Preface
Chapter 1 Introduction of the Semi-tensor Product of Matrices
1.1 Definition of STP
1.2 Basic Properties of STP
1.3 Special Properties of STP
1.4 Conclusion
References
Chapter 2 Solving General Type-2 Fuzzy Relation Equations
2. l Introduction
2.2 Problem Formulation
2.2.1 Type-2 FRs and Their Compositions
2.2.2 STP Method of Solving Type-1 FREs
2.2.3 Problem Formulation
2.3 Type-2 Fuzzy Relation Equations
2.3.1 Properties of T2 FREs
2.3.2 Solving Type-2 Fuzzy Relation Equations
2.4 Illustrative Examples
2.5 Conclusion
References
Chapter 3 Solving Symmetrical-Valued Type-2 Fuzzy Relation Equations
3.1 Introduction i
3.2 Symmetrical-Valued T2 FRs
3.2.1 Symmetrical-Valued T2 FRs and Their Properties
3.2.2 Solving Symmetrical-Valued Type-2 FREs
3.3 Illustrative Examples
3.4 Conclusion
References
Chapter 4 Algebraic Approach to Construct Compatible State Set of
Finite State Machines
4.1 Introduction
4.2 Related Concepts of Finite State Machines
4.3 Problem Description
4.4 Bilinear Dynamics of FSMs
4.5 Criterion of k-Difference States
4.6 Construction of Incompatibility Graph
4.7 Generation of Compatible States
4.8 Conclusion
References
Chapter 5 Algebraic Simplification of Finite State Machines
5.1 Introduction
5.2 Compatible Cover of State Set (CCSS)
5.3 Representative Set of State Set (RSSS)
5.4 Minimum Representative Set of State Set (MRSSS)
5.5 Illustrative Examples
5.6 Conclusion
References
Chapter 6 Algebraic Criteria for Finite State Machine Understanding of Regular Language
6.1 Introduction
6.2 k-Connectivity Matrix
6.3 Algebraic Criteria of Understanding Regular Language
6.4 Further Results on Nondeterministie Finite State Machines
6.5 Illustrative Examples
6.6 Conclusion
References
Chapter 7 Reduction Conditions of State Space for Finite State Machines
7.1 Introduction
7.2 Related Concepts of Reduction Problem
7.3 Algebraic Conditions of Reduction of State Space
7.4 Mathematical Algorithms
7.5 Illustrative Examples
7.6 Conclusion
References
Chapter 8 Searching Control Sets of Graphs
8.1 Introduction
8.2 Preliminaries and Problem Statement
8.3 Searching Control Sets of Graphs
8.4 Searching k-Degree and k-Balance Control Sets of Graphs
8.5 Testing Examples
8.6 Conclusion
References
Chapter 9 Solutions of MTAP
9.1 Introduction
9.2 Preliminaries on k-Stable Sets of Graphs
9.3 Algebraic Approach to Search k-SSes and k-AMSSs
9.3.1 Searching k-stable sets
9.3.2 Searching k-absolute maximum internally stable set
9.4 Solvability of MATP
9.5 Illustrative Examples
9.6 Conclusion
References

This book mainly introduces some recent applications of the theory of semi-tensor product of matrices. In particular, we put emphasis on the applications in the fields of fuzzy logical systems, finite state machines and graphs. In the area of the fuzzy logical systems, we limit our discussions to the method of solving the fuzzy logical equation, which is a key technology in the analysis and synthesis of the logical dynamical systems. On the side of the applications in the finite state machines, we present the advances on the mathematical formulation, compatible analysis, reduction and language recognition. In the field of graph theory, we focus on the structure analysis and its applieations.
This book is not only suitable for professional researchers in the fields of control science and engineering, industrial automation, electrical automation and mechanical engineering, but also can be used as a reference material for relevant scientific and technical engineers.