Modelling Invasive Alien Plant Species: Fuzzy Based Uncertainty presents the application of different fuzzy set theory techniques in developing risk assessment models for invasive plant species- those whose introduction and spread outside their natural range threatens local biodiversity. Invasion risk of species is expressed by biological traits which would be considered as the risk factors accompanied with uncertainty and imprecision. The book considers both quantitative and qualitative inputs in modelling the invasive risk by incorporating different mathematical models based on fuzzy set theory operators, interval methods, and fuzzy linguistic operators. The proposed models can be applied for investigating risk of invasive alien plant species in various regions and conditions.
Features:
- Uniquely merges mathematical models with biological expressions.
- Presents different factor-based models as a case study on the risk of invasive alien plant species.
- Explains how users can perform primary-level risk assessment through fuzzy modeling techniques.
Appropriate for upper-level students, researchers, and practicing professionals, this book shows how conventional approaches such as probability theory can be of limited use to solve issues of uncertainty, and how they fuzzy set theory plays a better role in understanding uncertain system dynamics, such invasive plant modelling.
Author(s): H.O.W. Peiris, S. Chakraverty, S.S.N. Perera, S.M.W. Ranwala
Publisher: CRC Press
Year: 2021
Language: English
Pages: 208
City: Boca Raton
Cover
Half Title
Title Page
Copyright Page
Contents
List of Figures
List of Tables
Preface
Acknowledgments
Chapter 1: Invasive Alien Plant Species
1.1 Invasive Alien Plant Species (IAPS) and Their Impact on the Environment
1.2 How Can An Alien Species Become Invasive?
1.3 Management of Invasive Alien Plant Species
Chapter 2: Risk Assessment of Invasive Alien Plant Species
2.1 Risk Assessment(RA) – IAPS
2.2 Modeling Risks of Invasive Alien Plant Species
Chapter 3: Preliminaries
3.1 An Overview
3.2 Fuzzy Sets
3.3 Membership Function
3.3.1 Terminology of Membership Functions
3.3.2 Types of Membership Functions
3.3.3 Role of Linguistic Variables
3.4 Fuzzy Set - Theoretic Operations
3.5 More on Fuzzy Set - Theoretic Operators
Chapter 4: Modeling Quantitative Parameters
4.1 The Role of Fuzzy Set Theory in Modeling Quantitative Parameters
4.2 Fuzzy Sets and Membership Functions for Quantitative Parameters
4.3 Model Formulation
4.3.1 Aggregation of Fuzzy Sets
4.3.2 Important Degrees of the Parameters
4.3.3 Concentration/Dilation Operators
4.3.4 Model Output
4.4 Structure of the Model–Quantitative Parameters
4.5 Fuzzy Analytical Hierarchy Techniques for Evaluating Grade of Importance Weights
4.5.1 An Overview
4.5.2 Preliminaries - Evaluating the Grade of Importance Weights
4.5.3 Construction of Fuzzy Pairwise Comparison Matrix
4.5.4 Model Formulation
Chapter 5: Interval Function Approximation Techniques
5.1 An Overview
5.2 Preliminaries
5.2.1 Basic Concepts of Multivariate Linear Regression
5.2.2 Least Squares Estimation
5.2.3 Interval Multivariate Linear Regression Model
5.2.4 Interval Least Squares
5.2.5 Interval Arithmetic
5.3 Factor-based Model with Interval Inputs and Outputs
5.4 Approach I
5.5 Approach II
5.6 Approach III
