Fuzzy Relational Calculus Theory Applications And Software 1st Edition by Ketty Georgieva Peeva, Yordan Kostadinov Kyosev ISBN 978-9812560766 9812560769
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Product details:
ISBN 10: 9812560769
ISBN 13: 978-9812560766
Author: Ketty Georgieva Peeva, Yordan Kostadinov Kyosev
This book examines fuzzy relational calculus theory with applications in various engineering subjects. The scope of the text covers unified and exact methods with algorithms for direct and inverse problem resolution in fuzzy relational calculus. Extensive engineering applications of fuzzy relation compositions and fuzzy linear systems (linear, relational and intuitionistic) are discussed. Some examples of such applications include solutions of equivalence, reduction and minimization problems in fuzzy machines, pattern recognition in fuzzy languages, optimization and inference engines in textile and chemical engineering, etc. A comprehensive overview of the authors’ original work in fuzzy relational calculus is also provided in each chapter.The attached CD-Rom contains a toolbox with many functions for fuzzy calculations, together with an original algorithm for inverse problem resolution in MATLAB. This book is also suitable for use as a textbook in related courses at advanced undergraduate and graduate levels.
Table of contents:
Chapter 1 Introduction
1.1 Basic Concepts
1.2 Images and Compositions
1.3 Basic Problems in Fuzzy Relational Calculus
1.4 Aspects in Artificial Intelligence
1.5 Fuzzy Finite Machines and Fuzzy Algebras
1.6 Fuzzy Grammars in Syntactic Pattern Recognition
1.7 Bibliographical Notes
Chapter 2 Fuzzy Relations. Direct Problem Resolution
2.1 Basic Notions
2.2 Fuzzy Relations Compositions and Properties
2.3 Fuzzy Relations and Membership Matrices.
2.4 Bibliographical Notes
Chapter 3 Fuzzy Relational Equations
3.1 Inverse Problem Formulation
3.2 Fuzzy Linear Equations
3.3 Fuzzy Linear Systems of Equations
3.3.1 Basic Notions
3.3.2 Simplifications
3.3.3 Lower Solutions
3.3.4 Universal algorithm
3.4 Solving Fuzzy Relational Equations.
3.5 Bibliographical Notes
Chapter 4 Fuzzy Relational Inclusions
4.1 Preliminaries
4.2 Fuzzy Linear Systems of Inequalities
4.3 Fuzzy Relational Inclusions
4.4 Applications in Fuzzy Linear Programming
4.5 Bibliographical Notes
Chapter 5 Fuzzy Linear Systems Dual Approach
5.1 Basic Concepts
5.2 Solving Fuzzy Linear Systems
5.3 Fuzzy Relational Equations
5.4 Dual Approach to Inverse Problem Resolution
5.5 Bibliographical Notes
Chapter 6 Direct and Inverse Problems in Intuitionistic Fuzzy Re-lational Calculus
6.1 Intuitionistic Fuzzy Relations. Compositions
6.2 Intuitionistic Fuzzy Matrices. Direct and Inverse Problems
6.3 Intuitionistic Fuzzy Relational Equations
6.4 Bibliographical Notes
Chapter 7 L-Fuzzy Finite Machines
7.1 L-Fuzzy Finite Machines. Behavior
7.2 Equivalences
7.3 Reduction and Minimization
7.4 Intuitionistic Fuzzy Finite Machines
7.5 Bibliographical Notes
Chapter 8 Fuzzy Languages in Syntactic Pattern Recognition
8.1 Finite L-Fuzzy Acceptors and Regular L-Fuzzy Languages.
8.2 Intuitionistic Fuzzy Languages in Syntactic Pattern Recognition
8.3 Bibliographical Notes
Chapter 9 Applications as Inference Engine
9.1 Architecture of System with Artificial Intelligence
9.2 Fuzzy Linear System of Equations as Inference Engine
9.3 Intuitionistic Fuzzy Linear System as Inference Engine
9.4 Bibliographical Notes
Chapter 10 Software Description
10.1 Unary Matrix Operations
10.2 Binary Matrix Operations
10.3 Compositions
10.4 Inverse Problem
10.4.1 Max-Min Composition
10.4.2 Min-Max Composition
10.5 Intuitionistic Fuzzy Relational Calculus
10.6 Engineering Examples
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Tags: Ketty Georgieva Peeva, Yordan Kostadinov Kyosev, Fuzzy Relational, Theory Applications