Texture Spaces.

Format:

Book

Author/Creator:

Diker, Murat.

Series:

Studies in Fuzziness and Soft Computing Series

Studies in Fuzziness and Soft Computing Series ; v.411

Language:

English

Subjects (All):

Fuzzy sets.

Rough sets.

Physical Description:

1 online resource (258 pages)

Edition:

1st ed.

Place of Publication:

Cham : Springer International Publishing AG, 2024.

Summary:

This book, 'Texture Spaces' by Murat Diker, delves into the mathematical theory of texture spaces and its interrelation with fuzzy sets and rough sets. The author presents foundational concepts, historical context, and practical applications of texture spaces. This work synthesizes scattered observations in the literature, providing a cohesive theoretical tool for researchers and engineers in information sciences. The book is structured into seven chapters, covering topics such as lattice theory, fuzzy lattices, textural isomorphism, and the connections between rough sets and fuzzy sets. It serves as a resource for those interested in mathematical theories of textures and their applications in data-driven environments. Generated by AI.

Contents:

Intro

Preface

References

Acknowledgements

Contents

1 Introduction

1.1 Lattices

1.2 Completely Distributive Lattices

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

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

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

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

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

Appendix Index

Index.

Notes:

Description based on publisher supplied metadata and other sources.

Part of the metadata in this record was created by AI, based on the text of the resource.

Other Format:

Print version: Diker, Murat Texture Spaces

ISBN:

9783031397486

3031397487

OCLC:

1412622844