Bidirectional Comparison of Nominal Sets: Asymmetry of Proximity (Studies in Computational Intelligence, 1140)

Preface
Contents
List of Figures
List of Tables
1 Introduction and Main Assumptions
	1.1 Notation
	1.2 Remarks on Object Proximity
	References
2 Issues of Asymmetry of Data Proximity
	2.1 Preliminaries
	2.2 Feature Contrast Model
	2.3 Kahneman and Tversky: The Prospect Theory
	2.4 ``Salience\'\' and ``Goodness\'\' of Form
	2.5 Transformational and Directional Distance
	References
3 Matching Between Ordinary Sets
	3.1 Preliminaries
	3.2 Examples of Proximity Measures of Ordinary Sets
	3.3 Basics of Perturbation of Ordinary Sets
		3.3.1 The Concept of Perturbation of Ordinary Sets
		3.3.2 Measures of Perturbation of Ordinary Sets
		3.3.3 Properties of Measures of Ordinary Set Perturbation
	3.4 Representation of Multi-attribute Objects by Ordinary Sets
		3.4.1 Description of Multi-attribute Objects by Ordinary Sets
		3.4.2 Measure of Perturbation of Multi-attribute Objects
		3.4.3 Measure of Perturbation of Groups of Multi-attribute Objects
	3.5 Illustrative Examples
		3.5.1 Description of Group of Objects
		3.5.2 Grouping of Objects
	References
4 Matching Between Sets with Binary Coding
	4.1 Preliminaries
	4.2 Representation of Nominal Values by Binary Values
		4.2.1 Binary Encoding of Nominal Values
		4.2.2 Operations on Binary Vectors
		4.2.3 Notation Used
	4.3 Examples of Proximity Measures for the Binary Set Representations
		4.3.1 Symmetric Binary Case
		4.3.2 Asymmetric Binary Case
		4.3.3 Measures of Perturbation Versus Selected Proximity Measures of Sets Coded Through Binary Representation
	4.4 Illustrative Examples
		4.4.1 Grouping of Binary Vectors
		4.4.2 Validations of Perturbation Measure
	References
5 Matching Between Multisets
	5.1 Preliminaries
	5.2 Brief Introduction to Multisets Theory
		5.2.1 Operations on Multisets
		5.2.2 Examples of Proximity Measures of Multisets
	5.3 Basics of Perturbation of Multisets
		5.3.1 The Concept of Perturbation of Multisets
		5.3.2 Measure of Perturbation of Multisets
		5.3.3 Properties of Perturbation Measure of Multisets
		5.3.4 Graphical Illustration of the Multiset Perturbation Measure
		5.3.5 Measures of Perturbation Versus Selected Proximity Measures of Multisets
	5.4 Decomposition of Matrix of Measures
		5.4.1 Decomposition of the Matrix of Multiset Perturbation Measures
		5.4.2 Graphical Illustration of Decomposition of the Matrix of Multiset Perturbation Measures
	5.5 Representation of Multi-attribute Objects by Multisets
		5.5.1 Description of Multi-attribute Objects by Multisets
		5.5.2 Measure of Perturbation of Objects
		5.5.3 Measure of Perturbation of Group of Objects
	5.6 Illustrative Examples
		5.6.1 Exemplary Description of Students\' Semester Grades
		5.6.2 Learning Without Supervision - Preliminary Remarks
		5.6.3 Generation of Classification Rules
		5.6.4 Grouping of Text Documents
	References
6 Matching Between Fuzzy Sets
	6.1 Preliminaries
	6.2 Brief Introduction to Fuzzy Sets Theory
		6.2.1 Operations on Fuzzy Sets
		6.2.2 Axiomatic Definitions of Measure of Similarity of Fuzzy Sets
		6.2.3 Examples of Measures of Similarity of Fuzzy Sets
		6.2.4 Axiomatic Definitions of Measures of Dissimilarity  of Fuzzy Sets
		6.2.5 Examples of Measures of Dissimilarity of Fuzzy Sets
		6.2.6 Tversky\'s Model for Fuzzy Sets
	6.3 Basics of Perturbation of Fuzzy Sets
		6.3.1 The Concept of Perturbation of Fuzzy Sets
		6.3.2 Graphical Illustration of Perturbation of Fuzzy Sets in Two-Dimensional Space
		6.3.3 Graphical Illustration of Perturbations of Fuzzy  Sets in Three-Dimensional Space
		6.3.4 Measures of Perturbation of Fuzzy Sets
		6.3.5 Properties of Measures of Perturbation of Fuzzy Sets
		6.3.6 Graphical Illustration of Measures of Perturbations  of Fuzzy Sets
	6.4 Illustrative Examples
		6.4.1 Comparison of Selected Proximity Measures
		6.4.2 Measures of Perturbations Versus Hamming Distance
	References
7 Matching Between Intuitionistic Fuzzy Sets
	7.1 Preliminaries
	7.2 Brief Introduction to the Intuitionistic Fuzzy Sets Theory
		7.2.1 Operations on Intuitionistic Fuzzy Sets
		7.2.2 Examples of Proximity Measures of Intuitionistic Fuzzy Sets
		7.2.3 Extensions of Fuzzy Sets
	7.3 Fundamentals of Perturbation of Intuitionistic Fuzzy Sets
		7.3.1 The Concept of Perturbation of Intuitionistic Fuzzy Sets
		7.3.2 Measures of Perturbation of Intuitionistic Fuzzy Sets
		7.3.3 Properties of Measure of Perturbation of Intuitionistic Fuzzy Sets
		7.3.4 Graphical Illustration of Measures of Perturbation of Intuitionistic Fuzzy Sets
	7.4 Representation of Multi-attribute Objects by Intuitionistic Fuzzy Sets
	7.5 Illustrative Examples
		7.5.1 Pattern Matching
		7.5.2 Generation of Classification Rules
	References
8 Summary and Perspectives
Index