How Fuzzy Concepts Contribute to Machine Learning

Preface
Contents
1 Preliminaries
	1.1 Fuzzy Notions
		1.1.1 Fuzzy Sets
		1.1.2 Membership Functions
		1.1.3 Hesitant Fuzzy Sets
	1.2 Decision Tree
		1.2.1 Fuzzy Decision Tree
	1.3 Dimensionality Reduction and Related Subjects
		1.3.1 Pearson's Correlation Coefficient Measure
		1.3.2 Correlation Coefficient of Hesitant Fuzzy Sets
		1.3.3 Correlation-Based Merit
		1.3.4 Similarity Measures
		1.3.5 Rough Set and Fuzzy-Rough Set Basic Concepts
		1.3.6 Weighted Rough Set Basic Concepts
		1.3.7 Fuzzy Rough Set Basic Concepts
	1.4 Fuzzy Clustering
		1.4.1 Fuzzy c-Means Clustering
		1.4.2 Subtractive Clustering
		1.4.3 Fuzzy Partitions
		1.4.4 I-Fuzzy Partitions
	1.5 Linear Regression
		1.5.1 Ridge Regression
		1.5.2 LASSO Regression
		1.5.3 Elastic Net Regression
	References
Part I Unsupervised Learning
2 A Definition for Hesitant Fuzzy Partitions
	2.1 Introduction
	2.2 H-Fuzzy Partition
		2.2.1 Construction of H-Fuzzy Partitions
	2.3 Discussion
	2.4 Computer Programming Exercises for Future Works
	References
3 Unsupervised Feature Selection Method Based on Sensitivity and Correlation Concepts for Multiclass Problems
	3.1 Introduction
		3.1.1 GA for Feature Selection
	3.2 Proposed Unsupervised Feature Selection Method
		3.2.1 Feature Relevance Evaluation via Sensitivity Analysis Based on Subtractive Clustering
		3.2.2 A General Scheme for Sensitivity and Correlation Based Feature Selection (SCFS)
	3.3 Discussion
	3.4 Computer Programming Exercise for Future Works
	References
Part II Supervised Learning Classification and Regression
4 Fuzzy Partitioning of Continuous Attributes Through Crisp Discretization
	4.1 Introduction
	4.2 Discretization Methods
	4.3 Employing Discretization Methods for Fuzzy Partitioning
		4.3.1 Defining MFs Over Crisp Partitions
		4.3.2 Fuzzy Entropy Based Fuzzy Partitioning
	4.4 Discussion
	4.5 Computer Programming Exercises for Future Works
	References
5 Comparing Different Stopping Criteria for Fuzzy Decision Tree Induction Through IDFID3
	5.1 Introduction
	5.2 Stopping Criteria
	5.3 Iterative Deepening FID3
		5.3.1 The Stopping Criterion of IDFID3
		5.3.2 Comparison Method for Various Stopping Criteria
	5.4 Discussion
	5.5 Computer Programming Exercise for Future Works
	References
6 Hesitant Fuzzy Decision Tree Approach for Highly Imbalanced Data Classification
	6.1 Introduction
	6.2 Hesitant Fuzzy Decision Tree Approach
		6.2.1 Data Balancing
		6.2.2 Generating the Membership Functions
		6.2.3 Construction of Fuzzy Decision Trees
		6.2.4 The Aggregation of FDTs
		6.2.5 Notations for Different FDT Classifiers
	6.3 Discussion
	6.4 Computer Programming Exercise for Future Works
	References
7 Dynamic Ensemble Selection Based  on Hesitant Fuzzy Multiple Criteria Decision-Making
	7.1 Introduction
	7.2 Multiple Classifier Systems and Dynamic Selection Techniques
		7.2.1 Neighborhood Selection Techniques
		7.2.2 Competence Level Calculation
		7.2.3 Classifier Selection
	7.3 Dynamic Ensemble Selection Based on Hesitant Fuzzy Concepts
	7.4 Discussion
	7.5 Computer Programming Exercises for Future Works
	References
Part III Dimension Reduction
8 Ensemble of Feature Selection Methods: A Hesitant Fuzzy Set Based Approach
	8.1 Introduction
	8.2 The MRMR-HFS Method
	8.3 Discussion
	8.4 Computer Programming Exercises for Future Works
	References
9 Distributed Feature Selection:  A Hesitant Fuzzy Correlation Concept for High-Dimensional Microarray Datasets
	9.1 Introduction
	9.2 Distributed HCPF Feature Selection Algorithm
		9.2.1 The Partitioning Process in the Distributed Version  of HCPF
		9.2.2 HCPF: A Feature Selection Algorithm Based on HFS
		9.2.3 The Merging Process in the Distributed Version  of HCPF
	9.3 Discussion
	9.4 Computer Programming Exercises for Future Works
	References
10 A Hybrid Filter-Based Feature Selection Method via Hesitant Fuzzy and Rough Sets Concepts
	10.1 Introduction
	10.2 Proposed Hybrid Filter-Based Feature Selection Method
		10.2.1 Sample Weighting Approach
		10.2.2 Primary Feature Subset Selection
		10.2.3 Fuzzy Rough-Based Elimination
	10.3 Discussion
	10.4 Computer Programming Exercises for Future Works
	References
11 Feature Selection Based on Regularization of Sparsity Based Regression Models by Hesitant Fuzzy Correlation
	11.1 Introduction
	11.2 Feature Selection Method Based on Regularization
		11.2.1 Regularized Ridge Regression
		11.2.2 Regularized LASSO and Elastic Net Regression
	11.3 Alternative Sparsity Based Regression Methods
	11.4 Discussions
	11.5 Computer Programming Exercises for Future Works
	References