Chapter 6: Modeling with the Fuzzy Linguistic Approach
6.1 An Overview
6.2 Development of Factor-based Models based on the Symbolic Approach
6.2.1 The Linguistic Terms Set
6.3 Symbolic Approach - Method I - Fuzzy Linguistic Aggregation Operators
6.3.1 Model with Non-weighted Linguistic Parameters
6.3.1.1 Linguistic Ordered Weighted Averaging (LOWA) Operator
6.3.1.2 The Concept of Fuzzy Majority in the Aggregation of LOWA Operator
6.3.1.3 Setting Up Model I-Non-weighted
6.3.2 Model with Weighted Parameters
6.4 Symbolic Approach - Method II - Fuzzy 2-tuple
6.5 Fuzzy 2-tuple Linguistic Representation
6.5.1 Symbolic Translation of Fuzzy 2-tuple Linguistic Representation
6.5.2 Fuzzy 2-tuple Aggregation Operators
6.5.3 Setting up Model IV
6.6 Approximation Approach
6.6.1 Method to Merge Linguistic Terms Set
6.6.2 Setting up Model V
Chapter 7: Modeling with the Fuzzy Linguistic 2-tuple Approach with Unbalanced Linguistic Terms Set
7.1 An Overview
7.2 Semantics of Unbalanced Linguistic Terms Set
7.3 Model Based on Unbalanced Linguistic Terms Set
Chapter 8: Evaluation of Invasion Risk with Quantitative Parameters
8.1 Quantitative Parameters/Factors in Invasiveness
8.2 Evaluation of Dispersal Risk Models
8.3 Model I—Hamacher t-norm Operator
8.4 Model II—Yager t-norm Operator
8.5 Model III—Dombi t-norm Operator
8.6 Model IV—Dubois and Prade t?norm Operator
8.7 Discussion Model I—Model IV
8.8 Evaluating Importance Weights using Fuzzy Analytical Hierarchy Techniques
8.8.1 Models—Proposed Method I
8.8.2 Discussion—Models I and II
8.9 Models—Proposed Method II
8.9.1 Construction of Models III and IV
8.9.2 Model III
8.9.3 Model IV
8.10 Discussion—Models III and IV
Chapter 9: Evaluation of Invasion Risk Intervals with Quantitative and Qualitative Parameters
9.1 An Overview
9.2 Model Parameters
9.3 Model—Invasion Risk Intervals of IAPS
9.3.1 Formulation of Interval-valued Data
9.4 Model I
9.5 Model II
9.6 Comparison of Quality of Models I and II
9.7 Validation Results
9.8 Discussion - Models I and II
9.9 Model III
9.10 Quality Measurement of Model III
9.11 Validation - Model III
9.12 Discussion - Model III
Chapter 10: Evaluation of Invasion Risk Levels with Symmetrically Distributed Linguistic Terms Sets
10.1 An Overview
10.2 Models – Fuzzy Linguistic Operators
10.2.1 Identifying Parameters
10.2.2 Selection Procedure of Linguistic Term Set
10.2.3 Model I – LOWA
10.2.4 Discussion – Model I
10.2.5 Model II – LWA
10.2.6 Discussion – Model II – LWA
10.2.7 Model III – MLIOWA
10.2.8 Discussion – Model III
10.3 Models – Fuzzy 2-tuple Approach
10.3.1 Model I – 2-tuple (Non-weighted)
10.3.2 Discussion – Model I – 2-tuple (Non-weighted)
10.3.3 Model II – 2-tuple (Weighted)
10.3.4 Discussion – Model II – 2-tuple (Weighted)
10.4 Models – Approximation Approach
10.4.1 Model I – Approximation Approach
10.4.2 Discussion Model I – Approximation Approach
10.5 Model II – Approximation Approach
10.5.1 Discussion – Model II – Approximation Approach
Chapter 11: Evaluation of Invasion Risk Levels with Asymmetrically Distributed Linguistic Terms Sets
11.1 An Overview
11.2 Model I - Unbalanced
11.2.1 Aggregation of Sub Parameters
11.2.2 Aggregation of Main Parameters
11.2.3 Discussion Model I - Unbalanced
11.3 Model II - Unbalanced
11.3.1 Discussion - Model II - Unbalanced
Bibliography
Index
