is confronted with a classic regression model, named Geographically Weighted Regression (GWR), which constitutes a spatial statistics method. The fifth chapter regards fuzzy linear regression based on symmetric triangular fuzzy numbers. The sixth chapter treats fuzzy linear regression based on trapezoidal membership functions. The main application of this chapter concerns the dependence of rainfall records between neighboring rainfall stations for a small sample of data. The next chapter refers to the multivariable crisp and fuzzy linear regression. The eighth chapter deals with the fuzzy linear regression, with crisp input data and fuzzy output data. All the 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"-- Provided by publisher.

Contents:

Intro

Contents

Preface

Chapter 1

Fuzzy and Crisp Regression Analysis between Sediment Transport Rates and Stream Discharge in the Case of Two Basins in Northeastern Greece

Abstract

CRISP Conventional Regression

CRISP, No Conventional Regression

Fuzzy Regression

Case Studies

Κimmeria Torrent Basin

Kosynthos River Basin

Conclusion

Appendix I

Fuzzy Numbers and Fuzzy Sets

L-fuzzy Numbers

Appendix II

Extension Principle

Appendix III

References

Biographical Sketches

Chapter 2

The Best Fit Model for the Relationships of Heavy Metals between Selected Parts of Telescopium telescopium and Habitat Sediments Using Five Models of Regressions

Introduction

Materials and Methods

Models Considered for Simple Regression Analysis

Results and Discussion

Model I: BCF Values or Correlation Analysis

Models II, III, IV, V and VI

Acknowledgments

About the Author

Chapter 3

Regression Analysis, Introduction, Theory and Applications in Telecommunications

1. Introduction

2. Theory

2.1. Simple Linear Regression

2.1.1. Example 1: Simple Linear Regression

2.2. Multiple Linear Regression

2.2.1. Example 2: Multiple Linear Regression with One Dependent Variable and Two Independent Variables

2.2.2. Example 3: Multiple Linear Regression with One Dependent Variable and Three Independent Variables

2.3. Logistic Regression

2.3.1. Example 4: Logistic Regression

2.4. Polynomial Regression

2.4.1. Example 5: Polynomial Regression (Quadratic Model)

2.4.2. Example 6. Polynomial Regression (Cubic Model)

2.5. Gaussian Process Regression

2.5.1. Example 7: Gaussian Process Regression

3. Applications of Regression Analysis in Telecommunications

3.1. Prediction in Wireless Systems.

3.2. Predictive Analytics in Internet of Things (IoT) Based Systems

3.3. Coding Theory: Extrinsic Information Scaling in Turbo Codes

About the Authors

Chapter 4

From Global to Local: GWR as an Exploratory Tool for Spatial Phenomena

Issues Emerging in Spatial Phenomena Research

Spatial Dependence and Spatial Autocorrelation

Spatial Heterogeneity/Spatial Non-Stationarity

Spatial Expansion Method and Local Weighted Regression

Geographically Weighted Regression (GWR)

GWR Equation, Kernel and Bandwidth Choice

Statistical Significance Levels and Statistical Significance of Coefficient Non-Stationarity

Multicollinearity in GWR

GWR Extensions

Example

Data

Methodology

Results

Chapter 5

Fuzzy Regression Using Triangular Fuzzy Number Coefficients: Similarities of the Calibrated Fuzzy Models

Symmetric Triangular Fuzzy Numbers

Principles of Fuzzy Linear Regression

An Application of Fuzzy Linear Regression Based on Symmetric Triangular Fuzzy Numbers

Forecast with the Method of Fuzzy Linear Regression

Comparison of the Forecasting Accuracy and Ability of the Fuzzy and the Classical Linear Regression

Similarities in Fuzzy Regression Models

Fuzzy Classification Using Similarity Ratios

An Application of Similarity Ratios and Fuzzy Classification

Discussion

Chapter 6

Models of Fuzzy Linear Regression with Trapezoidal Membership Functions: Application in Hydrology

2. Mathematical Model

2.1. Bisserier Model (2010)

2.1.1. Generalities

2.1.2. Identification Procedure

2.1.2.1. Optimization Criterion

2.1.2.2. Constraints.

2.1.3. Tendency Problem

2.2. Fung et al. (2006) Model

2.2.1. Generalities

2.2.2. Identification Procedure

2.2.2.1. Optimization Criterion

2.2.2.2. Constraints

2.2.3. Modified Model

2.3. Model of Tzimopoulos et al. (2016)

2.3.1. Generalities

2.3.2. Step 1

2.3.2. Step 2

3. Applications

3.1. Application 1

3.1.1. Bisserier Shift Model

3.1.2. Fung et al. Model (initial)

3.1.3. Fung et al. Model (modified)

3.1.4. Tzimopoulos et al. Model

3.2. Application 2: A Hydrological Problem in the Region of Western Macedonia (Northern Greece)

3.2.1. Step 1

3.2.2. Step 2

Chapter 7

Strength Determination of Fiber-Reinforced Soils Based on Multivariable Ordinary and Fuzzy Linear Regression Analyses

Experimental Measurements

Methods of analysis

Multivariable Ordinary (Conventional) Linear Regression Method

Fuzzy Linear Regression Method

Determination of Model Credibility

Development of Models

Efficiency and Comparison of Models

Chapter 8

Eutrophication in a Mediterranean Lake using Fuzzy Linear Regression Method with Fuzzy Data

2. Methodology

2.1. Study Area and Data Base

2.2. Description of the Fuzzy Model

2.2.1. Min Problem

2.2.2. Max Problem

2.2.3. The Least Squares Model

3. Results-Discussion

An Application in Engineering Using the Methods of Min, Max and Least Squares

About the Editors

Index

Blank Page.

Notes:

Description based on print version record.

ISBN:

9781536137996

1536137995

OCLC:

1065107763