Texture Spaces (Studies in Fuzziness and Soft Computing, 411)

✍ Scribed by Murat Diker

• Publisher: Springer
• Year: 2023
• Tongue: English
• Leaves: 258
• Category: Library

✦ Synopsis

This book provides a complete framework for the fundamental concepts and results of texture spaces and its applications. The principal aim is to present a comprehensive arguments due to connections among the textures, fuzzy sets and rough sets. In this context, direlations, fuzzy direlations and fuzzy relations constitute a bridge for the remarkable observations on rough set theory. In a more general setting, the approximation operators are also inspected for fuzzy rough set models with two domains of discourse.

Since the book is self-contained and reader-friendly, the respected researchers may utilize this source for further investigations of the necessary results for their studies on rough set theory using textures. Therefore, prospective readers are not only mathematicians who interest in purely mathematical theories related to textures, but also engineers of information sciences who need more information for their interdisciplinary studies with respect to rough sets and fuzzy sets.

✦ Table of Contents

Preface
References
Acknowledgements
Contents
1 Introduction
1.1 Lattices
1.2 Completely Distributive Lattices
References
2 Textures
2.1 Basic Concepts and Results
2.2 p-Set and q-Set
2.3 Equivalences of Completely Distributivity in Texture Spaces
2.4 Simple and Plain Textures
References
3 Brown's Representation Theorem
3.1 Textural Isomorphisms
3.2 Product of Textures
3.3 L-Fuzzy Set Texturing mathcalP(U)otimesmathcalML
3.4 Orthopair (Intuitionistic) Textures
References
4 Direlations
4.1 Basic Concepts
4.2 Textural Image of a Set: Sections
4.3 Composition of Direlations
4.4 Seriality and Injectivity
5 Rough Sets
5.1 Pawlak's Approximation Spaces
5.2 Generalized Approximation Spaces
5.3 Generalized Approximation Spaces with Two Domains of Discourse
5.4 Textural Rough Sets
5.5 Textural Definability
References
6 Basic Results in Rough Set Theory via Textures
6.1 Generalized Approximation Spaces and Discrete Textures
6.2 Definability in Generalized Approximation Spaces with Two Domains of Discourse
6.3 Revised Textural Rough Sets
6.4 Revised Rough Set Approximations
References
7 Fuzzy Rough Sets
7.1 Fuzzy Logical Connectives
7.2 Continuity of Fuzzy Logical Connectives
7.3 Textural Fuzzy Direlations
7.4 Fuzzy Direlations Defined by Fuzzy Logic Connectives
7.5 Adjointness and Duality
7.6 The Well-Known Fuzzy Rough Set Models Obtained by t-Fuzzy Direlations
7.7 Basic Properties of Fuzzy Relations
7.8 t-Fuzzy Rough Set Approximations with Two Domains of Discourse
7.9 Definability in t-Fuzzy Approximation Spaces
7.10 Basic Properties of Fuzzy Rough Sets with Two Domains of Discourse
7.11 Definability in Terms of Fuzzy Logic Connectives
7.12 Revised t-Fuzzy Rough Set Models
7.13 Revised Fuzzy Rough Set Models with Two Domains of Discourse
References
Appendix Index
Index